ELEC15 Engineering Economics and Finance Day 5 Session 4: Financial management Dr. Wilton Fok.

ELEC15 Engineering Economics and Finance

Day 5Session 4: Financial management

Dr. Wilton Fok

Content

• 4.1 Introduction• 4.2 Net Present Value• 4.3 Payback• 4.4 Internal Rate of Return• 4.5. Mortgage Plan Selection

4.1 Introduction

• 4.1.1. What’s Financial management– The art & science of managing a firm’s money so

that it can meet its goals.

• 4.1.2. The Role of Finance – Goal:

• To maximize the value of the firm to its owners

• To balance risk and return

RiskReturn

4.1 Introduction

• Financial Management (also refer to Managerial finance)– It concerns with the managerial significance of finance

techniques

– It helps project or investment decision making

– It analyzes working capital to anticipate future cash flow problems and potential risk

– It compares the returns to other businesses in their industry and evaluates if the company is performing better or worse than its peers from the financial perspective

NPV, IRR, Payback

Risk Analysis

Ratio Analysis

4.2. Net Present Value

Is money a function of time? Profit can be realized only after capital has

been invested (i.e. the former has a time lag). And cash thus generated may come back (be

generated) over several years.

The question is, when you get $1 in some years’ time, does that $1 carry the same value

as it was at Year 0?

Is its present value (PV) at a “Discounted rate”?

4.2. Net Present Value• Discounting is valid because of inflation (or

depreciation in particular cases) Hence when we evaluate success of an investment, we

should take into account of the time and discounted rate.

• Also when we compare two or more projects, we should take the same into our consideration. Purpose is to normalize all sums with the same timing consideration (usually time zero).

20122008Not just to compare “Apple” to

“Apple”, but also compare “Today apple” to “Today apple”

4.2. Net Present Value• NPV and Opportunity Cost

– Opportunity Cost is the amount lost by not using a resource (labour, capital or any factor of production) in its best alternate use.

– Usually there are more than one opportunities for investment. Each carries different risks, yield different returns over a different period of time.

– Yet on the other hand, your investment capital is limited.

– If you invest in project A, you may lose the opportunity of investing in B.

– You may lose all the possible profits yielded by B when you invest in A; or you are paying the opportunity cost of B for A.

– Present Value analysis should also be considered for comparison between opportunity costs.

4.2. Net Present Value

• Net Present value (NPV)– NPV is a standard method for the financial appraisal of

long-term projects.

– NPV is used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met.

4.2. Net Present Value • Formula

– Each cash inflow/outflow is discounted back to its PV. Then they are summed.

– Where• t - the time of the cash flow

• N - the total time of the project

• r - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)

• Ct - the net cash flow (the amount of cash) at time t (for educational purposes, C0 is commonly placed to the left of the sum to emphasize its role as the initial investment.)

4.2. Net Present Value• Example

– X corporation must decide whether to introduce a new product line. – The new product will have startup costs, operational costs, and incoming cash

flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs).

– Other cash outflows for years 1-6 are expected to be $5,000 per year.– Cash inflows are expected to be $30,000 per year for years 1-6. – The required rate of return is 10%. The present value (PV) can be calculated for

each year:

• T=0 -$100,000/ 1.100 = -$100,000 PV. • T=1 ($30,000 - $5,000) / 1.101 = $22,727PV

• T=2 ($30,000 - $5,000) / 1.102 = $20,661PV

• T=3 ($30,000 - $5,000) / 1.103 = $18,783PV

• T=4 ($30,000 - $5,000) / 1.104 = $17,075PV

• T=5 ($30,000 - $5,000) / 1.105 = $15,523PV • T=6 ($30,000 - $5,000) / 1.106 = $14,112PV

4.2. Net Present Value• The sum of all these present values is the net present value, which equals

$8,881.

• Since the NPV > 0, the corporation should invest in the project.

(Refer to the Excel Spreadsheet)

4.2.1 NPV Discount Rate

• The rate used to discount future cash flows to their present values is a key variable of this process.

• Three ways to determine the right Discount Rate?– (A) By the firm's weighted average cost of capital (e.g. bank lending

rate)

– (B) By deciding the rate which the capital needed for the project could return if invested in an alternative venture (or call reinvestment rate)

?


• Example– Capital required for Project A can earn 5% elsewhere, use

this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative.

– Reinvestment rate can be defined as the rate of return for the firm's investments on average.

– When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted average cost of capital as the discount factor.

– It reflects opportunity cost of investment, rather than the possibly lower cost of capital.


• Variable discount rates– In reality, discount rate should not be constant through out years.– If we can predict the variable discount rate, we can calculated

from with a more realistic discount rate for the entire investment duration.

Year Cash inflow Cash outflow Interest rate PV

0 50000 2% 50000

1 10000 3% 9708.738

2 20000 4% 18670.65

3 30000 5% 26672.36

4 40000 6% 33550.13

NPV 88601.88

NPV= Ct (1+r1).(1+r2). .. (1+rt) instead of

Refer to the sample Excel (NPV1)

4.2.2 What does NPV means?

• NPV is an indicator of how much value an investment or project adds to the value of the firm.

• With a particular project– If Ct is a +ve value, the project is in the status of discounted cash

inflow in the time of t.

– If Ct is a -ve value, the project is in the status of discounted cash outflow in the time of t.

• In general– An appropriately risked projects with a +ve NPV could be accepted.


• This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost– i.e. comparison with other available investments.

– Other factors such as cash flow and risk factor should be considered

• But in theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected.


• The following sums up the NPVs in various situations.

• NPV = 0 does not mean that a project is only expected to break even, in the sense of undiscounted profit or loss (earnings). – It will show net total positive cash flow and earnings over its life.– Decision should be based on other criteria, e.g. strategic positioning or other

factors not explicitly included in the calculation

NPV Impact to the firm Decision

>0 The investment would add value to the firm

Project may be accepted

< 0 The investment would subtract value to the firm

Project should be rejected

= 0 The investment would neither gain nor lose value for the firm

Indifferent in the decision whether to accept or reject the project.

This project adds no monetary value.

4.2.3. Solving NPV

• There are 2 ways to find NPV

By look up tables By Excel spreadsheet

4.2.3. Solving NPV

• Solving NPV by look up tables– E.g. PV in year 10 at discount rate 8%

4.2.3. Solving NPV

• Solving NPV by look up tables

4.2.3. Solving NPV

• Solving NPV by Excel

• Excel Function NPV– Calculates the net present value of an investment by using a discount rate and a

series of future payments (negative values) and income (positive values).

• SyntaxNPV(rate,value1,value2, ...)

• Where– Rate is the rate of discount over the length of one period.– Value1, value2, ... are 1 to 29 arguments representing the payments and

income. They must be equally spaced in time and occur at the end of each period.

4.2.3. Solving NPV

• Remarks– The NPV investment begins one period before the date of

the value1 cash flow and ends with the last cash flow in the list.

– The NPV calculation is based on future cash flows.

– If your first cash flow occurs at the beginning of the first period, the first value must be added to the NPV result, not included in the values arguments.

4.2.3. Solving NPV

• Present Value– Returns the present value of an investment. The present value is the total amount that a series of future payments is worth

now. For example, when you borrow money, the loan amount is the present value to the lender.

• Syntax

PV(rate,nper,pmt,fv,type)

• Where– Rate is the interest rate per period.

• E.g., if you obtain an automobile loan at a 10 percent annual interest rate and make monthly payments, your interest rate per month is 10%/12, or 0.83%. You would enter 10%/12, or 0.83%, or 0.0083, into the formula as the rate.

– Nper is the total number of payment periods in an annuity. • E.g., if you get a four-year car loan and make monthly payments, your loan has 4*12 (or 48) periods. You would enter 48 into the

formula for nper.

– Pmt is the payment made each period and cannot change over the life of the annuity. Typically, pmt includes principal and interest but no other fees or taxes.

• E.g., the monthly payments on a $10,000, four-year car loan at 12 percent are $263.33. You would enter -263.33 into the formula as the pmt. If pmt is omitted, you must include the fv argument.

– Fv is the future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0).

• E.g. if you want to save $50,000 to pay for a special project in 18 years, then $50,000 is the future value. You could then make a conservative guess at an interest rate and determine how much you must save each month. If fv is omitted, you must include the pmt argument.

4.2.3. Solving NPV

1 \ A B C

2 Data Description

3 500

Money paid out of an insurance annuity at the end of every month

4 8%Interest rate earned on the

money paid out

5 20Years the money will be paid

out

6 Formula Description (Result)

7 ($59,777.15)

Present value of an annuity with the terms above (-59,777.15).

8"=PV(A3/12, 12*A4, A2, ,

0)"

• Present Value Syntax

PV(rate,nper,pmt,fv,type)

4.2.3. Solving NPV

• Solving NPV by Excel– In the previous example

• T=0 -$100,000/ 1.100 = -$100,000 PV. • T=1 ($30,000 - $5,000) / 1.101 = $22,727 PV. • T=2 ($30,000 - $5,000) / 1.102 = $20,661 PV. • T=3 ($30,000 - $5,000) / 1.103 = $18,783 PV. • T=4 ($30,000 - $5,000) / 1.104 = $17,075 PV. • T=5 ($30,000 - $5,000) / 1.105 = $15,523 PV. • T=6 ($30,000 - $5,000) / 1.106 = $14,112 PV.

Rate 10%

Cash In Cash Out NPV

-100000

1 25000 $22,727.27

2 25000 $43,388.43

3 25000 $62,171.30

4 25000 $79,246.64

5 25000 $94,769.67

6 25000 $108,881.52 Refer to spreadsheet NPV2

4.2.4 Using NPV to explain the stock market

• Why an increase in interest rate could drop a stock price? (Explanation by using Present Value)– The price of a stock an expectation of its future earnings

– In theory, the price of a stock should equal to the Total Present Value of its all future earnings.

Stock price Earnings

– E.g. If it is expected that company ABC could earn $8 (per share) for 10 years (if r = 0%), then it should worth $80

– But when discount rate is taken into account, r increase price decreases

4.2.5 Common Pitfalls in NPV

• There are some common pitfalls in NPV– (1) Negative cash flow seems to be favorable

when discount rate is high?

– (2) Adjusting risk factor by adding a premium to the discount rate?


• (1) Negative cash flow seems to be favorable when discount rate is high?– If some (or all) of the Cashflow have a negative value,

then paradoxical results are possible.

– Example• For project which might have clean-up and restoration

costs (e.g, an industrial or mining project), Cashflow are generally negative during the late period

An increase in the discount rate can make the project appear more favorable.

• This is a problem with NPV.

– Solution• To include explicit provision for financing any losses

after the initial investment, i.e, explicitly calculate the cost of financing such losses.

t

Cash flow

t

Cash flow

4.2.5 Common Pitfalls in NPV• (2) Adjusting risk factor by adding a premium to the discount rate

– Pitfalls• A bank might charge a higher rate of interest for a risky project (e.g. 15%

instead of 10%), that does not mean that this is a valid approach to adjusting the NPV for risk,

(it can be a reasonable approximation in some specific cases)

– Problem:• Such approach may not work well because if some risk is incurred resulting in

some losses, then a discount rate in the NPV will reduce the impact of such losses below their true financial cost.

Year Cash inCash

Out Rate NPV Remarks

0 　 -50000 15% -50000 Initial Investment

1 20000 　 15% 17391.3 Net operating income




　　　 NPV 7099.567 　

10% 15%+

Refer to spreadsheet NPV3


• (2) Adjusting risk factor by adding a premium to the discount rate

– Solution:

• A rigorous approach to risk requires identifying and valuing risks explicitly, e.g. by actuarial and explicitly calculating the cost of financing any losses incurred.

Year Cash inCash

Out Remarks NPV Remarks

0 　 -50000 10% -50000 Initial Investment





4 　 -7000 10% -4781.09 The risk for losing 10k in year 4 is 70%

　　　 NPV 8616.215 　


• More realistic problems would need to consider other factors, generally including:– Calculation of taxes, – Cash flows– Risk factors (amount and possibility of potential

loss) – Availability of alternate investment opportunities.

4.3. Payback period

• 4.3.1 Introduction

– Payback period in business and economics refers to the period of time required for the return on an investment to "repay" the sum of the original investment.

– Example:• A $1000 investment which returned $500 per year would have a two year

payback period.

– It is intuitively the measure that describes how long something takes to "pay for itself“

• shorter payback periods are obviously preferable to longer payback periods (all else being equal).

4.3. Payback period

• 4.3.2. Formula

– For cash flows are the same for the duration of a project

Payback period = Investment

Cash flow Used

4.3. Payback period

• Example– In the previous example, the

payback period is 5 year

• T=0 -$100,000

• T=1 ($30,000 - $5,000)

• T=2 ($30,000 - $5,000)

• T=3 ($30,000 - $5,000)

• T=4 ($30,000 - $5,000)

• T=5 ($30,000 - $5,000)

• T=6 ($30,000 - $5,000)

5 years

6½ years

4.3. Payback period

• Payback is also widely used in other types of investment areas– often with respect to energy efficiency technologies,

maintenance, upgrades, or other changes.

• Example– A fluorescent light bulb may be described of having a payback

period of a certain number of years or operating hours– Here, payback means “the return to the investment” consists

of reduced operating costs.

• The concept of a payback period is occasionally extended to other uses, such as (the period of time over which the energy savings of a project equal the amount of energy expended since project inception)

Initial: $30Operation: $0.05 per hr

Initial: $5Operation: $0.2 per hr

4.3. Payback period

• 4.3.3 Pos and cons of Payback Period– Pos

• Payback period as a tool of analysis is often used because it is easy to apply and easy to understand for most individuals

• When used carefully or to compare similar investments, it can be quite useful. • It can be used to compare which investment is better, but may just mean less

loss!

– Cons• It does not properly account for the time value of money, inflation, risk, financing

or other important considerations. • An implicit assumption in the use of payback period is that returns to the

investment continue after the payback period. Payback period does not specify any required comparison to other investments or even to not making an investment.

• Alternative measures of "return" preferred by economists are internal rate of return and net present value.

4.3. Payback period

• 4.3.4. Limitations of Payback period– Payback Period analysis has been widely adopted in some

corporations without considering some of the limitations or scope of applicability of the concept.

– Major Limitations

• Timing of Cash Flows

• Risks and Time Value of Money

4.3. Payback period

• Limitation #1: Timing of Cash Flows– It ignores any benefits that occur after the

breakeven point.– This simplification can cause problems when

projects have identical payback periods but one has greater cash flows following the breakeven point.

the tool may not accurately estimate the value of the project whose benefits occur after the initial investment costs are repaid.

– The Payback period calculation favors projects with early positive cash flows.

– This is problematic for those long-term projects.

Net Cash flow

Time

Same paybackperiod

But more net cash flow in the future

4.3. Payback period

• Limitation #1: Timing of Cash Flows– Example:

• A pharmaceutical company is considering developing a new drug.

• The pharmaceutical company should not use the Payback Period methodology to analyze the viability of investing in this project as drugs usually take 3 to 5 years to develop while having substantial benefits at later stages of market introduction.

• The pharmaceutical company would be better off using a financial evaluation tool that incorporates the benefits and costs of the project during its entire lifespan.

– For these reasons, the payback period methodology is more appropriate to situations when projects have similar time span characteristics.

4.3. Payback period

• Limitation #2: Risks and Time Value of Money

– The methodology does NOT take into account risks and the time value of money. The methodology foregoes any discounting and the opportunity cost of capital.

– These omissions in the payback period methodology will overvalue the investments on an absolute basis.

5 years

6½ years

Payback Period calculation can still be useful for comparing projects that are assumed to have equal risk

4.4. Internal Rate of Return (IRR)• 4.4.1 What is Internal Rate of Return (IRR)?

– Mathematically, each long term investment project shall yield an annual rate of return. This is called the internal rate of return (IRR).

– The IRR or yield for an investment is the discount rate that equates the present value of the expected cash outflows with the expected inflows.

• IRR is– a capital budgeting metric used by firms to decide whether they

should make investments. – an indicator of the efficiency of an investment

• (opposed to net present value (NPV), which indicates value or magnitude)– the annualized effective compounded return rate which can be

earned on the invested capital• i.e., the yield on the investment.

4.4. Internal Rate of Return (IRR)

• An investment is good if its IRR is greater than the rate of return that could be earned by alternative investments– E.g. investing in other projects, buying bonds, even putting the money

in a bank account

IRR should be compared to an alternative cost of capital including an appropriate risk premium.

• Mathematically the IRR is defined as any discount rate that results in a NPV=0 of a series of cash flows.

• In general, if the IRR is greater than the project's cost of capital, the project will add value for the company.


• 4.4.2 Formula– To find the internal rate of return, find the values of

r that satisfies the following equation:

• Example– Internal Rate of Return (IRR)

YearCash

Flow

0 -100

1 30

2 35

3 40

4 45


• Example – Thus using r = IRR = 17.09%,

Graph of NPV as a function of i for the example


• Example– Initial investment $16,200

– Estimated life 10 years

– Annual cash inflows $ 3000

– Cost of capital (minimum required of return) 10%

– What is the IRR?

– Because the investment's IRR (around 13.12%) is greater than the cost of capital (10%), the investment should be accepted.

Refer to the excel spreadsheetIRR1


• Example– Aa company is considering an investment project that promises cash

inflows of $400,000, $600,000, and $1,000,000 for each of the next 3 years for a given investment of $1,490,000.

– The IRR is found by selecting a rate and discounting the cash inflows.– If the PV is greater than I, select a higher rate until one is found that

equates the PV of the cash inflows with I. – In this example, the IRR is approximately 14%, determined as follows:

Present Value

Annual Cash Flow 12% 14%

400000 357200 350800

600000 478200 461400

1000000 712000 675000

Total 1547400 1487200



• Example:– There are 3 investment opportunities: A, B and C with the following

cash flow. Which one is better?

Year 0 1 2 3 4 5

A -20000 +10,000 +10,000 +10,000 +10,000 +10,000

B -20000 +15,000 +15,000 +15,000 - -

C 8% Risk Free Investment


• 4.4.3 Solving IRR by Excel

• Syntax– IRR(values,guess)

• Values– is an array or a reference to cells that contain numbers for which you want to

calculate the internal rate of return.

– Values must contain at least one positive value and one negative value to calculate the internal rate of return.

– IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.

– If an array or reference argument contains text, logical values, or empty cells, those values are ignored.

Don’t need to

memorize, you can

find it in Excel Help

IRR(values, guess)



– Guess• is a number that you guess is close to the result of IRR.

• Microsoft Excel uses an iterative technique for calculating IRR.

• Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent.

• If IRR can't find a result that works after 20 tries, the #NUM! error value is returned.

• In most cases you do not need to provide guess for the IRR calculation. If guess is omitted, it is assumed to be 0.1 (10 percent).

• If IRR gives the #NUM! error value, or if the result is not close to what you expected, try again with a different value for guess.

IRR(values, guess)



– Remarks• IRR is closely related to NPV, the net present value function. • The rate of return calculated by IRR is the interest rate

corresponding to a 0 (zero) net present value.

• The following formula demonstrates how NPV and IRR are related:

– NPV(IRR(B1:B6),B1:B6) equals 3.60E-08 (Within the accuracy of the IRR calculation, the value 3.60E-08 is

effectively 0 (zero).)

= NPV(IRR(B1:B6),B1:B6)


• 4.4.3 Solving IRR by Excel– Example Year Data Description

-70,000 Initial cost of a business

1 12,000 Net income for the first year

2 15,000 Net income for the second year

3 18,000 Net income for the third year

4 21,000 Net income for the fourth year

5 26,000 Net income for the fifth year

Formula Description (Result)

-2%Investment's internal rate of return after four years (-2%)

9%Internal rate of return after five years (9%)

-44%

To calculate the internal rate of return after two years, you need to include a guess (-44%)



• 4.4.4 Pos and Cons of IRR– Pos

• It considers the Time Value of Money and is therefore more exact and realistic than Accounting Rate of Return.

– Cons• (1) it fails to recognize the varying size of investment in

competing projects and their respective dollar profitability

• (2) in limited cases, where there are multiple reversals in the cash-flow streams, the project could yield more than one internal rate of return.


• 4.4.5 Problems with using IRR– (1) IRR is not effective for considering two

mutually exclusive projects– (2) IRR does not consider cash flow and

reinvestment– (3) IRR may have multiple solutions

4.4. Internal Rate of Return (IRR)• (1) Not effective for considering two mutually exclusive

projects– As an investment decision tool, the calculated IRR should

NOT be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in.

– E.g. when a project has a higher initial investment than a second mutually exclusive project,

• Project A may have a lower IRR (expected return), but a higher NPV (increase in shareholders' wealth)

• It should thus be accepted Project A over Project B

• In this case, Project A is very sensitive to the discount rate


• (2) Does not consider cash flow and reinvestment

– IRR makes no assumptions about the reinvestment of the positive cash flow from a project.

As a result, IRR should not be used to compare projects of different duration and with a different overall pattern of cash flows.

Year Project A Project B Project C

0 -10000 -15000 -20000

1 2000 2000 2000

2 3000 2500 -10000

3 2000 3000 80000

4 2500 3000 -20000

More Suitable using IRR

– The IRR method should not be used in the usual manner for projects that start with an initial positive cash inflow (or in some projects with large negative cash flows at the end)

Less Suitable using IRR


• (3) May have multiple solutions– If there are multiple sign changes in the series

of cash flows, e.g. (- + - + -), there may be multiple IRRs for a single project, so that the IRR decision rule may be impossible to implement.

– Example• Strip mines and nuclear power plants project

have such characteristic (because of the clean-up and restoration costs), where there is usually a large cash outflow at the end of the project.

– Importantly, the IRR equation cannot be solved analytically (i.e. in its general form) but only via iterations.

t

Cash flow

4.4. Internal Rate of Return (IRR)• 4.4.6 Comparing IRR and NPV

– Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV.

– Apparently, managers find it easier to compare investments of different sizes in terms of percentage rates of return than by dollars of NPV.

– However, NPV is more accurate to reflect the value of a project or investment

– IRR, as a measure of investment efficiency may give better insights in capital constrained situations.

– However, when comparing mutually exclusive projects, NPV is the appropriate measure.

NPV IRR

Academic Business Absolute Value

% of return Efficiency Compare exclusive projects


• 4.4.6 What if there is conflict between NPV and IRR?– If the NPV of Project A is higher than Project B but Project

B has a higher IRR then which one, IRR or NPV, should we rely on?

NPVIRR


• 4.4.6 What if there is conflict between NPV and IRR?– At different discount rate therefore NPVs of the same project will be

different.

R

– If we plot a graph with the NPV on the Y-axis and the discount rate on the X-axis. We get a downward sloping NPV curve for each project.

– If the two curves they will not intersect each other. There is no problem in this case.

– The conflict arises if the NPV curves of two projects intersect at discount rate, R.

4.4. Internal Rate of Return (IRR)• At all discount rates <R, the NPVs of

Project A, is higher than the NPVs of another project B. (Region 1)

• At all discount rates >R, NPVs of project B is higher than the NPVs of project A. (Region 2)

• At the point R, NPVs of both the projects are equal (Called the switching point).

• Before this point, project A is to be preferred because it has higher NPV

• After this point project B will be preferred because project B's NPV is now higher.

R A B


• According to different interaction points (R, A and B), we can made the investment decision as follow:

– Case 1: A> B> R• then you chose project A

irrespective of project NPV positions

– Case 2: B> A> R• Then you choose project B

irrespective of project NPV positions

– Case 3: R>A , R.> B• Then you should choose the

projects based on NPV values.

R A B

4.5 Mortgage Plan Selection

• The concept of NPV and time value of money can be applied to making decision on mortgage plan selection.

4.5 Mortgage Plan Selection

• You have just purchased a HK$2 million apartment and you decide to apply for mortgage

• HSBC and Hang Seng Bank offer 2 different Mortgage plan for you to select.– HSBC

• Cash rebate: 1% of the loan amount• Interest rate: P-2.6%• Repayment period: monthly

– Hang Seng Bank• Cash rebate: 1.5% of the loan amount • Interest rate: P-2.5%• Repayment period: Bi-weekly

• You can afford 30% down payment. Your preferred mortgage period is 15 years. The current prime rate is 5%. Which offer is better?

Exercise• Example

– Dr. Wong is considering to purchase an ultrasound analyzer for his clinic. The machine can yield cash return in every of the next 4 years.

– If he buys the machine, HK$200,000 to be paid in Year 0 and Year 1. There will also be operating expenses between Year 2 and Year 4.

– Dr. Wong plans to sell the machine at the end of the 4th year.

– The current interest rate is 8%.

Exercise

• Including the sale of equipment at the end of the Year 4, they estimate the cash flows of the project as follows:

• Determine the investment return using various analysis methods such as NPV, IRR and Payback…etc.

• Is it worthwhile to invest on this machine?

End of Year

Cash Outflow ($) Cash Inflow ($)

0 80000 0

1 120000 90000

2 10000 130000

3 20000 120000

4 10000 110000

Q&A

ELEC15 Engineering Economics and Finance Day 5 Session 4: Financial management Dr. Wilton Fok.

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