Solutions Corporate Finance[1]

8/4/2019 Solutions Corporate Finance[1]

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Autumn 2007

Q.No.1 a) The discount rate is the rate at which the company will be able to invest its cash flows. Is thatright? Why or Why not? Please discuss with the help of practical examples.

b) Consider the following projects

Project C0 C1 C2 C3 C4 C5A -1,000 0 0 0 0 0B -2,000 +1,000 +1,000 +4,000 +1,000 +1,000

C -3,000 +1,000 +1,000 0 +1,000 +1,000

i) If the opportunity cost of capital is 10 percent, which projects have a positive NPV?

ii) Calculate the payback period for each project.

iii) Which project(s) would a firm using the payback rule accept if the cutoff period 3 yearswere?

Q.No.2 Consider the following three stocks:

Stock A is expected to provide a dividend of Rs. 10 a share forever.

Stock B is expected to pay a dividend of Rs. 5 next year. Thereafter, dividend growth isexpected to be 4 percent a year forever.

Stock C is expected to pay dividend of Rs. 5 next year. Thereafter, dividend growth isexpected to be 20 percent a year for 5 yeas (i.e. until year 6 and zero thereafter).

If the market capitalization rate for each stock is 10 percent, which stock is the most valuable?What if the capitalization rate is 7 percent?

Q.No.3 Issuing shares is a source of financing for the company. In some countries IPO of commonstock are so9ld by auction. Another procedure is for the underwriter to advertise the issuepublicly and invite applications for shares at the issue price. If the applications exceed thenumber of shares offer, then they are scaled down in proportion. If there are too fewapplications, any unsold shares left with the underwriters. Compare there procedures inPakistan. Can you think of any better way to sell new shares?

Q.No.4 Suppose a manager has already estimated a projects cash flows, calculated its NPV, and donea sensitivity analysis. Explain the additional steps required to carry out a Monte Carlo simulationof project cash flows.

Q.No.5 Suppose it is your task to evaluate two different investments in new subsidiaries for yourcompany, one in your own country and the other in a foreign country. You calculate the cashflows of both projects to be identical after exchange-rate differences. Under what circumstancesmight you choose to invest in the foreign subsidiary? Give an example of a country wherecertain factors might influence you to alter this decision and invest at home?

Q.No.6 Galaxy Company has an agreement with the National Bank by which the bank handles Rs. 4million in collection each day and requires a Rs. 500,000 compensating balance. Galaxy

Company is contemplating canceling the agreement and dividing its Northern region so that twoother banks will handle its business. Banks 1 and 2 will each handle Rs. 2 million of collectionseach other, requiring a compensating balance of Rs. 300,000. Galaxy Companys financialmanagement expects that collection will be accelerated by one day if the Northern region isdivided. The T-bill rate is 7 percent. Should the Galaxy Company implement the new system?What will the annual net savings?

Q.No.7 Compare and contrast three alternative valuation methods with the help of practical examples ofany manufacturing organization.

Q.No.8 What do you understand by warrants and convertibles as used in corporate finance and what isthe underlying logic to explain why firms issue them?

Solution to Paper-Autumn 2007

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Q.No.1 a) Most often the discount rate is the rate at which the company will be able to reinvest itscash flows whenever a project proposal is examined and analyzed, it is definitely assumedthat periodic cash flows would be invested at opportunity cost of capital which is also used todiscount future cash inflows and outflows to determine the NPV of a project.

b)Practice Question No. 1 of Chapter 5:

I. Project NPV

A - $ 90.91B +$4,044.73

C +$ 39.47

ii. Project Payback period

A 1 year

B 2 years

C 4 years

iii.A & B

Q.No.2 (Practice Question No. 7 of Chapter 4)

(A) - $100

(B) = $83.33

Year Dividend PV @ 10%

1 $5.00 $4.55

2 6.00 4.96

3 7.20 5.41

4 8.64 5.90

5 10.37 6.44

6 12.44 7.02

Total: 34.28

P6 = = $124.40

PV $124.40/(1.10)6 = $70.22

Current Market Price or Po $ 34.28 + $ 70.22 = $104.50

Q. 3When companies finance their long term needs externally, they may use three primary methods.

A public issue of securities placed through investment bankers.

A privileged subscription to the companys own shareholders.

A private placement to institutional investors.

When a company issues securities to general, public, it usually uses the services of investmentbankers. The investment bankers principal functions are risk bearing or underwriting, and selling thesecurities. For performing these functions investment bankers are compensated by the spread between theprice they pay for the securities and the price at which they re sell the securities to investors. For detaileddiscussion please refer to chapter 19 of Financial Management.

Q. 4

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Sensitivity analysis allows you to consider the effect of changing one variable at a time. By lookingat the project under alternative scenarios, we can consider the effect of a limited number of plausiblecombinations of variables.Monte Carlo stimulation is a tool for considering all possible combinations. It therefore enables us toinspect the entire distribution of project outcomes.

Following steps are required to be carried out under Monte Carlo stimulation.Steps 1 Modeling the project

2 Specifying probabilities3 Simulate the cash flows4 Calculate present valueFor detailed discussion pleas refer to chapter 10 of Corporate Finance.

Q. 5Although cash flows of both projects are identical, I would choose to make investment in foreign subsidiaryunder the following circumstances.

1. Political and socio economic situation is stable.

2. The currency of the country is quoted at a premium.3. There are no sanctions from UNO and other international agencies.4. Business activities are not facing recession period.

For example if we are asked make investment in a subsidiary in Afghanistan or Iraq, we wouldhesitate definitely for the known reasons.

For comprehensive answer please refer to chapters 24 of Financial Management titled as InternationalFinancial Management.

Q. 6

Similar to Q 2 of Chapter 9 of Financial Management:

Particulars National Bank Bank 1 Bank 2

Daily Collection Rs. 4,000,000 Rs. 2,000,000 Rs. 2,000,000

CompensatingBalance

Rs. 500,000 Rs. 300,000 Rs. 300,000

Funds Available Rs. 3,500,000 Rs. 1,700,000 Rs. 1,700,000

Annual Earnings @7%

Rs. 245,000 Rs. 119,000 Rs. 119,000

Rs. 238,000

One Day

Expected Reduction in Float Time: One DayEarnings because of reduction in Float Time: Rs.4, 000,000 x 1 x 7/100 Rs. 280,000/-

The company should implement new system.

Q. 7

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Financial distress occurs when promises to creditors are broken or honored with difficulty. Sometimesfinancial distress leads to bankruptcy. Sometimes it only means skating on thin ice.The value of company is equal to its value if all equity financed plus present value of tax shield minuspresent value of cost of financial distress. According to the trade-off theory of capital structure, themanagement should choose the debt ratio that maximizes the value of the company.The optimum is reached when the present value of tax savings due to further borrowing is just offset byincrease in the present value of cost of financial distress. This is called the trade-off theory of capitalstructure.

This trade-off theory of capital structure recognizes that target ratios may vary from company to company.The companies with safe, tangible assets and plenty of taxable income to shield ought to have high targetratios. Unprofitable companies with risky, intangible assets ought to rely primarily on equity financing.The packing orders theory starts with asymmetric information--a term indicating that managers know moreabout their companies prospects, risks and values than do outside investors. Managers obviously knowmore than investors.

Asymmetric information affects the choice between internal and external financing, and between thenew issues of debt and equity securities. This leads to a packing order in which investment is financed firstwith internal funds, re-invested earnings primarily, then by new issue of debt and finally with new issues ofequity. New equity issues are a last resort when the company runs out of debts capacity.

Q. 8:In addition to straight debt and equity instruments, a company may finance with an option, a contract givingits holders the right to buy common stock or to exchange something for it within specified period of time. Asa result, the value of the option instrument is strongly influenced by changes in the value of stock.

A convertible security is a bond or preferred stock that can be converted at the option of the holder intocommon stock of the same company. The convertibles give the investor a fixed return from a bond orpreferred stock. In addition, the investor receives an option on the common stock. Because of this option,the company can sell the convertible security at a lower yield that it would have to pay on a straight bond orpreferred stock issue.A warrant is an option to purchase common stock at a specified exercise price (usually higher than the

market price at the time of warrant issuance) for a specified period.

Warrants often are employed as sweeteners to a public issue of debt that is privately placed. As a result,the company should be able to obtain a lower interest rate than it would otherwise.

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Autumn 2005Q.No.1 James Consol Company present pays a dividend Rs. 2 per share on its common stock. The

Company expects to increase the dividend at a 20% annual rate the first four years and at a15% rate the next four years and then grow the dividend at 8% rate theater. This phasedgrowth-pattern is in keeping with the expected life cycle of earnings. You require a 15%return to invest in this stock. What value should you place on a share of this stock?

Q. No.2

Q. 3

a) Which financial ratios would you be most likely to consult if you were the following? Why?A banker considering the financing of seasonal inventory

A wealthy equity investorThe manager of a pension found considering the purchase of a firms bondsThe president of a consumer products firm

b. Why is the analysis of trends in financial ratios important?---------------------------------------------------------------------------------------------------------------------------ABC Company is planning to change its credit terms. The firms current credit terms are net60 days, and the firms current daily sales average Rs. 100,000/-. The firm is experiencing acash flow problem and wants to change the terms to net 30 days. In order to offset customerill will, ABCs credit manager is proposing a 2% discount for payments received within 10days of the invoice. Management feels that the firm will be able to maintain the same monthlysales and that about 80% of its customers will take the discount. Will the firm be better off

with the new terms assuming its discounts rate is 12%?Q. No.4 You are offered a new computer for Rs. 22,500/- and the sale person promises it will cut

processing and wage costs by Rs. 6000/- before taxes for each of the next five years. If yourfirms cost of capital is 15% and the tax rate if 40% should you purchase the computer? Baseyour decision on the NPV and use straight line depreciation.

Q. No.5

Forecasted sales of PLEASANT Products for the next six months are given below:March Rs. 40,000 June Rs. 35,000April 50,000 July 30,000May 40,000 August 30,000

In the past, 20 percent of sales have been for cash and the rest have been on credit.PLEASANT expects to collect 10 percent of these credit sales during the month of sales, 70percent in the following month, and 18 percent in the second month following the sales (2percent are uncollectible). Make a cash receipts schedule for PLEASANT for this six-monthperiod.

Q.No.6 You have just bought a house, and the mortgage company offers you $65,000 loan withpayments of $9,282.18 per year for 30 years. What interest rate are you paying, and what isthe total amount of interest you will pay?

Q. 7 Zaman & Co. is a soft-drink manufacture. Zamans capital structure is 100 percent equity,and management intends to keep the capital structure all equity. Zamans current annualdividend to its common shareholders is Rs. 3.50 per share, and the current price is Rs. 40per share. Ten yeas ago the firms dividend was Rs. 2.36 per share. Assuming floating costsare zero, answer the following questions.

Estimate the cost of capitalCalculate the firms cost of capital assuming a floatation cost of 6%Q. 8 XYZ Inc. is contemplating investment in a new project; XYZ is an all equity company. It has a

beta of 1.5. The required return on a market portfolio is 12 percent, and the current risk-freerate is 9 percent.

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Solution to Paper-Autumn 2005Q# 1

year Dividend PV @ 15%

1 2.40 2.09

2 2.88 2.18

3 3.46 2.27

4 4.15 2.37

5 4.77 2.376 5.49 2.37

7 6.31 2.37

8 7.25 2.37

Total Rs.18.39

Thereafter constant growth @ 8%P8 = 7.83 ___ =Rs. 111.86

0.15--0.08PV of 111.86 @ 15% = Rs.36.57

Current Value= Rs.36.57+Rs.18.39 = Rs.54.96 or Rs. 55

Q# 2Please refer to Ch6 of Financial Management for purpose and use of various ratios.

Q# 3Annual Sales Rs.36,000,000 Rs.36,000,000Collection Period 60 Days 30 DaysAverage Recoverable Rs.6,000,000 Rs.3,000,000Earnings on reduction in receivable @ 12% Rs. 360,000Amount of discount Rs. 576,000

The firm will not be better off with new terms as amount of discount is greater than expectedincrease in annual earnings.

Q# 4Cash Flow from Y-1 to Y-5Gross Earnings Rs.6000Depreciation (4500)Savings before tax Rs1500Tax @ 40 % (600)Saving after tax Rs.900Add Back Depreciation Rs.4500Net Cash Flows Rs.5400

NPV @ 15% using PVA formula = Rs.18, 102 - Rs.22, 500 = (Rs.4398)Purchase of Computer is not recommended because of negative NPV.

Q# 5March April May June July Aug

Sales 40,000 50,000 40,000 35,000 30,000 30,000020 % 8000 10,000 8000 7000 6000 600010% 3200 4000 3200 2800 2400 240070% 22400 28000 22400 19600 1680018% 5760 7200 5760 5040

11200 36400 44960 39400 33760 30240

Q# 6

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Principle = $65,000n =30 Yearsi =?Installment = $9,282.18

Rate of interest can be found through interpolation. Using the formula of PVA, first use the rate of13%, and then use the rate of 15%. Then through interpolation you can find i =14%.

Total amount of interest =(Number of Installments) X (Amount of installment) -- (Principle Amount)

= 30 X 9,282.18 -- 65,000 = $ 213,465.40Q# 7

Dividend per share10 Years Ago = Rs.2.36Currently = Rs.3.50

So we can find growth rate (g) as Follows:-

Rs.3.501/10

-- 1 = 0.04 or 4%Rs.2.36

(a)

Cost of capital = Ke = D1 + g

Po

= 3.64 + 0.04 = 0.131 or 13.1%

40

(b) 3.64 __ + 0.04 = 0.1368 or 13.68%

40(1 -- 0.06)

QUESTION # 8

If Beta is 1.5 then

Ke = Rf + (Rm Rf) Beta

= 9 + (12 - 9) 1.5

= 13.5 %

If Beta is 1.6 then

Ke = 9 + (12 9) 1.6

= 13.8 %

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Spring 2004Q. 1 As a recently hired financial manager you are asked to e valuate the benefits of the leasing

rather than purchasing a new computer. You need the asset for three years, and the tax rateis 40 percent. Relevant data are provided in a, b and c below.

a. The computer costs $150,000 and could be depreciated over a few years period using the200 percent declining balance method for depreciation. The financial manager anticipates

that the computer will have a market value of $10,000/- at the end of three years. Themanufacturer offers a maintenance contract for $3,000/- per year.b. If you decide to purchase the computer your bank will loan you $125,000/- of the $150,000/-

purchase price. The interest rate on the loan is 10 percent. The loan is traditional term loanwith equal annual payments starting in one year, and the loan will be for three years.

c. A leasing agent offers the same computer with three annual lease payments of $55,000/-per years with the first lease payment being paid immediately. A maintenance provision isincluded in the lease contract. Finally you have the option to purchase the computer at theend of three years for $10,000/-. However this time you do not anticipate taking thepurchase option intending instead to upgrade the hardware in three years.

Q. 2 Stylo, Inc, pays a $2 cash dividend per share to its common shareholders. Stylos stock

currently sells for $20 per share and is expected to sell for $25 per year. Earning per shareis currently equal to $4 per share. Calculate the dividend payout ratio the current dividendyield and the expected return anticipated over the coming year if the stock was purchased atthe current price of $20.

Q. 3 a) discuss the different between the declaration date, the record rate, the payment date andthe ex-dividend date.b) What are the five characteristics looked at by the financial manager in making a creditdecision on a customer?

Q. 4 Distinguish between reorganization and liquidation. What circumstances dictate whetherreorganization is preferred over liquidation?

Q. 5 The financial manager of sea burg, Inc, is currently analyzing two different financingalternatives. Sea burg currently has an EBIT level of $ 1,000,000 and is all equity financedwith 500,000 shares of common stock outstanding. The firms tax rate is 30 percent. Tofinance the proposed capital budget sea burg must acquire $2 million of new external funds.Sea burgs financial manager is analyzing two plans: Plane 1 calls for issuing 100,000shares of new stock at $20 per share and plan 2 calls for issuing $2 million of debt at a 7percent coupon rate (assume issue cost are negligible and thus ignored). Construct anEBIT-EPS chart for sea burg. Calculate the EBIT break-even level and the EBIT indifferencelevel. Assuming the EBIT is expected to be $1.5 million next year and to remain at that levelfor the foreseeable future what is your recommendation? To construct a chart use thefollowing EBIT level: $ 1,000,000/- $1,500,000 and $ 2,000,000.

Q. 6 a) Choctaw Oilfield Services made a $225,000 operating profit last year and paid $160,000in interest expenses. How much financial leverage doses Choctaw have? If operating profitsdrop 50 percent this year, what effect does it financial leverage has on Choctaws newprofits?b) What are the weaknesses of break-even analysis?

Q. 7 GC investment has $100,000 in a money market fund that it wants to invest. GC has twoalternatives with different after-tax cash flows, each costing $100,000.

Year A B

1 $0 $35,0002 0 35,0003 75,000 35,000

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4 100,000 35,000

The cost of capital is 10 percent. Calculate the following and state for each criterion whether or notyou should invest.a) NPVb) IRR

Solution to Paper-Spring 2004

Q. 1 Please refer to chapter 26 page 707 (8th Edition) for same type of problem.

YO Y1 Y2 Y3Cost of new Computer 150,000Lost Depreciation tax shield - (40,000) (13,333) (2667)Lease payments (55,000) (55,000) (55,000) -Tax Shield on Lease Payment 22,000 22,000 22,000 -Maintenance Cost - 3,000 3,000 3,000Residual Value (10,000)Net Cash Flow 117,000 (70,000) (43,333) (9,667)

Shield of Depreciation:Double (200%) Declining method

Year Particulars YearlyDepreciation

Book Value

1 150,000 x 2/3 100,000 50,0002 50,000 x 2/3 33,333 16,6673 16,667 10,000 6,667 10,,000

NPV lease: 117,000 7,000 43,333 9,667 @ 6% = $4,279As NPV Lease is positive, the company should acquire the asset on lease.

Q. 2

Divided Payout Ratio =Dividend Per shareEarnings per share

= 0.50 = or 50%

Dividend yield:Dividend Per shareEarnings per share

= X 100 = 10%

Expected Return anticipated over the coming year.

= 0.35 or 35%

Q. 3(a) Declaration date:

The date on which the board of directors announces the amount of dividend or its percentage of face value

Record Date:The date set by the board of directors when a dividend is declared, on which an investor must be ashareholder as per companys record to be entitled to the upcoming dividend.

Payment Date:The date when the company actually pays the declared dividend

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(b) Five characteristics looked at by the financial manager in making a credit decision on a customer.1. Good Character:Character: customers desire or willingness to honor obligations2. Sufficient capacity:Customers ability to generate cash to meet obligations3. Sound financial position:Customers net worth and relationship of net worth to debt4. Clean track record:

Customers status and record of previous payments5. Fair market reputationWhat others say about your customer?

Q.4Distinction between Reorganization and Liquidation:Reorganization means recasting of the capital structure of a financially troubled company in order toreduce fixed financial charges. Claim holders may be given substitute securities. Whereas Liquidation isthe sale of assets of a company either voluntarily or in bankruptcy.

For detailed discussion please refer to chapter 23 of Fundamentals of Financial Management.

Q. 5

Commonstock

Debt Commonstock

Debt

EBIT $1,000,000 1,000,000 1,500,000 1,500,000Interest - 140,000 - 140,000EBT 1,000,000 860,000 1,500,000 1,360,000Tax 30% 300,000 258,000 450,000 408,000EAT 700,000 602,000 1,050,000 952,000No. of shares 600,000 500,000 600,000 500,000EPS $1.167 $1.204 $1.750 $1.904

At all the three levels of EBIT, we recommend that the company should acquire $2 million by issuing

debt at a 7 percent coupon rate because of highest EPS.

Common Debt2,000,000 2,000,000- 140,0002,000,000 1,860,000

600,0001,400,000

558,0001,302,000

600,000 500,000$2.333 2.604

Indifference point in EBIT is that amount of EBIT which generate same EPS for two or more

financing plans. Formula to calculate indifference point(EBIT i) (I T) PD____

Number of Common shares

=

350 EBIT = 420 EBIT 58,80058,800 = 420 EBIT 350 EBIT58,800 = 70 EBIT840 = EBIT

So indifference point in EBIT is $840,000.

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Q. 6(a) Degree of Financial Leverage

Or DFL = EBIT or Operating Profit $225,000 _________ = 3.46 Times

Operating Profit Interest Expenses $225,000--$160,000

Effect on Change in Net Profit = Change in Operating Profit X DFL50% x 3.46 = 173%

(b)Weakness of break even analysis:Please refer to chapter 16 of Financial Management.

Q. 7

Project A Project BNPV @10% $24,650 $ 10,945Internal Rate of ReturnIRR

17.06% 14.96 %

IRR may be calculated through interpolation.The company should make investment in project A because of higher NPV.

Autumn 2006

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Q. 1 Galaxy has an agreement with the National Bank by which the bank handles Rs. 4 million incollections each day and requires a Rs. 500,000 compensating balance. Galaxy Company iscontemplating canceling the agreement and dividing is Northern region so that two otherbanks will handle its business. Banks 1 and 2 will each handle Rs. 2 million collection eachday requiring a compensating balance of Rs. 300,000 Galaxy Companys financialmanagement expects that collections will be accelerated by one day if the Northern region isdivided. The T-bill rate is 7 percent. Should the Galaxy Company implement the newsystem? What will the annual net saving?

Q. 2 a) The discount rate is the rate which the company will be able to reinvest its cash flows. Isthat right? Why or why not? Please discuss with the help of practical examples.b) Consider the following projects:

Project C0 C1 C2 C3 C4 C5A -1,000 0 0 0 0 0B -2,000 +1,000 +1,000 +4,000 +1,000 +1,000C -3,000 +1,000 +1,000 0 +1,000 +1,000

i. If the opportunity cost of capital is 10 percent, which projects have a positiveNPV?

ii. Calculate the pay back period for each project.

iii. Which project (s) would a firm using the pay back rule accept if the cutoff period 3years were?Q. 3 Issuing shares a source of financing for the company. In some countries IPO of common

stock are sold by auction. Another procedure is for the underwriter to advertise the issuepublicly and invite application for shares at the issue price. If the applications exceed thenumber of shares offer, then they are scaled down in proportion. If there to few applications,any unsold shares left with the underwriters. Compare there procedures in Pakistan. Can youthink of any better way to sell new shares?

Q. 4 Bond prices can fall either because of a change in the general level of interest rates orbecause of an increased risk of default. To what extent do floating rate bonds and putt ablebonds protect the investor against each of these risks?Explain your answer with the help of practical examples.

Q.5 Compare and contrast three alternative valuation methods with the help of practicalexamples of any manufacturing organization.

Q.6 Suppose that there is no relationship between beta and expected returns. Does that meanthat beta is an uninteresting statistic? What would you do as an investor? What strategiesshould a company adopt? Give explanation with the help of practical examples fromPakistan?

Q.7 Suppose the trade-off theory of capital structure is true. Can you prodict how companys debtratios should change over time? How do these predictions differ from the packing ordertheories?

Q.4 Retractable (or puttable bonds)Retractable (or puttable bonds) give investors the right to demand early repayment; extendable bonds givethem the option to extend the bonds life.

Putt able bonds exist largely. Because bonds indentures cannot anticipate every action the company maytake that could harm the bondholders. If the value of the bonds is reduced the put option allows thebondholders to demand repayment.

Potables bonds can sometimes get their issuers into big trouble. During 1990, many bonds issued by Asiancompanies gave their lenders a repayment option. Consequently, when Asian crises struck in 1997, thesecompanies were faced by a flood of lenders demanding their money back.So it would be beneficial for bondholders to have puttable bonds or bonds with floating rates with some

ceiling to protect them against increased risk of default and increasing interest rates. But as these featuresin bonds are not favorable to the issuing companies which in turn prefer to issue bonds with call option.

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For remaining questions, please refer to solution of Autumn 2007 as most of the questions havebeen repeated.


Q. 1First of all, present value of outflows (Costs) @ 6%

Project A= Rs. 66,730

Project B= Rs. 77,721

Now you have to give either of the machines on lease (rent), so calculate annual lease payments

for economic life of machine. Be careful that lease payments are calculated through formula of

annuity due (to be paid in advance).

Lease Rent Machine A Machine B

3 payments Rs. 23,551


So Machine A is preferred.

Q.2 Quiz 1 of chapter 7 (Corporate Finance)

Probability Payoff (Probability) (Payoff)

0.10 $500 (0.10) ($500) = $50

0.50 100 (0.50) ($100) = 50

0.40 0 (0.40) ($0) = 0

Expected Payoff =$100

Expected Rate of Return: As you are investing Rs. 100 and expected payoff is Rs.100, your

return would be zero; so expected rate of return is zero.

Please note that Variance and standard deviation is not required in the paper question.

Q.3

Decision tree:

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In operations research, specifically in decision analysis, a decision tree (ortree diagram) is

a decision support tool that uses a graph or model of decisions and their possible

consequences, including chance event outcomes, resource costs, and utility. A decision tree is

used to identify the strategy most likely to reach a goal. Another use of trees is as a descriptive

means for calculating conditional probabilities.

Sensitivity Analysis: Analysis of the effect on project profitability of possible

changes in sales, costs, and so on.

Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the output of amathematical model can be apportioned, qualitatively or quantitatively, to different sources ofvariation in the input of a model.

Break-even analysis is used to determine the level of sales and the mix of products which are

required to just recover all costs incurred during the period. The break-even point is the point at

which cost and revenue are equal. There is neither a profit nor a loss at the break-even point. The

objective ofcost-volume-profit analysis is to determine the level of sales and mix of products

which are required to achieve a targeted level of profit. Although management typically plans for a

profit each period, the break-even point is of concern. If sales fall below the break-even point,

losses will be incurred. Management

Project Analysis is the process of identifying, analyzing and deciding (select or reject) investment

projects.

Reference may be made to the detailed notes emails to all the students.

Q.4 (a)

Many new companies rely initially on family funds and bank loans. Some of them continue to grow

with the aid of equity investment provided by individuals or institutional investors. However, many

adolescent companies raise capital from specialist venture-capital firms, which pool funds from avariety of investors, seek out fledgling companies invest in, and then work with these companies

as they try to grow.

The success of a new business depends critically on the efforts put in by the managers. Therefore,

venture capital firms try to structure a deal or prefer to advance money in stages so that

management has a strong incentive to work hard.

(b) Please refer to the chapters 19 & 20 of Financial Management.

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Q.5 Quiz # 6 of Chapter 16 Corporate Finance

(a) Rs.130-Rs.2.75 = Rs.127.25

(b) Nothing the stock price will stay at Rs.130Number of shares to be repurchased: Rs. 40,000,000 x Rs.2.75= 846,154 shares

Rs.130

Stock Price:On announcement=Rs. 130

Ex-Dividend= Rs. 124.50

Number of shares to be issued: 40,000,000 x Rs.2.75 = 883,534 shares

Rs.124.75

Q.6 (a) & (b): Instead of issuing convertible bonds, companies sometimes sell a package of

straight bonds and warrants. Warrants are simply long term call options that give the right to buy

the companys common stock. For example, each warrant might allow the holder to buy a share of

stock for $50at any time during the next five years. Obviously the warrant holders hope that the

companys stock will zoom up, so that they can exercise their warrant at a profit. But, if the

companys stock price remains below $50, holders will choose not to exercise, and the warrants

will expire worthless. Occasionally the companies extend the life of warrants. The cost to do so is

not noticeable.

For further study, please refer to chapter 22 of Financial Management.

Q.7

For detailed discussion please refer to chapter 20 of Financial Management or chapter 14 of

Corporate Finance.

Q.8 Retention Growth Model: g= b (r) where b is retention ratio and r is Return of Equity

(a) 0.40(0.20) = 0.08 or 8%

(b) Total Assets= Rs.1,000,000 growth= 30 %

Assets Requirements: Rs. 300,000

Equity= Rs. 1,000,000 ROE= 20%

Earnings after tax or Net Income= Rs.200, 000

External Financing Requirements= Rs.300,000-[ 40% of Rs.200,000]

= Rs. 220,000

Corporate Finance Solution to Paper-Autumn 2004

Q.1

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(a) Capital Rationing: A situation where a constraint or budget ceiling is placed on the total

size of capital expenditure during a particular period. Such constraints or limitations are prevalent

in a number of firms, particularly in those that have a policy of internally financing all capital

expenditures. Another example of capital rationing occurs when a division of a large company is

allowed to make capital expenditures only up to a specified budget ceiling, over which the division

usually has no control. With a capital rationing constraint, the company attempts to select thecombination of investment proposals that will provide the greatest increase in the value of the

company subject to not exceeding the budget ceiling constraint.

Soft Rationing:Many firms capital constraints are Soft. They reflect no imperfections in capital

markets. Instead they are provisional limits adopted by management as an aid to financial control.

Some ambitious divisional managers habitually overstate their investment opportunities. Rather

than trying to distinguish which projects really are worthwhile, headquarters may find it simpler toimpose an upper limit on divisional expenditures and thereby force the divisions to set their own

priorities.

Hard Rationing: Soft rationing should never cost the firm anything. If capital constraints become

tight enough to hurt, then the firm raises more money and loosens the constraints. But what it cant

raise more moneywhat if it faces hard rationing?

Hard rationing implies market imperfections, but it does not necessarily mean we have to throw

away net present value as a criterion for capital budgeting. It depends on the nature of

imperfections. For detailed discussions please refer to chapter 5 of Corporate Finance (page 100

to 103)

Quiz Number 5 of Chapter Number 5 .

Multiple Internal Rates of Return (IRRS): There is one other situation in which the IRR approach may n

be usablethis is when non-normal cash flows are involved. A project has normal cash flows when onemore cash inflows (costs) are followed by a series of cash inflows. If, however, a project calls for a lar

cash outflows either sometime during or at the end of its life, then it has non-normal cash flows. No

normal cash flows can present unique difficulties when evaluated by the IRR method. The most comm

problem encountered when evaluating non-normal projects is multiple IRRS.

This project has two internal rate of return. -50% and +50 %. If we calculate projects NPV by

using either of the above rates, it would come to zero.

If opportunity cost is 20% then project is attractive because ofpositive NPV of $14.58.

Q.2

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Weighted Average Cost of Capital or WACC: (Ke) (We) + (Kd) (Wd) where:

Ke= Cost of Equity We= Weightage or Proportion of Equity

Kd= Cost of Debt Wd= Weightage or Proportion of Debt

(a) Long Term Debt= Rs. 300,000 Equity= 10,000xRs.50= Rs.500, 000

So Weightage of Debt would be 3/8 & Weightage of Equity would be 5/8WACC= (0.15) (5/8) + (0.08) (3/8) = 0.12375 or 12.375%

(b) Now stock price falls to Rs.25 per share, therefore amount of equity would decline to Rs.250,000 (10,000xRs.25) whereas amount of debt remains the same. In this situation theWACC would be as under:

(0.15) (2.5/5.5) + (0.08) (3/5.5) = 0.1118 or 11.18 %

Q.3 (a) Project Analysis involves:

Generating investment project proposals consistent with the firms strategic objectives.

Estimating after-tax incremental operating cash flows for the investment projects.

Estimating project incremental cash flows.

Selecting projects based on a value-maximizing acceptance criterion.

Reevaluating implemented investment projects continually and performing pre-audits for completprojects.

For detailed answer please refer to Chapter 12 of Financial Management.

(b) Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the output of amathematical model can be apportioned, qualitatively or quantitatively, to different sources ofvariation in the input of a model.

In more general terms uncertainty and sensitivity analyses investigate the robustness of a studywhen the study includes some form of mathematical modeling. While uncertainty analysis studiesthe overall uncertainty in the conclusions of the study, sensitivity analysis tries to identify whatsource of uncertainty weights more on the study's conclusions. For example, several guidelines formodeling or for impact assessment prescribe sensitivity analysis as a tool to ensure the quality ofthe modeling/assessment.

To sum up Analysis of the effect on project profitability of possible changes in sales, costs, and so

on is called Sensitivity analysis.

C. Monte Carlo methods in finance is a method of using the random sampling of numbers inorder to estimate the solution to a numerical problem. [Monte Carlo in Monaco, famous for itsgambling casino]Monte Carlo stimulation is a tool for considering all possible combinations.It therefore enables us to inspect the entire distribution of project outcomes.

Following steps are required to be carried out under Monte Carlo stimulation.

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Steps 1: Modeling the project

2: Specifying probabilities

3: Simulate the cash flows

4: Calculate present value

For detailed discussion pleas refer to chapter 10 of Corporate Finance.

(d) Decision tree: In operations research, specifically in decision analysis, a decision tree (or

tree diagram) is a decision support tool that uses a graph or model of decisions and their possible

consequences, including chance event outcomes, resource costs, and utility. A decision tree is

used to identify the strategy most likely to reach a goal. Another use of trees is as a descriptive

means for calculating conditional probabilities.

In data mining and machine learning, a decision tree is a predictive model; that is, a mappingfrom observations about an item to conclusions about its target value. More descriptive names for

such tree models are classification tree (discrete outcome) or regression tree (continuous

outcome). In these tree structures, leaves represent classifications and branches represent

conjunctions of features that lead to those classifications. The machine learning technique for

inducing a decision tree from data is called decision tree learning, or (colloquially) decision trees.

Q.4

(a) & (b): Economists often define three levels ofMarket Efficiency.In the first level, prices reflect the information contained in the record of past prices. This is called

weak form of efficiency. If the markets are efficient in the weak sense, then it is impossible to

make consistently superior profits by studying past returns. Prices will follow a random walk.

The second level of efficiency requires that prices reflect not just past prices but all other published

information, such as we might get from reading financial press. This is known as semi-strong

form of market efficiency. If markets are efficient in this sense, then prices will adjust

immediately to public information such as announcement of last quarters earnings, a new issue of

stock, a proposal to merge two companies, and so on.

Finally, we might envisage a strong form of efficiency, in which prices reflect all the information

that can be acquired by the painstaking analysis of the company and the economy. Is such a

market we would observe lucky and unlucky investors, but we wouldnt find any superior

investment managers who can consistently beat the market.

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Q.5

Quiz # 6 of Chapter 16 Corporate Finance

(a) Rs.130-Rs.2.75 = Rs.127.25

(c) Nothing the stock price will stay at Rs.130

Number of shares to be repurchased: Rs. 40,000,000 x Rs.2.75= 846,154 shares

Rs.130

Stock Price:On announcement=Rs. 130


Number of shares to be issued: 40,000,000 x Rs.2.75 = 883,534 shares

Rs.124.75

Q.6

(a) Bonds Conversion Value: 4xRs.30= Rs.120

(b) One of reasons bonds are selling above conversion value is current interest rates. Thesebonds were issued at 10% interest rates. It appears that presently new bonds are issued at lowerrates or we can say yield to maturity is less than coupon rate. The other reason could be greaterEPS and handsome payouts.

( c) If interest rates have dropped substantially and calling old bonds and issuing new one donot carry heavy expenses the company should call old bonds to save annual interest expense.

Q.7

(a) Retractable (or puttable bonds)

Retractable (or puttable bonds) give investors the right to demand early repayment; extendable

bonds give them the option to extend the bonds life.

Putt able bonds exist largely. Because bonds indentures cannot anticipate every action the

company may take that could harm the bondholders. If the value of the bonds is reduced the put

option allows the bondholders to demand repayment.

Potables bonds can sometimes get their issuers into big trouble. During 1990, many bonds issued

by Asian companies gave their lenders a repayment option. Consequently, when Asian crises

struck in 1997, these companies were faced by a flood of lenders demanding their money back.

So it would be beneficial for bondholders to have puttable bonds or bonds with floating rates with

some ceiling to protect them against increased risk of default and increasing interest rates. But as

these features in bonds are not favorable to the issuing companies which in turn prefer to issue

bonds with call option.

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Project Finance means debt supported by the project, not by the project sponsoringcompanies. Project finance is largely a claim against cash flows from a particular project ratherthan against the company as a whole.

No two project financing are alike but they have some common features:

The project is established as a separate company.The contractors and the plant managers become major shareholders in the project and thus share

in the risk of projects failure.The project company enters into a complex series of contracts that distributes risk among the

contractors, the plant managers, the suppliers and the customers.The government may guarantee that it would provide the necessary permits, allow the purchase of

foreign exchange, and so on.The detailed contractual arrangements and the government guarantees allow a large part of

capital for the project to be provided in the form of bank debt or other privately placedborrowing.

For comparison between direct debt and project finance please refer to chapter 25 of Corporate

Finance.

Q.8

(A) Credit Scoring System: Quantitative approaches have been developed to estimate the abilityof businesses to serve the credit to them; however, the final decision for most companiesextending trade credit (credit extended from one business to another) rests on credit analysts judgment in evaluating available information. Strictly numerical evaluations have beensuccessful in determining the granting of credit to consumers, where various characteristics ofan individual or firms are quantitatively rated and a credit decision is made on the basis of totalscore.

The plastic credit cards many of us hold are often given out on the basis of a credit scoring systemin which things such as age, occupation, duration of employment or business, home-ownership,years of residence, and annual income are taken into account. With the overall growth of tradecredit, a number of companies are finding it worthwhile to use numerical credit-scoring systems toidentify clearly unacceptable and acceptable applicants.

For further study please refer to chapter 11 of Financial Management.

(B) Firms grant free credit because they have to follow the practices in the line in trade in whichthey are doing business. A single firm cannot be strict enough in granting trade credit otherwise

it would be out of business. For example it a toy manufacturing company decides not to sellany product on credit or if any customer demands credit, a percentage of discount is to becharged. And we assume that other toy manufacturers in the same market are extending creditperiod up to 30 days. Now we can imagine what would happen, the firm following strict creditpolicy would experience gradual decline in its sales.


Q. 1 First of all, present value of outflows (Costs) @ 6%

Project A= Rs. 66,730

Project B= Rs. 77,721

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Now you have to give either of the machines on lease (rent), so calculate annual lease payments

for economic life of machine. Be careful that lease payments are calculated through formula of

annuity due (to be paid in advance).

Lease Rent Machine A Machine B



So Machine A is preferred.

Q.2 Quiz 1 of chapter 7 (Corporate Finance)


0.10 $500 (0.10) ($500) = $50

0.50 100 (0.50) ($100) = 50

0.40 0 (0.40) ($0) = 0

Expected Payoff =$100

Expected Rate of Return: As you are investing Rs. 100 and expected payoff is Rs.100, your

return would be zero; so expected rate of return is zero.

Please note that Variance and standard deviation is not required in the paper question.

Q.3

Decision tree:

In operations research, specifically in decision analysis, a decision tree (or tree diagram) is a

decision support tool that uses a graph or model of decisions and their possible consequences,

including chance event outcomes, resource costs, and utility. A decision tree is used to identify the

strategy most likely to reach a goal. Another use of trees is as a descriptive means for calculating

conditional probabilities.

Sensitivity Analysis: Analysis of the effect on project profitability of possible changes in sales,

costs, and so on. Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the

output of a mathematical model can be apportioned, qualitatively or quantitatively, to different

sources of variation in the input of a model.

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Break-even analysis is used to determine the level of sales and the mix of products which are

required to just recover all costs incurred during the period. The break-even point is the point at

which cost and revenue are equal. There is neither a profit nor a loss at the break-even point. The

objective ofcost-volume-profit analysis is to determine the level of sales and mix of products

which are required to achieve a targeted level of profit. Although management typically plans for a

profit each period, the break-even point is of concern. If sales fall below the break-even point,losses will be incurred. Management

Project Analysis is the process of identifying, analyzing and deciding (select or reject) investment

projects.

Reference may be made to the detailed notes emails to all the students.

Q.4 (a)Many new companies rely initially on family funds and bank loans. Some of them continue to grow

with the aid of equity investment provided by individuals or institutional investors. However, many

adolescent companies raise capital from specialist venture-capital firms, which pool funds from a

variety of investors, seek out fledgling companies invest in, and then work with these companies

as they try to grow.

The success of a new business depends critically on the efforts put in by the managers. Therefore,

venture capital firms try to structure a deal or prefer to advance money in stages so that

management has a strong incentive to work hard.

(c) Please refer to the chapters 19 & 20 of Financial Management.

Q.5 (a) Rs.130-Rs.2.75 = Rs.127.25

(d) Rs.130Number of shares to be repurchased: Rs. 40,000,000 x Rs.2.75= 846,154 shares

Rs.130

Stock Price: On announcement=Rs. 132.75


Number of shares to be issued: 40,000,000 x Rs.5.50 = 1,657,250 shares.

Rs.132.75

Q.6 (a) & (b):

Instead of issuing convertible bonds, companies sometimes sell a package of straight bonds and

warrants. Warrants are simply long term call options that give the right to buy the companys

common stock. For example, each warrant might allow the holder to buy a share of stock for $50at

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any time during the next five years. Obviously the warrant holders hope that the companys stock

will zoom up, so that they can exercise their warrant at a profit. But, if the companys stock price

remains below $50, holders will choose not to exercise, and the warrants will expire worthless.

Occasionally the companies extend the life of warrants. The cost to do so is not noticeable.

For further study, please refer to chapter 22 of Financial Management.

Q.7

For detailed discussion please refer to chapter 20 of Financial Management or chapter 14 of

Corporate Finance.

Q.8

Retention Growth Model: g= b (r) where b is retention ratio and r is Return of Equity

(c) 0.40(0.20) = 0.08 or 8%

(d) Total Assets= Rs.1,000,000 growth= 30 %

Assets Requirements: Rs. 300,000

Equity= Rs. 1,000,000 ROE= 20%

Earnings after tax or Net Income= Rs.200, 000

External Financing Requirements= Rs.300,000-[ 40% of Rs.200,000]

= Rs. 220,000


Q.1 (A)

Cost of capital = Ke = D1 + g Rs.1.823 +0.085 = 0.10997 or 11%

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Po Rs.73

(B) Now we have to calculate rate of growth by using growth retention formula:

g = b (r) where b = retention ratio and r = Return of Equity

g = 0.50 (0.12) = 0.06 or 6%

Q.2 (a) Practice Question 13 of Chapter 7 (Corporate Finance)

(b) Almost similar to Quiz 1 of Chapter 7, however for your convenience the solution is as

under:


0.333 $10 = $3.33

0.333 (20) = (6.67)

0.333 0 = 0 Expected Payoff = ($3.34)

Q.3 If a baby has been given a hammer we all know what could be the repercussions. So if an

MBA student who has learnt about Discounted Cash Flows would be applying DCF techniques to

all the projects and making entire decisions on the results derived without going into other factors

like project classifications, uncertainty of cash flows, reinvestments of inflows, and other multiple

variables. So whenever we are making decisions on selection or rejection of a project it should not

be based on DCF techniques. A lot of experience and skill is required to take a rational decision.Simply knowledge of DCF techniques without practical exposure in the relevant field would be like

a baby with hammer.

Q.4 Economists often define three levels ofMarket Efficiency.

In the first level, prices reflect the information contained in the record of past prices. This is called

weak form of efficiency. If the markets are efficient in the weak sense, then it is impossible to

make consistently superior profits by studying past returns. Prices will follow a random walk.

The second level of efficiency requires that prices reflect not just past prices but all other published

information, such as we might get from reading financial press. This is known as semi-strong

form of market efficiency. If markets are efficient in this sense, then prices will adjust

immediately to public information such as announcement of last quarters earnings, a new issue of

stock, a proposal to merge two companies, and so on.

Finally, we might envisage a strong form of efficiency, in which prices reflect all the information

that can be acquired by the painstaking analysis of the company and the economy. Is such a

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market we would observe lucky and unlucky investors, but we wouldnt find any superior

investment managers who can consistently beat the market.

Q.5 Net Lease Payment would be = Rs. 100,000 Rs.35, 000 (35% tax) = Rs.65, 000

Please note the lease payments are made in the beginning of each period so present value of five

annual payments should be calculated by using formula of PVA (annuity due). If we use 9% ratethe value would be Rs. 275,582.

Formula of PVA due:

(1+i) n1

PVA= R orPMT - ------------- (1+i) =

i (1+i) n

(1.09)5-1

PVA = Rs.65, 000 ------------- (1.09) = Rs, 275,582

0.09(1.09)5

----------------------------------------------------------------

Q.6 Call Option: A contract that gives the holder the rights to purchase a specified quantity of

the underlying asset at a predetermined price on or before a fixed expiration date.

The price at which the shares can be purchased is referred to as the exercise or strike price of the

option. Typically one option gives you the right to purchase 100 shares. European options differ

from American options in than European options can only be exercised on the expiration date.

American options can be exercised any time up to the expiration date.

If investors purchase a call option, they are anticipating the price of the underlying stock will

increase. Through the purchase of an option they ensure that they can purchase shares at a price

that will be below their forecasted market price at the date they exercise the option. If the marker

price of underlying shares is below or equal to the option strike price, the purchaser will let the

option expire without exercising it. The most that a purchaser will lose by purchasing a call option

is the price paid for the option.

Gains/Losses on Call Options: Lets assume you have purchased a call option for $100. The

agreed exercise or strike price is $45 per share. Remember a call option gives the right to

purchase 100 shares of underlying stock.

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Now we assume that the market price of the underlying share increases to $50, you will have a

profit if you decide to exercise your option. The gain is calculated as the difference between the

market price of the shares and the strike price multiplied by 100 shares less the cost of option as

per calculated below:

$50-$45 X 100- $100= $400

if the market price of shares is equal to or less than the strike price, the amount of loss incurred byyou is simply the option price of $100,

Put Option: A contract that gives the holder the right to sell a specified quantity of the underlying

asset at a predetermined price on or before a fixed expiration date.

If investors purchase a put option, they are anticipating the price of the underlying stock will

decline. Through the purchase of an option they ensure that they can sell shares at a price that will

be greater their forecasted market price at the date they exercise the option. If the marker price ofunderlying shares is greater than or equal to the option strike price, the purchaser will let the

option expire without exercising it. The most that a purchaser will lose by purchasing a call option

is the price paid for the option.

Gains/Losses on Put Options: Lets assume you have purchased a put option for $100. The

agreed exercise or strike price is $45 per share. Remember a put option gives the right to sell 100

shares of underlying stock.

Now we assume that the market price of the underlying share decreases to $41, you will have a

profit if you decide to exercise your option. The gain is calculated as the difference between the

strike price of the shares and the market price multiplied by 100 shares less the cost of option as

per calculated below:

$45-$41 X 100- $100= $300

if the market price of shares is equal to or greater than the strike price, the amount of loss incurred

by you is simply the option price of $100,

One important item to note about options is that they are not used to raise capital for a company,

as the company whose stock are contracted for does not participate in the option contract no does

it receive any funds as a result of the option contract or option exercise. Options are attractive to

investors as a means of protecting their investment positions.

Q.7 Leases come in many forms, but in all cases the lessee (user) promises to make a series

of payments to the lessor (owner). The lease contract specifies the monthly or semi-annually

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payments, with the first payment usually due as soon as the contract is signed. The payments are

usually level, but their time pattern can be tailored to the user needs. When a lease is terminated,

the leased equipment reverts to the lessor. However, the lease agreement often gives the user the

option to purchase the equipment by making payment of agreed residual value.

A lease is a contract. By its terms the owner of an asset (the lessor) gives another party (thelessee) the exclusive right to use the asset, for a specified period of time, in return for the payment

of rent.

Recent decades have seen an enormous growth in the leasing of business assets such as cars

and trucks, computers, machinery and even manufacturing plants. An obvious advantage to the

lessee is the use of an asset without having to buy it. For this advantage, the lessee incurs several

obligations. First and foremost is the obligation to make periodic lease payments, usually, monthlyor quarterly.

Also the lease contract specifies who is to maintain the asset. Under full-service (or

maintenance lease), the lessor promises to maintain and insure the asset and to pay any

property taxes due on it. Under a net lease, the lessee agrees to maintain the asset, insure it, and

pay any property taxes. Financial leases are usually net leases.

The lease may be cancelable of non-cancelable. An operating lease for office space, for example,

is relatively, short-term and is often cancelable at the option of the lessee with proper notice. The

term of this type of lease is shorter than the assets economic life. Other examples of operating

leases include the leasing of copying machines, certain computer hardware, and automobiles. In

contrast, financial leases extend most of the estimated economic life of the asset and cannot be

cancelled at the option of the lessee. The lessee is obligated to make lease payments until the

lease expiration which generally corresponds to the useful life of the asset. These payments not

only amortize the cost of the asset but provide the lessor an interest thereon. Financial leases are

also known as capital or full pay-out lease.

Most financial leases are arranged for brand new assets. The lessee identifies the equipment,

arranges for leasing company to buy it from the manufacturer, and signs a contract with the

leasing company. This called a direct lease.

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In other cases, the firm sells an asset it already owns and gets it on lease from the buyers. These

sale and lease-back arrangements are common in real estate.

A special form of leasing has become popular in financing of big-ticket assets such as aircrafts, oil-

rigs, and railway equipment. This device is known as leveraged leasing. The lessor borrows part

of the purchase price of the leased asset, using the lease contract as security for the repayment ofloan. There are three parties in a leveraged leasing: (1) the lessee, (2) the lessor (or equity

participant), and the lender. From the standpoint of lessee, there is no difference between a

leveraged lease and other type of lease.

Q.8 We make Income Statement assuming the companys sales would increase by 10% and all

other items increase correspondently.

Income StatementFor the Year ending December 31, 2009

Sales: Rs.4, 400 (10% increase)

Cost & Expenses including interest: 3, 850 (87.5% of Sales as before)

Gross Profit: Rs. 550 (12.5% of Sales as before)

We have to calculate rate of growth by using growth retention formula:

g = b (r) where b = retention ratio and r = Return of Equity

Retention Ratio = 1 - payout ratio = 50%

g = 0.50 (0.25) = 0.125 or 12.5%

g = 0.50 (0.275) = 0.1375 or 13.75%

Solutions Corporate Finance[1]

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