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Lecture 1 Financial Strategy


Shareholder Wealth - Illustration 1

Year Share Price Dividend Paid

2007 3.30 40c

2008 3.56 42c

2009 3.47 44c

2010 3.75 46c

2011 3.99 48c

There are 2 million shares in issue.! ! ! ! ! ! ! ! ! ! ! ! Calculate the increase in shareholder wealth for each year:II. Per shareIII. As a percentageIV. For the business as a whole

Solution

Year Share Price

Share Price Growth

Div Paid

Increase in

S’holder Wealth

As a Percentage

Total Shareholder

Return

2007 3.30 40c

2008 3.56 (3.56 - 3.30) = 26c 42c (26 + 42) = 68c

(68 / 330) = 20.6%

2m x 68c = $1.36m

2009 3.47 (3.47 - 3.56) = -9c 44c (-9 + 44) = 35c

(35 / 356) = 9.8%

2m x 35c = $0.70m

2010 3.75 (3.75 - 3.47) = 28c 46c (28 + 46) = 74c

(74 / 347) = 21.3%

2m x 74c = $1.48m

2011 3.99 (3.99 - 3.75) = 24c 48c (24 + 48) = 72c

(72 / 375) = 19.2%

2m x 72c = $1.44m


EPS - Illustration 2

2010$‘000

2011$‘000

PBIT 2000 2100

Interest 200 300

Tax 300 400

Profit After Tax 1500 1400

Preference Dividend 300 400

Dividend 800 900

Retained Earnings 400 100

Share Capital (50c) 5000 5000

Reserves 3000 3100

Share Price $2.50 $2.80

Calculate the EPS for 2010 and 2011.

Solution

2010 2011

Profit After Tax 1500 1400

Preference Dividend 300 400

Earnings 1200 1000

No. Ordinary Shares (5000 / 0.50) 10,000 10,000

EPS (Earnings / No. Ordinary Shares) 12c 10c


Lecture 2 Performance Measurement


Performance Analysis Illustration

X1 X2 X3

Non Current Assets 500 700 1000

Current Assets 150 200 300

650 900 1300

Ordinary Shares ($1) 300 300 300

Reserves 100 280 430

Loan Notes 150 200 300

Payables 100 120 270

650 900 1300

Revenue 3000 3500 4200

COS 2000 2400 3200

Gross Profit 1000 1100 1000

Admin Costs 300 350 400

Distribution Costs 200 250 300

PBIT 500 500 300

Interest 100 150 220

Tax 120 90 50

Profit After Tax 280 260 30

Dividends 100 110 30

Retained Earnings 180 150 0

Share Price $3.30 $4.00 $2.20

Using the information calculate and comment on the following Ratios:

I. Return on Capital EmployedII. Return on EquityIII. Gross MarginIV. Net MarginV. Operating MarginVI. Revenue GrowthVII. GearingVIII. Interest CoverIX. Dividend CoverX. Dividend YieldXI. P/E Ratio


Solution

ROCE

X1 X2 X3

Equity + LT Liabilities

Shares 300 300 300


LT Loan Notes 150 200 300

Capital Employed 550 780 1030

Non Current Assets + Net Current Assets

Non Current Assets 500 700 1000

Net Current Assets (Current Assets - Current Liabilities)

(150 - 100) = 50 (200 - 120) = 80 (300 - 270) = 30


Total Assets - Current Liabilities

Total Assets 650 900 1300

Current Liabilities 100 120 270


PBIT 500 500 300

Return on Capital Employed

PBIT / Capital Employed

(500 / 550) = 90.91%

(500 / 780) = 64.10%

(300 / 1030) = 29.13%


X1 X2 X3

Return on Capital Employed (ROCE) 90.91% 64.10% 29.13%

In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.

In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.

In the year X3 the ROCE is 29.13%. This is a fall of 54.55% indicating that there may be some serious underlying problems which are affecting the ability of the business to generate the return on capital previously generated.




ROE

X1 X2 X3


Ordinary Shares 300 300 300


Total 400 580 730

Return on Equity (PAT / Ord Shares + Reserves)

(280 / 400) = 70%

(260 / 580) = 44.8%

(300 / 730) = 41%

In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.

In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.

In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.


Margins

X1 X2 X3

Revenue 3000 3500 4200


PAT 280 260 30

PBIT 500 500 300

Gross Margin (Gross Profit / Revenue) (1000 / 3000) = 33.33%

(1100 / 3500) = 31.42%

(1000 / 4200) = 23.89%

Net Margin (PAT / Revenue) (280 / 3000) = 9.3%

(260 / 3500) = 7.4%

(30 / 4200) = 0.7%

Operating Margin (PBIT / Revenue) (500 / 3000) = 16.66%

(500 / 3500) = 14.28%

(300 / 4200) = 7.1%

The Gross Margin is 33.33% in X1 and holds reasonably steady in X2 at 31.42%. However in X3 the Gross Margin falls to 23.89% indicating that the business has either had to cut prices to sell the greater volume it has, or the cost of it’s purchases have gone up.




The Net Margin is 9.3% in X1 but begins to fall in X2 with 7.4% achieved, before falling dramatically to 0.7% in X3. The main reason for this is the fall in Gross Profit as other costs have risen in line with expectations given the increase in sales. However another point to note is that interest costs have risen with the increase in long term loans. The extra interest costs have put pressure on the business.




The Operating Margin dropped slightly in X2 to 14.28% from 16.66% the previous year - a fall of almost 15%. In X3 the Operating Margin fell away to 7.1%, a decrease of over 50%. This is due to the decreasing Gross Margin achieved as well as rises in the other expenses.





Gearing

X1 X2 X3

Debt 150 200 300

Equity Number of Shares

300 300 300

Share Price 3.30 4 2.20

Market Value (300 x 3.30) = 990

(300 x 4) = 1200

(300 x 2.20) = 660

Gearing (Debt / Equity) (150 / 990) = 15%

(200 / 1200) = 16.66%

(300 / 660) = 45.45%

Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.

In year X2 gearing increases slightly to 16.66%, an increase of 11% from year X1. This is due to debt levels increasing to 200 from 150, although this is offset by the increase in the share price from $3.30 to $4.





In year X3 gearing increases dramatically to 45%, an increase of over 180%. This is due to debt levels rising to 300 from 200 and the share price dropping to $2.20 due to the deteriorating results of the business.






Interest Cover

X1 X2 X3

PBIT 500 500 300


Interest Cover (PBIT / Interest) (500 / 100) = 5 times

(500 / 150) = 3.33 times

(300 / 220) = 1.36 times

Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.

In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.

In year X3 interest coverage has decreased again to 1.36 times. This is caused by the PBIT achieved decreasing to 300 combined with the increase in the interest charge to 220. The increase in interest is caused by the increase in the long term debt of the company as shown by the gearing ratios calculated above.




Dividend Cover

X1 X2 X3

PAT 280 260 30


Dividend Cover (PAT / Dividends) (280 / 100) = 2.8 times

(260 / 110) = 2.36 times

(30 / 30) = 1 time

Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.

In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.

In year X3 dividend coverage has decreased to 1 time. This is caused by the decrease in profit achieved by the company restricting the level of dividend payable. This will be of concern to investors and their concern is reflected in the fall in the share price from $4 in year X2 to $2.20 in year X3.





Dividend Yield

X1 X2 X3

Number of Shares (300 / 1) 300 300 300


Dividends Per Share (100 / 300) = 33c (110 / 300) = 36c (30 / 300) = 10c

Dividend Yield (Dividends Per Share / Share Price)

(33 / 330) = 10% (36 / 400) = 9% (10 / 220) = 4.5%

The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.

In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.

In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.

P/E Ratio

X1 X2 X3

Share Price $3.30 $4 $2.20


No. Ordinary Shares 300 300 300

EPS (280 / 300) = 93c (260 / 300) = 86c (30 / 300) = 10c

P/E Ratio (Share Price / EPS) (330 / 93) = 3.54 (400 / 86) = 4.65 (220 / 10) = 22

The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.

In year X2 the P/E Ratio increases to 4.65. This indicates that the market expectations for this share have risen since X1 and that investors are now willing to pay 4.65 times what the business earns in a year to own the share.




In year X4 the P/E ratio has increased dramatically to 22. This is unusual as the earnings have decreased to 12% of the previous year. The share price has fallen to reflect this, but not by as much as would be expected. This may indicate that the market feels that the results in year X3 were perhaps a one-off and that next years results will improve.





Lecture 3Finance Sources


Rights Issue - Illustration 1

XYZ Ltd. intends to raise capital via a rights issue.

The current share price is $8.

They are offering a 1 for 4 issue at a price of $6.

Calculate the Theoretical Ex-rights Price.

Solution

Number of Shares Share Price Total

4 $8 (4 x $8) = 32

1 $6 (1 x $6) = 6

5 38

We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60


Rights Issue - Illustration 2

ABC Ltd. has decided to raise capital via a rights issue.

The share price is currently $5.50 and ABC intends to raise $5m.

There are currently 6.25m shares in issue and ABC is offering a 1 for 5 rights issue.

Calculate the Theoretical Ex-Rights Price.

Solution

Amount of Capital to raiseAmount of Capital to raise $5m

No. of shares issued (6.25m / 5)No. of shares issued (6.25m / 5) 1.25m

Share issue price ($5m / 1.25m)Share issue price ($5m / 1.25m) $4

Number of Shares Share Price Total

5 $5.50 (5 x 5.50) = 27.5

1 $4 (1 x 4) = 4

6 31.5

We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25


Lecture 5 Investment Appraisal I


ARR - Illustration 1

ABC Ltd are considering expanding their internet cafe business by buying a business which will cost $275,000 to buy and a further $175,000 to refurbish.

They expect the following cash to come in:

Year Net Cash Profits (£)

1 45,000

2 75,000

3 80,000

4 50,000

5 50,000

6 60,000

The equipment will be depreciated to a zero resale value over the same period and, after the sixth year, they can sell the business for $200,000

Calculate the ARR or ROCE of this investment


Solution

Total Profit over 6 years 45,000 + 75,000 + 80,000 + 50,000 + 50,000 + 60,000

360,000

Total Depreciation Equipment of $175,000 fully depreciated

175,000

Total Profits 185,000

Average Profits $185,000 / 6 years 30,833

Average Investment (Capital Investment + Residual Value) / 2

(450,000 + 200,000) / 2 325,000

ROCE (Ave. Profit / Ave Investment)

30,833 / 325,000 9.5%


Relevant Cash Flow Criteria - Illustration 2

A business is considering investing in a new project. They have already spent $20,000 on a feasibility study which suggests that the project will be profitable.

The headquarters of the company has spare floor space which will be allocated to the project with $7,000 of the current monthly rent allocated to the project.

New equipment costing $2.5m will have to be bought and will be depreciated on a straight line basis over 10 years.

A manager who earns $30,000 per year and currently runs a similar project will also manage the new project taking up 25% of his time.

State whether each of the following items are relevant cash flows and explain your answer.

I. The cost of the feasibility study.

II. The rent charged to the project.

III. The new equipment.

IV. The depreciation on the new equipment.

V. The Managers salary.

Item Relevant Cash Flow?

Explain

Feasibility Study No This is a sunk cost as it has already been paid.

Rent No The rent is not relevant as it must be paid whether the project goes ahead or not. It is not incremental.

New Equipment Yes This is a relevant cash flow.

Depreciation No Depreciation is not a cash-flow but an accounting entry.

Managers Salary No The managers salary must be paid whether the project goes ahead or not so is not relevant.


Payback Period - Illustration 3

Initial Investment of $5.8m.

Annual Cash Flows of $400,000.

Calculate the Payback Period.

Solution

Payback Period (Initial Investment / Annual Cash Flows)

$5.8m / $400,000 14.5 years


Payback Period - Illustration 4

Initial Investment of $6.2m.

Cash Flows of:

Year 1: ! $1,200,000

Year 2:! $2,200,000

Year 3:! $2,500,000

Year 4:! $1,700,000

Calculate the Payback Period.

Solution

Year Cash Flows Cumulative Cash Flows

1 1,200,000 1,200,000

2 2,200,000 3,400,000

3 2,500,000 5,900,000

4 1,700,000 7,600,000

Payback period is between 3 and 4 yearsPayback period is between 3 and 4 yearsPayback period is between 3 and 4 years

Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000

Total cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 monthsTotal cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 monthsTotal cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 months


Discounted Cash-flows - Illustration 5

An investor wants a real return of 10%. Inflation is 5%

What is the MONEY/NOMINAL rate required?

Solution

Use Formula: 1+m = (1+r) x (1+inf)

We are looking for m, therefore:

1+m = (1+0.10) x (1+0.05)

1+m = 1.155

m = 0.155 = 15.5%



A company undertakes a project with the following cash-flows:

Year Cash-Flows

1 5,000

2 7,000

3 8,000

4 10,000

5 11,000

6 9,000

The company has a cost of capital of 10%.

Calculate the present value of the cash flows for each of the six years and in total.

Solution

Year Cash-Flows Discount Rate (From Tables)

Present Value

1 5,000 0.909 4,545

2 7,000 0.826 5,782

3 8,000 0.751 6,008

4 10,000 0.683 6,830

5 11,000 0.621 6,831

6 9,000 0.564 5,076

Total 35,072



A company undertakes a project with the following cash-flows:

Year Cash-Flows

1 5,000

2 5,000

3 5,000

4 5,000

5 5,000

6 5,000

The company has a cost of capital of 10%.

Calculate the present value of the total cash flows for the six years

Solution

Year Cash-Flows Discount Rate (From Tables)

Present Value

1 5,000 0.909 4,545

2 5,000 0.826 4,130

3 5,000 0.751 3,755

4 5,000 0.683 3,415

5 5,000 0.621 3,105

6 5,000 0.564 2,820

Total 21,770

Years Cash-flow Discount Rate (Annuity Tables)

Present Value

1 - 6 5,000 4.355 21,775



A company expects to receive $100,000 per year forever.

Their cost of capital is 10%.

Calculate the present value of the perpetuity.

Solution

Annual Cash Flow $100,000

Cost of Capital (10%) 0.10

Perpetuity (Cash-Flow / Cost of Capital) 100,000 / 0.10 = $1m


Lecture 6 Investment Appraisal II


WDA - Illustration 1

A business buys a piece of equipment for $100.

Capital allowances are available at 25% reducing balance.

The tax rate is 30%

After the 4 year project the equipment can be sold for $25.

Solution

Period Balance 25% WDA 30% Tax Saving

Period

1 100.00 25.00 7.50 2

2 75.00 18.75 5.63 3

3 56.25 14.06 4.22 4

4 42.19

Sale of Item -25.00

17.19 5.16 5

Period 0 1 2 3 4 5

Tax Saving

- - 7.5 5.63 4.22 5.16


Working Capital - Illustration 2

A business requires the following working capital investment into a four year project:

Initial Investment:! ! 30,000

Year 1!! ! ! 35,000

Year 2!! ! ! 45,000

Year 3!! ! ! 32,000

Show the working capital line in the NPV calculation.

Solution

Period 0 1 2 3 4

Total Invested 30,000 35,000 45,000 32,000

Movement to NPV Calculation

-30,000 -5,000 -10,000 13,000 32,000


NPV - Illustration 3

A business is evaluating a project for which the following information is relevant:

I. Sales will be $100,000 in the first year and are expected to increase by 5% per year.

II. Costs will be $50,000 and are expected to increase by 7% per year.

III. Capital investment will be $200,000 and attracts tax allowable depreciation of the full value of the investment over the 5 year length of the project.

IV. The tax rate is 30% and tax is payable in the following year.

V. Working Capital invested will be 20% of projected sales for the following year.

VI. General inflation is expected to be 3% over the course of the project and the business uses a real discount rate of 9%.

Calculate the NPV for the project.

Solution

Working 1 - WDAs

Initial Investment WDAs Tax Saving Periods

200,000 (200,000 / 5) = 40,000

(40,000 x 30%) = 12,000

2 - 6


Working 2 - Inflation

Period 1 2 3 4 5

Sales 100,000 100,000 100,000 100,000 100,000

Inflation - 1.05 1.05 to power of 2

1.05 to power of 3

1.05 to power of 4

Inflated Sales

100,000 105,000 110,250 115,763 121,551

Costs 50,000 50,000 50,000 50,000 50,000

Inflation - 1.07 1.07 to power of 2

1.07 to power of 3

1.07 to power of 4

Inflated Costs

50,000 53,500 57,245 61,252 65,540

Working 3 - Discount Rate

Working

Real Discount Rate In Question 9%

Inflation In Question 3%

Nominal Discount Rate 1 + m = (1 + 0.09) x (1 + 0.03)1 + m = 1.12m = 0.12

12%


Working 4 - Working Capital

Period 0 1 2 3 4 5

Inflated Sales 100,000 105,000 110,250 115,763 121,551

Working Capital Required (20%)

20,000 21,000 22,050 23,153 24,310

Movement -20,000 -1,000 -1,050 -1,103 -1,158 24,310

NPV

Period 0 1 2 3 4 5 6

Inflated Sales (W2)

100,000 105,000 110,250 115,763 121,551

Inflated Costs (W2)

-50,000 -53,500 -57,245 -61,252 -65,540

Profit 50,000 51,500 53,005 54,510 56,011

Tax at 30% -15,000 -15,450 -15,902 -16,353 -16,803

Tax Saving (W1)

12,000 12,000 12,000 12,000 12,000

Capital Investment

-200,000

Working Capital (W4)

-20,000 -1,000 -1,050 -1,103 -1,158 24,310

Total Cash Flows

-220,000 49,000 47,450 48,452 49,451 75,968 -4,803

Discount Rate 12% (W3)

1 0.893 0.797 0.712 0.636 0.567 0.507

Discounted Cash Flows

-220,000 43,757 37,818 34,498 31,451 43,074 -2,435

NPV -31,838


Lecture 7 - Investment

Appraisal III


Illustration 1

ABC has evaluated a project and come to the following conclusions.

At a discount rate of 10% the NPV will be $100,000

At a discount rate of 15% the NPV will be -$75,000

What is the IRR?

Solution

10 + (100,000/(100,000 +75,000) 5 = 12.85%


Illustration 2

Initial Investment (5,000)

Period Cash Flows

1 2,000

2 (1,000)

3 3,500

4 3,800

Cost of Capital 10%

NPV = 1,216

IRR = 19%

Calculate the MIRR.


Solution

Terminal Value of Inflows

Period Inflow Inflate Value

1 2,000 (1.10)3 2,662

3 3,500 (1.10)1 3,850

4 3,800 1.10 3,800

Terminal ValueTerminal ValueTerminal Value 10,312

Present Value Outflows

Period Outflow Discount Rate PV

0 5,000 1 5,000

2 1,000 0.826 826

Present Value of OutflowsPresent Value of OutflowsPresent Value of Outflows 5,826

Discount Factor where 10,312 x DF (P4) = 5,826

5,826/10,312 = 0.565

Look at tables for Period 4 and find closest to 0.565.

MIRR = 15%


Lecture 8 - Foreign NPV


Illustration 1

Item costs $1,000

€/$ 1 : 2

However inflation in US is 5% and Eurozone 3%

Calculate the exchange rate in one years time.

Solution

Future exchange rate calculation

Exchange rate now x 1+ Inf (counter) / 1 + inf (base)

2 x 1.05 / 1.03 = 2.039


Illustration 2 (i)

US Interest rate = 10%

UK Interest rate = 8%

Exchange rate = €/$ 1 : 2

Predict the exchange rate in 1 year

Solution

Future exchange rate calculation

Exchange rate now x 1+ Int (counter) / 1 + int (base)

2 x 1.10 / 1.08 = 2.037


Illustration 2 (ii)

Current spot rate $/£ 1 : 1

The dollar is expected to strengthen by 7% per anum

Forecast the $:£ rate for the next 4 years.

Solution

Period 0 1 2 3 4

FX Rate 1 1.07 1.145 1.225 1.310


Illustration 3

ABC Ltd. is a UK company intending to undertake a project in Foreignland where the currency is the Franc (FR).

ABC uses a discount rate of 10% to evaluate projects in the UK and the current spot rate is £ / FR 2.000.

The risk free rate of interest in Foreignland is 5% with the UK rate being 7%.

The initial investment in the project will be FR 400,000 with net cash inflows over a 5 year project of FR 150,000 per year.

Ignore Tax.

Calculate the NPV of the project.


Solution

FX CalculationsFX CalculationsFX CalculationsFX CalculationsFX CalculationsFX Calculations

Period 1 2 3 4 5

Rate at start of period 2.000 1.963 1.926 1.890 1.855

IRP (1.05 / 1.07)

(1.05 / 1.07)

(1.05 / 1.07)

(1.05 / 1.07)

(1.05 / 1.07)

FX Rate to use 1.963 1.926 1.890 1.855 1.820

NPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV Calculations

Period 0 1 2 3 4 5

Investment -400

Cash Flows (FR) 150 150 150 150 150

FX Rate 2 1.963 1.926 1.890 1.855 1.820

Cash Flows (£) -200.00 76.41 77.88 79.37 80.86 82.42

Discount Rate (10%) 1 0.909 0.826 0.751 0.663 0.621

PV Cash Flows (£) -200.00 69.46 64.33 59.60 53.61 51.18

NPV 98.1998.1998.1998.1998.1998.19


Illustration 4




Solution

so....

(1 + DRFoR) / (1 + 0.16) = (1 + 0.07) / (1 + 0.09)

(1 + DRFoR) / (1 + 0.16) = 0.982

(1 + DRFoR) = (1.16 x 0.982)

(1 + DRFoR) = 1.138

DRFoR = 13.8%


Illustration 5



Sterling is expected to appreciate against the Franc by 10% per year.

Solution

so....

If £ appreciates by 10% it will be able to buy 10% more FR which makes one £ worth (2 x 1.1) = 2.2FR

(1 + DRFoR) / (1 + 0.20) = 2.2 / 2

(1 + DRFoR) / (1 + 0.20) = 1.1

(1 + DRFoR) = (1.20 x 1.1)

(1 + DRFoR) = 1.32

DRFoR = 32%


Illustration 6




The initial investment in the project will be FR 400,000 with net cash inflows over a 5 year project of FR 150,000 per year.

Ignore Tax.

Calculate the NPV of the project by adjusting the discount rate.


Solution

(1 + DRFoR) / (1 + 0.10) = (1 + 0.05) / (1 + 0.07)

(1 + DRFoR) / (1 + 0.10) = 0.981

(1 + DRFoR) = (1.10 x 0.982)

(1 + DRFoR) = 1.079

DRFoR = 7.9%...say 8%

NPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV CalculationsNPV Calculations

Period 0 1 2 3 4 5

Investment -400

Cash Flows (FR) 150 150 150 150 150

Discount Rate (8%) 1 0.926 0.857 0.794 0.735 0.681

PV Cash Flows (FR) -400.00 138.90 128.55 119.10 110.25 102.15

NPV (FR)NPV (FR)NPV (FR)NPV (FR)NPV (FR)NPV (FR) 198.95

Spot RateSpot RateSpot RateSpot RateSpot RateSpot Rate 2.00

NPV(£)NPV(£)NPV(£)NPV(£)NPV(£)NPV(£) 99.48

This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.This is the same as the NPV in illustration 3 with a slight rounding difference.


Lecture 9 WACC I


Cost of Equity using DVM - Illustration 1

ABC Company has just paid a dividend of 35c.

The current share price is $3.25.

Calculate the Cost of Equity (Ke) using DVM.

Solution

Dividend 35

Share Price 325

Cost of Equity (Dividend / Share Price) (35 / 325) = 10.76%


Cost of Equity using DVM - Illustration 2

ABC Company has just paid a dividend of 35c.

The dividend paid has grown by 4% per year for the past 5 years.


Calculate the Cost of Equity (Ke) using DVM.

Solution

Dividend 35

Share Price 325

Dividend Growth 4%

Cost of Equity (Dividend (1+g) / Share Price) +g

((35 x 1.04) / 325) + 0.04 = 0.152= 15.2%


Cost of Equity using CAPM - Illustration 3

Company A has a Beta of 1.2.

Government bonds are currently trading at 4%.

The average return than investors in the market can expect is 15%.

Calculate the Cost of Equity using CAPM.

Solution

Rf (Risk Free Rate) 4

Rm (Ave Return on the Market) 15

Beta 1.2

Ke = Rf + β(Rm - Rf) (4 + 1.2(15 - 4)) = 17.2%


Cost of Equity using CAPM - Illustration 4


Company B has a Beta of 1.


The average return than investors in the market can expect is 12%.

Calculate the Cost of Equity using CAPM for each company.

Solution

Company A Company B

Rf (Risk Free Rate) 5 5

Rm (Ave Return on the Market)

12 12

Beta 1.2 1

Ke = Rf + β(Rm - Rf) (5 + 1.2(12 - 5)) = 13.4% (5 + 1(12 - 5)) = 12%

Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.

Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.


Cost of Equity using CAPM Illustration 5


Company B has a Beta of 1.2.


The average market risk premium is 6%.

Calculate the Cost of Equity using CAPM for each company.

Solution

Company A Company B

Rf (Risk Free Rate) 5 5

Rm - Rf (Ave Market Risk Premium)

6 6

Beta 1.3 1.2

Ke = Rf + β(Rm - Rf) (5 + 1.3(6) = 12.8% (5 + 1.2(6)) = 12.2%

Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)

Again notice that a higher Beta leads to a higher Ke i.e. more risk.Again notice that a higher Beta leads to a higher Ke i.e. more risk.Again notice that a higher Beta leads to a higher Ke i.e. more risk.


Lecture 10WACC II


Irredeemable Debt - Illustration 1

A company has issued 10% irredeemable debt.

The market value of the debt is $90.

The tax rate is 30%

Calculate the cost of debt (Kd).

Solution

Interest paid (Per $100 nominal) $10

Tax Rate 30%

After tax interest (Amount Paid (1 - t)) $10 x (1 - 0.30) = $7

Market Value of Debt (Per $100 nominal) $90

Cost of Debt (After tax interest / Market Value of Debt) (7 / 90) = 7.7%


Redeemable Debt - Illustration 2

A Company has issued debt which is redeemable in 5 years time.

Interest is payable at 8%.

The current market value of the debt is $102.

Ignore taxation.

Calculate the Cost of Debt (Kd).

Solution

Period

Item $ DR 5% PV DR 15% PV

1 -5 Interest 8 4.329 34.63 3.352 26.82

5 Capital 100 0.784 78.40 0.497 49.70

Market Value -102 -102

11.03 -25.48

IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%


Redeemable Debt - Illustration 3

A Company has issued debt which is redeemable in 5 years time.



Tax is payable at 30%.


Solution

Period


1 -5 Interest (10 x (1 - 0.3)

7 4.329 30.30 3.352 23.46

5 Capital 100 0.784 78.40 0.497 49.70


4.70 -30.84



Convertible Debt - Illustration 4

A Company has issued debt which is convertible in 5 years time.



On conversion, investors will have a choice of either:

I. Cash at a 15% premium; or

II. 18 shares per loan note.

The current share price is $6 and it is expected to grow in value by 4% per year.

Tax is payable at 30%.


Solution

Working 1 - Cash or Convert?

Working

Cash (15% Premium) 100 x 1.15 $115

Shares

Current Value $6

Value in 5 years with 4% growth

6 x (1.04 to the power of 5) $7.30

Number of shares per $100 18

Conversion Value 7.30 x 18 $131.40

The conversion value is higher than the cash so the investors will choose to convert.The conversion value is higher than the cash so the investors will choose to convert.The conversion value is higher than the cash so the investors will choose to convert.

Do an IRR the same as for redeemable but filling $131.40 into the capital repaidDo an IRR the same as for redeemable but filling $131.40 into the capital repaidDo an IRR the same as for redeemable but filling $131.40 into the capital repaid


Cost of Debt

Period


1 -5 Interest (10 x (1 - 0.3) 7 4.329 30.30 3.352 23.46

5 Conversion Value 131.4 0.784 103.02 0.497 65.31


13.32 -31.23

IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%

Preference Shares - Illustration 5

A company has issued 8% preference shares with a nominal value of $1.

The market value of the shares is 80c.

The tax rate is 30%.

Calculate the cost of the preference shares (Kd).

Solution

Interest Paid 8

Market Value of share 80

Cost (Kd) (Interest Paid / Market Value) (8 / 80) = 10%


Bank Debt - Illustration 6

A company has a bank loan of $2m at an interest rate of 10%.


Calculate the cost of debt (Kd).

Solution

Interest Rate before Tax 10

Tax Rate 30%

After Tax Cost of Debt (10 x (1 - 0.3)) 7%


WACC - Illustration 7

Company A is funded as follows:

Item Capital Structure Cost

Equity 85% 15%

Debt 15% 7%

Calculate the Weighted Average Cost of Capital.

Solution

Item Capital Structure Cost Ave

Equity 85% 15 12.75

Debt 15% 7 1.05

WACC 13.8




Balance Sheet Extract

Ordinary Shares (50c) 3000

Loan Notes 2000

Bank Loan 1000

The cost to the company of each of the above items has been calculated as:

Ordinary Shares 13%

Loan Notes 8%

Bank Loan 5%

The Loan notes are currently trading at $94.

The current share price is $1.50


Solution

Working 1 - Calculate Cost of Capital for each item.

Given in the QuestionGiven in the Question

Ordinary Shares 13%

Loan Notes 8%

Bank Loan 5%


Working 2 - Calculate the Market Value of Debt and Equity.

SFP Market Value

Ordinary Shares (50c)

3000 No. of shares (3000 / 0.50) = 6000Share Price = $1.50

(6000 x $1.50) = 9000

Loan Notes 2000 Loan Notes nominal value (on SFP) = 100Market Value = 94

(2000 x (94 / 100) = 1880

Bank Loan 1000 No market for this so use SFP value

1000

Working 3 - Calculate the weighting of each item.

Item Market Value Weighting

Equity 9000 (9000 / 11,880) = 75.75%

Loan Notes 1880 (1880 / 11,880) = 15.82%

Bank Loan 1000 (1000 / 11,880) = 8.41%

11880

Working 4 - Weighted Average Cost of Capital

Item Market Value

Weighting Cost (W1)

Ave

Equity 9000 (9000 / 11,880) 13 (9000 / 11,880) x 13 = 9.85

Loan Notes 1880 (1880 / 11,880) 8 (1880 / 11,880) x 8 = 1.27

Bank Loan 1000 (1000 / 11,880) 5 (1000 / 11,880) x 5 = 0.42

11880 WACC 11.54%




Balance Sheet Extract

Ordinary Shares (50c) 2000

12% Loan Notes 1500

8% Preference Shares ($1) 500

Bank Loan 750

Details on these are as follows.

The company has an equity beta of 1.2. Government bonds are currently trading at 6% and the average market risk premium is 7%.

The Loan notes are currently trading at $106 and are redeemable at par in 5 years time.

The preference shares are trading at 92c.

The bank loan has an interest rate of 10%.





Solution

Working 1 - Calculate Cost of Capital for each item.

Cost of Equity using CAPM


(Rm - Rf)(Ave market risk premium) 7

Beta 1.2

Ke = Rf + β(Rm - Rf) (6 + 1.2(7)) = 14.4%

Cost of 12% Loan Notes

Period


1 -5 Interest (12 x (1 - 0.3)

8.4 4.329 36.36 3.352 28.16

5 Capital 100 0.784 78.40 0.497 49.70


8.76 -28.14


Cost of Preference Shares

Interest Paid 8

Market Value of share 92

Cost (Kd) (Interest Paid / Market Value) (8 / 92) = 8.7%


Cost of Bank Debt

Interest Rate before Tax 10

Tax Rate 30%

After Tax Cost of Debt (10 x (1 - 0.3)) 7%

Working 2 - Calculate the Market Value of Debt and Equity.

SFP Market Value

Ordinary Shares (50c)

2000 No. of shares (2000 / 0.50) = 4000Share Price = $1.25

(4000 x $1.25) = 5000

12% Loan Notes

1500 Loan Notes nominal value (on SFP) = 100Market Value = 106

(1500 x (106 / 100) = 1590

8% Preference Shares ($1)

500 Preference shares nominal value (on SFP) = $1Market Value = 92c

(500 x (92 / 1)) = 460

Bank Loan 750 No market for this so use SFP figure

750

Working 3 - Calculate the weighting of each item.

Item Market Value Weighting

Equity 5000 (5000 / 7800)

Loan Notes 1590 (1590 / 7800)

Preference Shares 460 (460 / 7800)

Bank Loan 750 (750 / 7800)

7800


Working 4 - Weighting & Weighted Average Cost of Capital

Item Market Value

Weighting Cost (W1)

Ave

Equity 5000 (5000 / 7800) 14.4 (5000 / 7800) x 14.4 = 9.23

Loan Notes 1590 (1590 / 7800) 7.37 (1590 / 7800) x 7.37 = 1.50

Preference Shares

460 (460 / 7800) 8.7 (460 / 7800) x 8.7 = 0.51

Bank Loan 750 (750 / 7800) 7 (750 / 7800) x 7 = 0.67

7800 WACC 11.91%


Lecture 11 Capital Structure


Capital Structure - Illustration 1

A company has total capital of $1,000 with debt making up $300 and equity making up $700 of the total. The company’s cost of debt is 5% and cost of equity is 14%.

I. Calculate the company’s current WACC.II. Calculate the WACC if the company substitutes $200 of equity for $200 of debt

causing their cost of equity to rise to 16%.III. Calculate the WACC if the company substitutes $300 of equity for $300 of debt

causing their cost of equity to rise to 25%.

Solution

I.

Item Market Value Weighting Cost WACC

Debt 300 300 / 1000 5% 1.5

Equity 700 700 / 1000 14% 9.8

1000 11.3

II.


Debt 500 500 / 1000 5% 2.5

Equity 500 500 / 1000 16% 8

1000 10.5

III.


Debt 600 600 / 1000 5% 3

Equity 400 400 / 1000 25% 10

1000 13


Lecture 12 M & M Formulae


Illustration 1 ABC Ltd has a share price of 350c and 1m shares in issue. It currently has no debt. Current cost of capital is 13%. The directors have decided to replace $2m of equity with 10% debt. The tax rate is 30%. Required

(i) Calculate the new value of the geared firm.

(ii)Calculate the value of the Equity in the geared firm.

Value of Ungeared Firm (1m x 350c) 3,500

Market Value of Debt 2,000

Tax Rate 30%

Fill into Formula (Vg = Vu + TB) Vg = (3500 x (30% x 2000) 4,100

Value of Debt (In Question) 2,000

Value of Equity (4,100 - 2,000) 2,100


Illustration 2

ABC Co. and CD Co. operate in the same industry and are identical in their ability to generate cash flows.

ABC Co. is financed by Equity only of 3m shares with current value of $1 and has a cost of equity calculated at 15%.

CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m.


Required

(i) Calculate the value of CD Co.

(ii)Calculate the value of the Equity in CD Co.

Solution

Value of Ungeared Firm (3m x 100c) 3,000

Market Value of Debt 900

Tax Rate 33%

Fill into Formula (Vg = Vu + TB) Vg = (3,000 x (33% x 900) 3,297

Value of Debt (In Question) 900

Value of Equity (3,297 - 900) 2,397


Illustration 3



CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m and cost of debt of 8%.


Required

(i) Calculate the Cost of Equity for CD Co.

Solution

Keg = Keu + (Keu - Kd) Vd(1-t)/Ve

Keg = 15 + (15 - 8) 900(1-0.33) / 2397

Keg = 16.76%


Illustration 4



CD Co. has the same total capital but within it has irredeemable debt with a market value of $0.9m and cost of debt of 8%.


Required

(i) Calculate the WACC for CD Co.

Solution

Kadj = Keu (1 - tL)

Kadj = 15 (1 - (0.33 x (900 / 3,297)))

Kadj = 13.65


Lecture 14Risk Adjusted WACC


Risk Adjusted WACC - Illustration 1

Company A intends to undertake a project in an unrelated industry.

The following details are relevant:

Item Company A Proxy Company

Equity Beta (βe) 1.2 1.4

Value of Equity 1000 800

Value of Debt 400 500

The risk free rate is 4%.

The average return on the market is 12%.

The post tax cost of debt is 7%.

Calculate the risk adjusted WACC to be used in evaluating the project.

Ignore Tax

Solution

Working 1 - Un-gear the proxy βe to get βa.

Proxy Equity Beta 1.4

Value of Equity of Proxy 800

Value of Debt of Proxy 500

βu = βg(Ve / (Ve + Vd)) 1.4 (800 / (800 + 500)) = 0.86


Working 2 - Re-gear βa with our capital structure

βa 0.86

Value of Equity of Company A 1000

Value of Debt of Company A 400

βg = βu + (βu -βd) (Vd / Ve) 0.86 + (0.86 x (400 / 1000) = 1.20

Working 3 - Fill into CAPM


Rm (Ave return on the market) 12

Beta 1.2

Ke = Rf + β(Rm - Rf) (4 + 1.2(12 - 4)) = 13.6%

Working 4 - Risk Adjusted WACC

Item Market Value Weighting Cost Ave

Equity 1000 (1000 / 1400) 13.6 9.71

Debt 400 (400 / 1400) 7 2.00

1400 WACC 11.71


Risk Adjusted WACC - Illustration 2

Company A intends to undertake a project in an unrelated industry.

The following details are relevant:

Item Company A Proxy Company

Equity Beta (βe) 1.1 1.3

Value of Equity 1200 900

Value of Debt 500 450


The average return on the market is 12%.


The post tax cost of debt is 8%.

Calculate the risk adjusted WACC to be used in evaluating the project.

Solution

Working 1 - Un-gear the proxy βe to get βa.

Proxy Equity Beta 1.3

Value of Equity of Proxy 900

Value of Debt of Proxy 450

βu = βg(Ve / (Ve + Vd x 1-t)) 1.3 (900 / (900 + (450 x 0.7)) = 0.96


Working 2 - Re-gear βa with our capital structure

βa 0.96

Value of Equity of Company A 1200

Value of Debt of Company A 500

βg = βu + (βu -βd) (Vd (1-t)/ Ve) 0.96 + (0.96 x 500/1200) = 1.24

Working 3 - Fill into CAPM


Rm (Ave return on the market) 12

Beta 1.24

Ke = Rf + β(Rm - Rf) (4 + 1.24(12 - 4)) = 13.92%

Working 4 - Risk Adjusted WACC

Item Market Value Weighting Cost Ave

Equity 1200 (1200 / 1700) 13.92 9.83

Debt 500 (500 / 1700) 8 2.35

1700 WACC 12.18


Illustration 3

Company A Company B

Debt/Equity 1/3 1/4

Equity Beta 1.2

Debt Beta 0.3

Assume that the Asset Beta and the Debt Beta of each firm is the same.

Calculate the Equity Beta for Company B.

Solution

Ungear Equity Beta Company A:

Ba = (1.2 (3/4)) + (0.3 (1/4) = 0.9 + 0.075 = 0.975

Regear Asset Beta for Company B:

Be = 0.975 + ((0.975 -0.3) 1/4) = 1.14

or

0.975 = Be (4/5) + 0.3 (1/5)

0.975 - (0.3 x 1/5) = Be (4/5)

0.915 = Be (4/5)

Be = 0.915 x 5/4

Be = 1.14


Lecture 15 APV


Illustration 1

Cost of Equity in Geared Firm = 12%

Cost of Debt = 8%

Debt/Equity ratio = 1/2

Tax rate = 30%

Calculate the cost of equity in an ungeared firm.

Solution

12% = Keu + (Keu - 8%) (1(1 - 0.3) / 2)

12% = Keu + 0.35Keu - 2.8%

14.8% = 1.35 Keu

Keu = 10.96%


Illustration 2

Company AB has used $5m of 10% debentures to finance a project lasting for 4 years. The tax rate is 35%.

Issue costs are 3% and are tax deductible.

What is the PV of the issue costs for APV purposes?

Solution

Issue Costs:! $5m x 3% = $150,000

Tax Relief:! ! $150,000 x 35% = $52,500

Post Tax Cost:! $150,000 - $52,500 = $97,500


Illustration 3


Issue costs are 3% and are tax deductible. These are to be raised along with the finance.

What is the PV of the issue costs for APV purposes?

Solution

Required Finance: ! $5m is 97% of total to raise

! ! ! ! ...so ($5m / 0.97) $5,154,639 must be raised.

Issue Costs:! ! $5,154,639 x 3% = $154,639

Tax Relief:! ! ! $154,639 x 35% = $54,124

Post Tax Cost:! ! $154,639 - $54,124 = $100,515


Illustration 4


What is the PV of the tax relief available for APV purposes?

Solution

Annual Interest = $5m x 10% = $500,000

Annual Tax relief = $500,000 x 35% = $175,000

PV Tax relief = $175,000 x 3.170 = $554, 750


Illustration 5

Company AC needs to raise $10m in debt finance for 4 years.

Company AB has raised $7m of 10% debentures and the rest is provided by a subsidised government loan of $3m at 5%.


Calculate the financing effects of the debt for APV purposes.

Solution

PV Tax Shield

Annual Interest = ($7m x 10%) + ($3m x 5%) = $850,000


PV Tax relief = $255,000 x 3.170 = $808,350

Cheap Loan

Interest Saved = ($3m x (10% - 5%)) = $150,000

Tax Relief Lost = ($150,000 x 30%) = $45,000

Net Saving = ($150,000 - $45,000) = $105,000

Discount at the cost of debt as even though discounted it has the same risk as a normal loan...

PV Interest Saved = ($105,000 x 3.170) = $332,850


Illustration 6

ABC Co. is considering a project which is expected to generate cash inflows of $500,000 per year for 5 years and cost $500,000 of initial investment.

Costs have been estimated at $350,000 per year.

ABC has a current cost of equity of 14% and a cost of debt of 7% and a current debt to equity ratio of 1/3.

To undertake the the project the $500,000 will be raised through a bond issue of 8% with issue costs of 4% to be raised in addition to the finance.


Solution

Un-gear the cost of equity

14% = Keu + (Keu - 7%) (1(1 - 0.3) / 3)

14% = Keu + 0.23Keu - 1.63%

15.63% = 1.23 Keu

Keu = 12.71% say 13%

Base Case NPV

Discount at un-geared Ke of 13%

PV Cash Inflows = ($500,000 x 3.517) = $1,758,500

PV Outflows = ($350,000 x 3.517) = $1,230,950

Net Cash Inflow = $527,550

Initial Investment = $500,000

Base Case NPV = ($527,550 - $500,000) = $27,550


Issue Costs

Required Finance: ! $500,000 is 96% of total to raise

! ! ! ! ...so ($500,000 / 0.96) $520,833 must be raised.

Issue Costs:! ! $520,833 x 4% = $20,833

Tax Relief:! ! ! $20,833 x 30% = $6,250

Post Tax Cost:! ! $20,833 - $6,250 = $14,583

PV Tax Shield

Annual Interest = ($520,833 x 8%) = $41,666


PV Tax relief = $12,500 x 3.993 = $49,912

APV

Base Case NPV! = ! $27,550

PV Issue Costs ! = ($14,583)

PV Tax Shield ! = $38,040

APV! ! ! = $51,007


Lecture 16 More Risk


Illustration 1 ABC Ltd is undertaking a project costing $900m with expected net cash flows of $400m in years 1 & 2 then $600m in year 3.

The FD considers that these cash flows may be overestimated by as much as 10% in year 1, 15% in year 2 and 20% in year 3.

The risk free rate is 5% Required

Using certainty equivalents calculate the expected NPV of the project.

Solution

0 1 2 3

Cash Flows -900 400 400 600

Certainty Equivalents 1 0.9 0.85 0.80

CE Cash Flows -900 360 340 480

Discount Rate (5%) 1 0.952 0.907 0.864

Present Value -900 343 308 415

NPVNPVNPVNPV 166


Lecture 17 Options Pricing I


Illustration 1

Current Share Price:! ! $120Exercise Price:! ! ! $100Risk Free Interest Rate:! ! 10%Variance of Shares:!! ! 25%Time to Expiry:! ! ! 3 months

Solution

Time in Years to Expiry

3 months = 0.25 Years so 0.25 for formula

Standard Deviation of Share Price

Variance is 25% so that’s...0.25

To get SD we need to take square root of this which is 0.5

We work out d1 later but lets say it’s 0.95 when we calculate it....

Find 0.95 on Normal Distribution table.

Read table to find applicable number....0.3289.

0.95 is greater than 0 so add 0.5 to number from the table...

0.3289 + 0.5 = 0.8289....this is N(d1).

Find d1 first...

In(Pa/Pe) + (r + 0.5s2)ts√t

In(120/100) + (0.1 + 0.5 x 0.52)0.250.5 √0.25

0.1823 + 0.056250.25

d1 = 0.95





0.3289 + 0.5 = 0.8289....this is N(d1).

Now d2...

d2 = d1- s√t

d2 = 0.95 - 0.5 √0.25

d2 = 0.7




0.2580 + 0.5 = 0.7580....this is N(d2).

Fill into Black-Scholes model...

Call Option Value = PaN(d1) - PeN(d2)e-rt

Call Option Value = (120 x 0.8289) - 100 x 0.7580e-(0.1 x 0.25)

Call Option Value = (99.46 - 73.53) = 25.53

Intrinsic Value: (120 - 100) = $20

Time Value: (25.53 - 20) = $5.53


Illustration 2

Current Share Price:! ! $110Exercise Price:! ! ! $97Risk Free Interest Rate:! ! 8%Standard Deviation Shares:! 30%Time to Expiry:! ! ! 3 months

Solution

Time in Years to Expiry

3 months = 0.25 Years so 0.25 for formula

Standard Deviation of Share Price

This is given to us as 30%....so 0.3.

Find d1 first...


In(110/97) + (0.08 + 0.5 x 0.32)0.250.3 √0.25

0.126 + 0.031250.15

d1 = 1.05




0.3531 + 0.5 = 0.8531....this is N(d1).


Now d2...

d2 = d1- s√t

d2 = 1.05 - 0.3 √0.25

d2 = 0.9


Read table to find applicable number....0.3159


0.3159 + 0.5 = 0.8159....this is N(d2).



Call Option Value = (110 x 0.8531) - 97 x 0.8159 x e-(0.08 x 0.25)

Call Option Value = (93.84 - 77.58) = 16.26

Intrinsic Value: (110 - 97) = $13

Time Value: (16.26 - 13) = $3.26


Lecture 18 Options Pricing II


Illustration 1

Current Share Price:! ! $120Exercise Price:! ! ! $100Risk Free Interest Rate:! ! 10%Variance of Shares:!! ! 25%Time to Expiry:! ! ! 3 months

We already calculated in the last lecture that the call option value is $25.53.

Calculate the value of the corresponding put option.

Solution

Put Option Valuation is...

P = c - Pa + Pe x e-rt

P = 25.53 - 120 + 100 x e-(0.1 x 0.25)

P = 25.53 - 120 + 97.53

P = $2.53


Illustration 2

ABC Ltd. has an option in CD Ltd. which is due to expire in 6 months.

A dividend of 55 cents is due to be paid in 3 months time and the current share price is $15.


Calculate the dividend-adjusted share price.

Solution

We need the present value of the dividends so...

Divs x e-rt

55 x e-(0.1 x 0.25)

= 53.64c

Subtract this from the share price...

$15 - $0.54 = $14.46


Illustration 3

ABC Co. is planning to expand into Foreignland by opening a new distribution centre there.

The project would cost $20m and the present value of the cash flows are forecasted to be $17m leading to a negative NPV of $3m.

However, by undertaking the investment they could expand further into Foreignland with a second distribution centre.

The second centre is expected to have the following details:

Estimated Cost (Pe):! ! ! $30m

PV Expected Net Receipts (Pa):! ! $23m

Timing (t):! ! ! ! ! 5 years

Risk Free Rate (r):! ! ! ! 8%

Volatility (s):! ! ! ! ! 30%

Calculate the value of the call option on the second distribution centre (this is an option to expand).

Solution

Find d1 first...


In(23/30) + (0.08 + 0.5 x 0.32)50.3 √5

-0.266 + 0.6250.67

d1 = 0.54


Read table to find applicable number....0.2054


0.2054 + 0.5 = 0.7054....this is N(d1).


Now d2...

d2 = d1- s√t

d2 = 0.54 - 0.3 √5

d2 = -0.13



-0.13 is less than 0 so subtract number on the table from 0.5...

0.5 - 0.0517 = 0.4483....this is N(d2).



Call Option Value = (23 x 0.7054) - 30 x 0.4483 x e-(0.08 x 5)

Call Option Value = (16.22 - 9) = $7.22m

So...

NPV of first centre:! ! -$3mCall Option on 2nd:!! $7.22m

Total:! ! ! ! $4.22m


Lecture19 More on Cost of Debt


Illustration 1

ABC Co. has 5 year bonds in issue with a BBB credit rating which have a credit spread of 115.

5 year treasury bonds have a current return of 3.4%

What is the expected yield on ABC’s bonds?

Solution

A credit spread of 115 = 1.15%.

3.4% + 1.15% = 4.55%


Illustration 2

A government has three bonds in issue that all have a face or par value of $100 and are redeemable in one year, two years and three years respectively. Since the bonds are all government bonds, let’s assume that they are of the same risk class. Let’s also assume that coupons are payable on an annual basis. Bond A, which is redeemable in a year’s time, has a coupon rate of 7% and is trading at $103. Bond B, which is redeemable in two years, has a coupon rate of 6% and is trading at $102. Bond C, which is redeemable in three years, has a coupon rate of 5% and is trading at $98.

To determine the yield curve, each bond’s cash flows are discounted in turn to determine the annual spot rates for the three years, as follows:

Bond A:

$103 = $107 / (1+r1)

r1 = (107/103 – 1) = 0.0388 or 3.88%

Bond B:

$102 = $6 / 1.0388! = 5.78106 / (1+r2)2! = (102 - 5.78) = 96.22

r2 = [106 / 96.22]1/2 - 1= 0.0496 or 4.96%

Bond C:$98 =

$5 / 1.0388 ! = 4.81$5 / 1.04962 != 4.54105 / (1+r3)3 != (98 - 4.81 - 4.54) = 88.65

r3 = [105 / (88.65)]1/3 – 1 = 0.0580 or 5.80%

The annual spot yield curve is therefore:

Year1 3.88%2 4.96% 3 5.80%


Illustration 3

ABC Co. has 3 yr 8% bonds in issue which are redeemable at par after the 3 year term. The yield to maturity is 10% and they are trading at $95.

Calculate the Macauley Distribution.

Solution

Step 1 - PV of each future receipt:

Year DR = 10% Cash PV

1 0.909 8 7.27

2 0.826 8 6.61

3 0.751 108 81.11

Bond PriceBond PriceBond Price 95

Step 2 - Time to Maturity x PV Cashflow

Time Cash PV

1 7.27 7.27

2 6.61 13.22

3 81.11 243.33

SUMSUM 263.82

Step 3 - SUM / Bond Price

263.82 / 95 = 2.78 Years


Lecture 20 Corporate Failure I


No Illustrations


Lecture 21 Corporate Failure II


Illustration 1

$‘000

Assets 500

500

Equity & Liabilities

Issued Equity Shares @ $1 each 600

Share Premium 100

Retained Earnings -300

Liabilities 100

500

Dividends cannot be paid while accumulated losses exist.

Equity of $600,000 is only backed by assets of $500,000.

Loan finance cannot be raised due to the current financial position.

Required

Apply a capital reduction and restate the statement of financial position.


Solution

DR CR

Share Premium 100

Equity Share Capital 200

Retained Earnings 300

$‘000

Assets 500

500


Issued Equity Shares 400

Share Premium 0

Retained Earnings 0

Liabilities 100

500


Illustration 2

$‘000

Intangible Asset (Brand) 50,000

Non Current Assets 220,000

270,000

Inventory 20,000

Receivables 30,000

320,000


Issued Equity Shares @ $1 each 100,000

Share Premium 75,000

Retained Earnings -100,000

75,000

Debenture Loan 125,000

Overdraft 20,000

Payables 100,000

320,000

A reconstruction scheme is to take place under the following conditions:

(i) The equity shares of $1 nominal currently in issue will be written off and will be replaced on a one-for-one basis by new equity shares with nominal value of $0.25.

(ii)The debenture loan will be replaced by the issue of new equity shares - four new shares with nominal value of $0.25 each for every $1 debenture loan converted.

(iii)New shares with a nominal value of $0.25 will be offered to the existing equity holders in the ratio of three new shares for every one currently held. All current equity holders are expected to take this up.

(iv)Share premium account to be eliminated.(v)Brand to be written off as it is impaired.(vi)Deficit on the retained earnings to be eliminated.

Prepare the revised SFP and show any workings undertaken to achieve this.


Solution

Reconstruction AccountReconstruction AccountReconstruction AccountReconstruction Account

DRDR CRCR

New Equity Shares(100,000 x 0.25) Note (i)

25,000 Remove Equity SharesNote (i)

100,000

Conversion of Debenture (125,000 x 4 x 0.25) Note (ii)

125,000 Remove Debenture LoanNote (ii)

125,000

Brand Impairment Note (v)

50,000 Share Premium RemovedNote (iv)

75,000

Retained EarningsNote (vi)

100,000

300,000 300,000

$‘000

Intangible Asset (Brand) 0


220,000

Bank (-20,000 + 75,000) Note (iii) 55,000

Inventory 20,000

Receivables 30,000

325,000


Issued Equity Shares (125,000 + 25,000 + 75,000) 225,000

Share Premium 0

Retained Earnings 0

225,000

Debenture Loan 0

Overdraft 0

Payables 100,000

325,000


Lecture 22 Business Valuations

I


Net Assets Valuation Method Illustration 1


Current Assets 170,000

Current Liabilities -80,000

Share Capital 300,000

Reserves 200,000

10% Loan Notes 150,000

The Market Value of property in the Non Current Assets is $50,000 more than the book value.The Market Value of property in the Non Current Assets is $50,000 more than the book value.

The Loan Notes are redeemable at a 5% premium.The Loan Notes are redeemable at a 5% premium.

What is the value of a 70% holding using the net assets valuation basis?

Solution

Working $

Non Current Assets 550,000 + 50,000 (Property value) 600,000

Current Assets 170,000

Current Liabilities -80,000

10% Loan Notes 150,000 x 105% -157,500

532,500

Value of 70% 532,500 x 70% 372,750


DVM - Illustration 2

ABC pays a constant dividend of 45c. It has 3m ordinary shares.

The shareholders require a return of 15%.

What is the Value of the business?

Solution

Working

Constant Dividend In Question 45c

Required Return (Cost of Equity or Ke) In Question 15%

Share Price (Dividend / Ke) 45 / 0.15 300c

No. Ordinary Shares In Question 3m

Value of the business 300c x 3m $9m


DVM - Illustration 3

A business has Share Capital made up of 50c shares of $3 millionDividend per share (just paid) 30cDividend paid four years ago 22cRequired Return = 12%

Calculate the Value of the business using the dividend valuation method.

Solution

Working 1 - Dividend GrowthWorking 1 - Dividend Growth

Dividend Paid Now 30c

Dividend Paid 4 Years Ago 22c

Dividend Growth (4√(30 / 22))=1.08=8%

Working 2 - Business ValuationWorking 2 - Business Valuation

Dividend Paid 30c

Required Return (Ke) 12%

Dividend Growth 8%

Share Price (Dividend (1+g)) / (Ke - g) (30 x 1.08) / (0.12 - 0.08) = 810c

No Ordinary Shares ($3m / 0.5) = 6m

Value of business (6m x 810c) = $48.6m


P/E Ratio Method - Illustration 4

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3000 3500 4200

COS 2000 2400 3200




PBIT 500 500 300


Tax 120 90 50




Industry P/E Average 13 12 14

Calculate the Value of the Company for each of the 3 years using the P/E Ratio method.

Solution

Year Industry P/E Ratio Total Earnings Value of Company

1 13 280,000 (13 x 280,000) = $3.64m

2 12 260,000 (12 x 260,000) = $3.12m

3 14 30,000 (14 x 30,000) = $420,000


P/E Ratio Method - Illustration 5

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3200 3800 4800

COS 2000 2400 3200




PBIT 700 800 900


Tax 120 90 50




Industry P/E Average 17 15 18

Number of Shares 3m 3m 3m

Calculate the Earnings Per Share for each of the 3 years

Calculate the Value of the Company for each of the 3 years using the EPS you calculate.


Solution

Year Earnings No. Shares EPS (Earnings / No. Ordinary Shares)

1 480,000 3m 16c

2 560,000 3m 18.66c

3 630,000 3m 21c

Year Industry P/E Ratio

EPS Share Price(EPS x P/E Ratio)

Value of Company

1 17 16c $2.72 (2.72 x 3m) = $8.16m

2 15 18.66c $2.80 (2.80 x 3m) = $8.4m

3 18 21c $3.78 (3.78 x 3m) = $11.34m


Earnings Yield - Illustration 6

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3100 3700 4600

COS 2000 2400 3200




PBIT 600 700 700


Tax 120 90 50




Earnings Yield 0.15 0.18 0.17

Number of Shares 4m 4m 4m

Calculate the Earnings Per Share for each of the 3 years and the share price using the earnings yield.

Solution

Year Earnings No. Shares

EPS (Earnings / No. Ordinary

Shares)

Earnings Yield

Share Price(EPS / Earnings

Yield)

1 380,000 4m 9.5c 0.15 63.33c

2 460,000 4m 11.5 0.18 63.88c

3 430,000 4m 10.75 0.17 63.23c


Present Value of Future Cash Flows - Illustration 7

ABC Company earned $100,000 in cash inflows this year.

They expect this to increase in each of the next 5 years by 5% and after that to increase by 2% forever.

The company uses a cost of capital of 10%.

Calculate the value of the company using the present value of future cash flows method.

Solution

Period 0 1 2 3 4 5

Cash Inflows 100,000 105,000 110,250 115,763 121,551 127,628

Discount Rate 10%

1 0.909 0.826 0.751 0.683 0.621

PV Cash Flows

100,000 95,445 91,067 86,938 83,019 79,257

Total 535,725

Period Working $

Years 0 - 5 From Above 535,725

Post Year 5 (127,628 x (1+g)) / (Ke - g)(127,628 x 1.02) / (0.10 - 0.02)

1,627,257

Total Value of Company 2,162,982


Lecture 23Business Valuations

II


Illustration 1

Company A has 100m shares at £3 each. Company B has 50m shares of

£1 each.

Company A makes an offer of 1 new shares for every 5 held in B and has

worked out that the synergies available are valued at £20m

Calculate the expected value of a share in the combined company.

Solution

1. Value of Company A = (100m x 3) = 300m

2. Value of Company B = (50m x £1) = 50m

3. Value of Combination = (300 + 50 + 20*) = 370m *Synergies

4. No. Shares = 100 + (1/5)x50 = 110m

5. Value of one share = 370/110 = £3.45


Illustration 2

Post Tax Profit P/E Ratio Pre Aq. ValueCompany A £150m 10 £1500mCompany B £10m 7 £70m Estimating the post acquisition value of the combined business is done by applying the P/E ratio of Company A to the combined earnings of the new combination.

Solution

Value of individual companies = (£1,500 + £70) £1,570

Value of Combination = 10 x (£150m + £10m) = £1,600m

Value of Synergies = £1,600m - £1,570m = £30m


Lecture 24Advanced Business

Valuations


Illustration 1

ABC Ltd. uses a time horizon of 12 years to forecast free cash flows.

They use a planning horizon of 3 years after which they expect cash flows to remain at a steady level.

The cash flows projected are as follows:

Year $

1 3m

2 5m

3 7m

The stock market value of debt is $6m and the cost of capital is 10%.

Calculate the value of the firm and the value of the equity.

Solution

Year $ Discount Rate (10%) PV

1 3m 0.909 2.73

2 5m 0.826 4.13

3 7m 0.751 5.26

4 to 12 7m 5.335 x 0.751

28.05

Value of the FirmValue of the FirmValue of the Firm 40.16

Value of DebtValue of DebtValue of Debt -6.00

Value of EquityValue of EquityValue of Equity 34.16


Illustration 2

The following figures are relevant:

$m

Operating Profit 400

Depreciation 150

Increase in Working Capital 40

Capital Expenditure to replace assets 8

New Capital expenditure 18

Interest Paid 7

Loans Repaid 30

Tax Paid 120

Calculate the free cash flows before interest and dividends and then the free cash flows to equity.

Solution

$m


Less Tax -120

Add Depreciation 150

Operating Cash Flow 430

Replacement Capital Expenditure -8

Incremental Capital Expenditure -18

Incremental Working Capital -40

Free Cash FLows 364

Interest Paid -7

Loans Repaid -30

Free Cash FLows to Equity 327


Illustration 3

A company has NOPAT which has been adjusted for EVA purposes of $700m. It’s capital employed is $5,000m and it’s WACC is 8%. The total debt of the company is $1,000m.

Calculate the EVA for the company and use it to value the firm and the firm’s equity.

Solution

EVA = NOPAT - rC

EVA = 700 - (0.08 x 5000) = $300m

Firm Value = C + EVA/WACC

Firm Value = 5000 + 300/.08 = $8,750m

Value of Equity = 8750 - 1000 = $7,750m


Illustration 4

ABC Co. wants to value their company in order to raise more capital. They have a lot of intangible assets so wish to use the CIV method to put a value to these.

ABC has operating profit of $250m and has a WACC of 9% and an asset base of $700m.

CD Co. is a larger but similar firm which made an operating profit of $1,000m on an asset base of $5,500m.

Calculate the value of ABC Co. incorporating the CIV.

Solution

Proxy Firm ROA

1,000 / 5,500 = 18%

Value Spread

$m


Less

Proxy POA x Asset Base 18% x 700 126

Value Spread 124

Calculate CIV

Discount Value Spread at Cost of Capital = 124 / 0.09 = $1,377m

Value Firm

Assets (Capital Employed) + CIV

700 + 1,377 = $2,077m


Lecture 25Multinational

Companies


Illustration 1

Figures from the cash flow statement of ABC Ltd. are as follows:

20X1$m

20X0$m

Operating Cash Inflows 1,500 1,000

Capital Expenditure 250 200

Dividends from Joint Venture 130 100

Taxation Paid 200 170

Interest Paid 75 60

Disposal of Subsidiary 500 -

New Shares Issued 300 -

Calculate the free cash flows to equity or dividend capacity of ABC Ltd. for the year ended 20X1.

Solution

20X1$m

Operating Cash Inflows ADD 1,500

Capital Expenditure SUBTRACT 250

Dividends from Joint Venture ADD 130

Taxation Paid SUBTRACT 200

Interest Paid SUBTRACT 75

Disposal of Subsidiary ADD 500

New Shares Issued ADD 300

Dividend CapacityDividend Capacity 1905


Lecture 26F9 FX Risk Revision


Buy or Sell Currency - Illustration 1

You have an invoice to pay to a US business of $1250 and you are a UK business.

The rate offered by the bank is $:£ 1.2500 - 1.3500

How many £ will it take to pay the $125?

Solution

Bank sells low We want to buy $ with our £ and the bank will sell them to us at the low rate of 1.2500

For a receipt use the rate on the right

We are making a payment so we use the rate on the left i.e. 1.2500

Cost of $ (Amount of $ / FX Rate)

($1250 / 1.25) = £1,000


Buy or Sell Currency - Illustration 2

You have issued an invoice to a US customer of $2000 and you are a UK business.

The rate offered by the bank is $:£ 1.4500 - 1.5500

How many £ will you receive for the $2000?

Solution

Bank sells low We want to sell the $ we will receive. The bank will buy them from us at the high rate of 1.5500

For a receipt use the rate on the right

This is a receipt so use the rate on the right of 1.5500

Value of $ (Amount of $ / FX Rate)

($2000 / 1.55) = £1,290


Purchasing Power Parity Theory - Illustration 3

The current exchange rate is 2$ per £.

Inflation in the US is 6%.

Inflation in the UK is 8%.

What will the FX rate be in 1 years time?

Solution

Current Spot Rate 2

Inflation in Counter (US) 6%

Inflation in Base (UK) 8%

Forecast (Spot Rate Counter x (1 + Inf in Counter / 1 + Inf in Base)

2 x ((1 + 0.06) / (1 + 0.08)) = 1.96


Interest Rate Parity Theory - Illustration 4

The current exchange rate is 2$ per £.

The interest rate in the US is 3%.

The interest rate in the UK is 2%.

What will the FX rate be in 1 years time?

Solution

Current Spot Rate 2

Interest rate in Counter (US) 3%

Interest rate in Base (UK) 2%

Forecast (Spot Rate Counter x (1 + Int in Counter / 1 + Int in Base)

2 x ((1 + 0.03) / (1 + 0.02)) = 2.02


Forward Rate - Illustration 5

ABC Company has entered into a contract whereby they will receive $500,000 from a US customer in 3 months.

ABC is a UK company.

A 3 month forward rate is available at $:£ 1.6000 +/- 0.0500.

Calculate the amount of £ ABC would receive under the forward contract.

Solution

A rate quoted at $:£ 1.6000 +/- 0.0500 is the same as saying $:£ 1.5500 - 1.6500A rate quoted at $:£ 1.6000 +/- 0.0500 is the same as saying $:£ 1.5500 - 1.6500

Rate to use (For a receipt use the one on the right)

1.6500

Convert ($ amount / Forward rate) (500,000 / 1.6500) = £303,030


Money Market Hedge - Illustration 6

A UK business needs to pay $350,000 to a US supplier in 3 months time.

Exchange rate now: $:£ 1.6500 - 1.7000

Deposit rates UK 4% annual US 6% annual

Borrowing rates UK 5% annual US 6.5% annual

How much £ will the transaction cost using a money market hedge?

Solution

Step 1 - How much Foreign Currency?

Amount of $ to pay 350,000

We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.

Deposit Rate in US per year 6%

Deposit Rate for 3 months (Annual rate x 3/12)

6 x (3/12) = 1.5%

Amount to deposit (Total $ discounted at 1.5%)

350,000 x (100 / 101.5) = $344,827

We will deposit $344,827 in the US where it will earn interest of 1.5% over the 3 months making it worth $350,000 when the payment becomes due.We will deposit $344,827 in the US where it will earn interest of 1.5% over the 3 months making it worth $350,000 when the payment becomes due.

We transfer the money now so that there is no more FX risk. The transfer is made at the spot rate.We transfer the money now so that there is no more FX risk. The transfer is made at the spot rate.


Step 2 - Convert using the Spot Rate

Amount to Transfer (Step 1) $344,827


Spot rate (We are making a payment) 1.6500

Convert ($ Amount / Spot Rate) (344,827 / 1.6500) = £208,986

Step 3 - Borrow the Home Currency

Amount to Borrow (Step 2) £208,986

We will have to pay interest on the amount we have borrowed for 3 months.We will have to pay interest on the amount we have borrowed for 3 months.

Borrowing Rate per year in UK 5%

Borrowing Rate for 3 months (Annual Rate x 3/12)

(5 x 3/12) = 1.25%

Total Cost of transaction

Amount transferred to US £208,986

Interest on borrowings in UK (£ amount x 3 month UK borrowing rate)

(208,986 x 1.25%) = £2,612

Total Cost (Amount transferred + interest incurred)

(208,986 + 2,612) = £211,589


Money Market Hedge Illustration 7

A UK business will receive $350,000 from a US supplier in 3 months time.

Exchange rate now: $:£ 1.6500 - 1.7000

Deposit rates UK 4% annual US 6% annual

Borrowing rates UK 5% annual US 6.5% annual

How much £ will the business receive using a money market hedge?

Solution

Step 1 - How much foreign currency?

Amount of $ to receive 350,000

We will borrow the money in the US now and transfer it home.We will borrow the money in the US now and transfer it home.

Borrowing Rate in US per year 6.5%

Borrowing Rate for 3 months (Annual rate x 3/12)

6.5 x (3/12) = 1.625%

Amount to borrow (Total $ discounted at 1.625%)

350,000 x (100 / 101.625) = $344,403

We will borrow $344,403 in the US where it will earn interest of 1.625% over the 3 months making it worth $350,000 when the receipt becomes due. We will borrow $344,403 in the US where it will earn interest of 1.625% over the 3 months making it worth $350,000 when the receipt becomes due.

We will pay off the loan in the US when we receive the $350,000 in 3 months.We will pay off the loan in the US when we receive the $350,000 in 3 months.



Step 2 - Convert into home currency using spot rate.

Amount to Transfer (Step 1) $344,403


Spot rate (We are receiving the foreign currency)

1.7000

Convert ($ Amount / Spot Rate) (344,403 / 1.7000) = £202,590

Step 3 - Place the money on deposit in the UK

Amount to Deposit (Step 2) £202,590

We will receive interest on the money we deposit.We will receive interest on the money we deposit.

Deposit Rate per year in UK 4

Deposit Rate for 3 months (Annual Rate x 3/12)

(4 x 3/12) = 1%

Total Receipt

Amount transferred to UK £202,590

Interest on deposit in UK (£ Amount x 3 month UK borrowing rate)

(202,590 x 1%) = £2,026

Total Receipt (Amount transferred + interest received)

(202,590 + 2,026) = £204,616


Lecture 27FX Risk: Futures


Illustration 1

A UK company will receive $2.5m from an american customer in 3 months time in February.

The following information is relevant:

Futures: (contract size £62,500)

December 1.5830 $/£

March 1.5796 $/£

Forward Rates: Spot 1.5842 - 1.5851

1 month 0.0056 - 0.0053 pm

3 month 0.0172 - 0.0164 pm

28 February:

Assume that the spot rate moves to 1.6490 - 1.6510

March futures have a price of 1.6513

Required

Assess whether a future or forward currency hedge would have been better with hindsight.


Solution

Future

Step 1. Buy or sell

The contract currency is £.

We will buy £ with the $ receipt.

Therefore we will buy futures.

Step 2. Choose Expiry

We will get the money in February so we choose the March futures rate of 1.5796

Step 3. How many contracts?

Foreign Amount Future Price Base Amount

$2,500,000 1.5796 1,582,679

Base Amount Contract Size No. Contracts

1,582,679 62,500 25

Step 4. Profit or Loss on future?

Action Future Price Contract Size Amount

Bought at 1.5796 62,500 98,725

Sold at 1.6513 62,500 103,206

Profit 4,481

No. Contracts 25

Total Profit 112,031


Step 5. Total Receipt

Amount

Receipt of Dollars 2,500,000

Profit on future contract 112,031

Total Dollar Receipt 2,612,031

Spot rate on transaction day 1.6510

Total Sterling received 1,582,090

Forward Rate

$2.5m / (1.5851 - 0.0164) = £1,593,676 received

Using the forward rate would be better.


Illustration 2

MNO is a UK based company that has delivered goods, invoiced at $1,800,000 US dollars to a customer in Singapore. Payment is due in three months’ time, that is, in February 2007. The finance director of MNO is concerned about the potential exchange risk resulting from the transaction and wishes to hedge the risk in either the futures or the options market.

The current spot rate is $1·695/£. A three month futures contract is quoted at $1·690/£, and the contract size for $/£ futures contracts is £62,500.

Assuming that the spot rate and the futures rate turn out to be the same in February 2007, indicating that there is no basis risk, identify the cost of hedging the exchange rate risk using futures where the exchange rate at the time of payment is:

(i) $1·665/£

(ii) $1·720/£


Solution

Step 1. Buy or sell

The contract currency is £.

We will buy £ with the $ receipt.

Therefore we will buy futures.


We receive the money in Feb 2007 so choose 3 month future.



1,800,000 1.690 1,065,089


1,065,089 62,500 17



Bought at 1.6900 62,500 105,625

Sold at 1.6650 62,500 104,063

Profit/Loss -1,563

No. Contracts 17

Total Profit/Loss -26,563



Bought at 1.6900 62,500 105,625

Sold at 1.7200 62,500 107,500

Profit/Loss 1,875

No. Contracts 17

Total Profit/Loss 31,875


1.665 1.720

Receipt of Dollars 1,800,000 1,800,000

Profit/Loss on future contract -26,563 31,875

Total Dollar Receipt 1,773,437 1,831,875

Spot rate on transaction day 1.665 1.72

Total Sterling received 1,065,127 1,065,044


Illustration 3

ABC Co. is a sterling based company that expects to receive $250m in 4 months time.

The spot rate is £/$ 0.6690

Futures are available in $250,000 contracts as follows:

2 month expiry 0.6666

5 month expiry 0.6645

Estimate the result of the hedging transaction given that the spot rate is predicted to be 0.6674 in 4 months time and that basis risk reduces in a linear manner.

Solution

Basis Workings

Now

Spot now 0.6690

Future (5 month) 0.6645

Basis (Difference) 0.0045

Basis reduces to zero over 5 months so by 4 months time it will be (0.0045 / 5 x 1) = 0.0009 Basis reduces to zero over 5 months so by 4 months time it will be (0.0045 / 5 x 1) = 0.0009

Spot rate in 4 months 0.6674

Basis remaining at that time -0.0009

Futures Price in 4 months 0.6665

Step 1. Buy or sell

The contract currency is $.

We will sell the $ when we receive the money.

Therefore we will sell futures.



We will use the 5 month expiry of 0.6645



250,000,000 250,000 1,000


Action Future Price Contract Size Amount(in £)

Bought at 0.6665 250,000 166,625

Sold at 0.6645 250,000 166,125

Profit -500

No. Contracts 1,000

Total Loss -500,000


Amount

Receipt of Dollars in 4 months (250m x 0.6674) 166,850,000

Loss on future contract in £ -500,000

Total Receipt 166,350,000


Illustration 4

Using the information in illustration 3 calculate the total receipt using the ‘lock-in rate’.

Solution

Lock in rate = Opening Futures Price + Unexpired Basis (on transaction date)

Lock in rate = 0.6645 + 0.0009 = 0.6654£ / $

Total Receipt = $250,000,000 x 0.6654 = £166,350,000


Lecture 28FX Risk: Options &

Swaps


Illustration 1 A German company expects to receive $15m from a US company in December. The spot rate is $1.4850 – $1.4860. The premiums for $/€ Options of €32,500 are: Strike CALLS PUTS Price Oct Nov Dec Oct Nov Dec 1.4860 0.71 1.35 2.40 0.86 1.90 2.201.4870 0.71 1.35 2.30 0.86 1.90 2.25 The company is concerned that the $ may weaken. (i) Show how traded $/€ options may be used to hedge this risk. (ii) Assume the spot rate moves to either 1.600 or 1.400


Solution

The Contract Currency is €.

We will buy € with our $ receipt...so we need the option to buy €...

...we therefore want to buy a call option.

Cheapest strike price is one of 1.4860 which will cost 2.4 cents per €.

How many Contracts?


$15,000,000 1.4860 €10,094,213


€10,094,213 €32,500 311

Calculate Premium.

No. Contracts Contract Size Price per €/£ Premium

311 €32,500 $0.024 $242,580

Convert to €. $242,580 / 1.4850 = €163,353

Exercise?

€10,094,212 - €163,353 = €9,930,859

If the spot rate moves to 1.600 (15/1.6 = $9.375m) the company should exercise the option.

If the spot rate is 1.400 then the spot rate should be used for conversion.

Uncovered Amount

Base Amount Contract Size No. Contracts Covered Uncovered

€10,094,213 €32,500 311 €10,107,500 €13,287


Illustration 2

Evans Co. is an Australian firm looking to expand in France and is thus looking to raise €24m it can borrow at the following fixed rates:

A$ 7.0%€5.6%

Portmoth is a Spanish Co. looking to acquire an Australian firm and wants to borrow A$40m. It can borrow at the following rates:

A$7.2%€5.5%

The current spot rate is A$1 = €0.60

Show how a currency swap for 1 yr with interest paid at the end of the year would work.

Solution

! ! ! ! ! Evans Co PortmothBorrow from bank now A$40m at 7.0% €24m at 5.5%Exchange principles A$40m to Portmoth €24m to Evans Co.Pay interest to Bank A$2.8m €1.32mExchange Interest €1.32 to Portmoth A$2.8m to Evans Co.Swap back principle €24m to Portmoth A$40m to Evans Co


Illustration 3

ABC Co. is a German company considering a project in Zancar, a foreign country where the currency is the Franc (Fr). The investment in the project would be Fr250m and they expect to sell out of the project after 1 year for Fr350m.

The current exchange rate is 25Fr/£ and the government in Zancar has offered a forex swap at this rate. The borrowing rate in the Eurozone is 5% and it is expected that the FX rate in one year will be 40Fr/£.

Show the effect if ABC Co.

i. Undertakes the forex swap.

ii.Does not undertake the forex swap

Solution

i. Undertake Swap

Now One Year

Borrow money to buy Francs (250 / 25) -€10m

Swap back Francs at end of project (250 / 25) €10m

Convert Profit at Spot Rate (350 - 250) / 40 €2.5m

Interest on Loan in Euros (10m x 5%) -€0.5m

-€10m €12m

Net result is a profit of €2mNet result is a profit of €2mNet result is a profit of €2mNet result is a profit of €2m

ii. No Swap

Now One Year

Borrow money to buy Francs (250 / 25) -€10m

Convert Sale Proceeds at Spot Rate (350 / 40) €8.75m

Interest on Loan in Euros (10m x 5%) -€0.5m

-€10m €8.25m

Net result is a net loss of €1.75mNet result is a net loss of €1.75mNet result is a net loss of €1.75mNet result is a net loss of €1.75m


Illustration 4

Companies A, B and C are within the same group whereas company D is an external company. The following liabilities have been identified between the 4 companies:

Owed Form Owed to Amount(Millions)

A B £20

B C €30

C D $45

C A ¥100

C B £35

D B €20

D C $30

Mid-market spot rates are:

£1 = $1.45£1 = €1.20£1 = ¥200

Establish the net indebtedness that would require external hedging.

Solution

Set up Table

Owed to A Owed to B Owed to C Owed to D

Owed From A £20

Owed From B €30

Owed From C ¥100 £35 $45

Owed From D €20 $30


Convert to £

Owed Form Owed to Amount(Millions) Rate £

(Millions)

A B £20 - £20.00

B C €30 1.2 £25

C D $45 1.45 £31.03

C A ¥100 200 £0.50

C B £35 - £35.00

D B €20 1.2 £16.67

D C $30 1.45 £20.69

Fill in Table

Owed to A Owed to B Owed to C Owed to D Total

Owed From A 20 20

Owed From B 25 25

Owed From C 0.5 35 31.03 66.53

Owed From D 16.67 20.69 37.36

Total To 0.5 71.67 45.69 31.03

Total From 20 25 66.53 37.36

Net Total -19.5 46.67 -20.84 -6.33

SolutionSolutionSolutionSolutionSolutionSolution

Both A and C Pay the net amounts owed to BBoth A and C Pay the net amounts owed to BBoth A and C Pay the net amounts owed to BBoth A and C Pay the net amounts owed to B (19.5 + 20.84) 40.34

This leaves the amount outstanding to be paid by D to BThis leaves the amount outstanding to be paid by D to BThis leaves the amount outstanding to be paid by D to BThis leaves the amount outstanding to be paid by D to B 6.33

Total Paid to BTotal Paid to BTotal Paid to BTotal Paid to B 46.67

The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).The amounts from A and C were in £ in any case and the £6.33 payable from D to B can be converted back to € at the spot rate (£6.33 x 1.2 = €7.6).


Diagrammatical Method

Convert to base

Owed Form Owed to Amount(Millions) Rate £

(Millions)

A B £20 - £20.00

B C €30 1.2 £25

C D $45 1.45 £31.03

C A ¥100 200 £0.50

C B £35 - £35.00

D B €20 1.2 £16.67

D C $30 1.45 £20.69


Lecture 29Interest Rate Risk I


Illustration 1

ABC Ltd. has entered into a commitment to borrow $10m in 3 months time for a period of 3 months.

The bank has offered a 3v6 FRA at 6.00% - 5.65%.

Calculate the effect if the market rate in 3 months is

i. 7%ii.4%

Solution

7% 4%

Interest Payable (10m x 7% x 3/12) 175,000 (10m x 4% x 3/12) 100,000

FRA CompensationFRA Compensation

Receivable 10m x (7% - 6%) x 3/12 -25,000

Payable 10m x (4% - 6%) x 3/12 50,000

Net Interest PayableNet Interest Payable 150,000 150,000


Illustration 2

ABC Ltd. has entered into a commitment to borrow $10m in 3 months time for a period of 3 months.

The bank has offered an IRG at 6% for a premium of 0.075% of the loan capital.

Calculate the effect if the market rate in 3 months is

i. 7%ii.4%

Solution

7%(Exercise)

4%(Lapse)

Interest Payable (10m x 6% x 3/12) 150,000 (10m x 4% x 3/12) 100,000

Premium (10m x 0.075%) 7,500 7,500

Total PayableTotal Payable 157,500 107,500


Illustration 3

Company A is considering an interest rate swap with Company B. They can borrow at the following rates:

! ! Fixed FloatingA 10% LIBOR +1%B 12% LIBOR +1.5%

Show the effect of using an interest rate swap.

Solution

Working 1

Fixed Floating

Company A 10 L + 1

Company B 12 L + 1.5

Difference 2 0.5

The largest difference is on Fixed with a total of 2%The largest difference is on Fixed with a total of 2%The largest difference is on Fixed with a total of 2%

Total Saving (2 - 0.5) 1.5%

A B

Split Saving 0.75% 0.75%

Working 2

Co. A Co. B

Borrow -10 (L + 1.5)

Swap 10 -10

Swap (L + 0.25) L + 0.25

Total (L + 0.25) -11.25

Could have borrowed (L + 1) -12

Saving 0.75% 0.75%


Lecture 30Interest Rate Risk II


Illustration 1

ABC Ltd. wants to borrow $100m for 2 months with the current interest rate being 3%. It is currently January 31st.

They decide to hedge their risk by using interest rate futures which are currently quoted at:

March Price = 94.50

June Price = 94.85

The contract size is $500,000.

By the date of the transaction the futures price has moved to 94.25 and the base rate of interest has risen to 3.25%

Solution

Buy or Sell?

We learnt that borrowing is the same as selling bonds so we therefore sell the futures.

Number of Contracts

Number of Contracts = Loan/Deposit Amount X Term in Months! ! ! ! Contract Size Contract Duration

Number of Contracts = (100,000,000 / 500,000) x 2/3 = 133

Profit or Loss on Future

Bought at 94.25

Sold at 94.50

No. Ticks 25

Tick Value (500,000 x 0.0001 x 3/12) $12.50

Profit Per Contract $312.50

Total Profit (133 x 312.5) $41,562.50


Extra Interest on Loan

100,000,000 x 0.25% x 2/12 = $41,666

Net Effect

Gain on Futures = $41,563

Extra Interest = $41,666

Net Cost = $103


Illustration 2

LTG Co. decides on the 1st January to hedge $30m of borrowings that will start on 30th April and last for 3 months. The rate on the loan will be fixed at the LIBOR rate on that date.

A $500,000 futures contract is available for June at 94.80 with the LIBOR rate being 5.5%.

i. Assuming that the basis reduces in a linear manner and that LIBOR is 4.5% on 30 April calculate the financial result of the hedge.

ii.Calculate the lock-in rate for the transaction and the effect of using that rate.

Solution

Basis Workings

Now

LIBOR rate now 5.5%

Translates to (100 - 5.5) 94.50

Future (6 month) 94.80

Basis (Difference) 0.30

Basis reduces to zero over 6 months so by 4 months time it will be (0.30 / 6 x 2) = 0.10Basis reduces to zero over 6 months so by 4 months time it will be (0.30 / 6 x 2) = 0.10

LIBOR in 4 months 4.5%

Basis remaining at that time 0.10

Implied Interest Rate 4.4%

Futures Price in 4 months (100 - 4.4) 95.60


Buy or Sell?

We learnt that borrowing is the same as selling bonds so we therefore sell the futures.

Number of Contracts




Bought at 95.60

Sold at 94.80

No. Ticks -80

Tick Value (500,000 x 0.0001 x 3/12) $12.50

Profit Per Contract -$1000

Total Loss (60 x $1000) -$60,000

Net Interest on Loan

30,000,000 x 4.5% x 3/12 = $337,500

Loss on Future = $60,000

Net Payment = $397,500

Lock-In Rate

Implied Interest Rate (100 - Current Futures Price) + Unexpired Basis on Transaction Date

= (100 - 94.80) + 0.10% = 5.3%

Total Interest Payment = (5.3% x 30m x 3/12) = $397,500


Illustration 3

ABC Co. is borrowing $20m for 6 months with current market rate of 4%. They need the loan for 6 months beginning in 1 month’s time.

Interest rate options are available in $500,000 contracts for 3 month December interest rate futures. Today is the 30th September.

The following premiums are offered (quoted in %):

Exercise Price Call Put

95.50 1.35 -

95.75 1.06 0.16

96.00 0.56 0.56

96.25 0.17 1.07

Calculate the effect of an options hedge if the interest rate moves to 6% and if the December futures price moves to 95.00 in one month’s time.


Solution

Call or Put Options

We’re borrowing here so that means that we want the option to sell a future i.e. we want a Put Option.

Number of Contracts



Exercise Price

Exercise Price Implied Rate Premium Total Cost

95.75 4.25 0.16 4.41

96.00 4 0.56 4.56

96.25 3.75 1.07 4.82

The cheapest rate to use will be the 95.75 option.

Premium Payable

0.16% x 80 x $500,000 x 3/12 = $16,000



The interest rate has moved to 6% so we will exercise our option on the future.

Bought at 95.00

Sold at 95.75

No. Ticks 75

Tick Value (500,000 x 0.0001 x 3/12) $12.50

Profit Per Contract $937.50

Total Profit (80 x $937.50) $75,000

Net Interest on Loan

20,000,000 x 6% x 6/12 = $600,000

Gain on Option = $75,000

Premium = $16,000

Total Payment = $509,000


P4 ACCA Workbook Questions & Solutions - Mapit Accountancy

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