FINANCE 402 Capital Budgeting and Corporate Objectives

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1 FINNC 402 Capital Budgeting and Corporate Objectives Sample Final xam SOLUTIONS Professor Ron Kaniel FIRST NM: LST NM: Question Maximum Student Score Question 1 Bonds 15 Question 2 Stocks 13 Question 3 Portfolio nalysis 12 Question 4 CPM 20 Question 5 Leverage 10 TOTL 70 Instructions: Please read each question carefully Formula sheets are provided separately Show all work but keep your answers succinct Round all dollar amounts to the nearest cent and percentages to the nearest hundredth (e.g. 2.51%) Hand held calculators are allowed Please check that including the cover page the final contains 13 pages. Good luck! 1

2 Question 1: (Bonds, 15 points) (a) Find the price of a 10% Government coupon bond that pays annual coupons, matures in exactly 2 years, and has a face value of $1,000. The PR is 4% p.a. compounded annually. The bond has just paid its annual coupon, hence you need to price it assuming that the first coupon that you will receive is due in exactly one year. (6 points) nswer: The value of this bond is: 1 (1.04)2 P , (1.04) $1, (b) In addition to the 10% coupon bond you observe two more zero coupon bonds which will mature in 1 and 2 years from now, both with a face value of $100. The prices of these bonds are given below: Time to Maturity (years) Face value Price 1 $100 $ $100 $82.17 re the prices of these two zero coupon bonds consistent with the price of the 10% coupon bond? xplain your answer. If the prices are indeed inconsistent show, in detail, using an arbitrage table, how you can make risk-less arbitrage profits. Does your arbitrage profit depend on the possibility that the PR will change in one year? You are allowed to both buy or sell the coupon bond and any of the zero-coupon bonds. (5 points) nswer: The price of the replicating portfolio is equal to: *82.17 = Since it is lower than the market price of the coupon bond we have an arbitrage opportunity. Transactions today Inflow today Payoff in one Payoff in two year s time year s time Purchase 1-year zero coupon bond

3 Purchase 11 2-year zero-coupon bonds ,100 Sell the 10% coupon bond +1, ,100 Net cash-flows: The fact that the PR changes in one year does not affect these transactions. The purpose of the arbitrage is precisely to hedge any exposure to changes in market rates. (c) The current PR is 4%. You know that in exactly one year the PR can take two possible values. The PR can either remain at 4% or decline to 2%. Both of these possibilities are equally likely. Calculate the one-year return that an investor expects to earn by purchasing the 10% coupon bond in section (a) today and selling it in exactly one year after the payment of the next coupon. (4 points) nswer: In one year the coupon bond will have one more year to maturity. It s price then can take two possible values: 1,100/1.04 = 1, and 1,100/1.02 = 1, Hence, the expected return is [100 + (1, ,078.43)/2]/1, = or 4.93%. Question 2: (Stocks, 13 points) GreenHead Inc. is a well-established company with a long tradition of steady dividend payments that grow at 5% per year. GreenHead pays dividends annually and has just paid a dividend of $2 per share. The cost of capital is 10% compounded annually. (a) What is the value of GreenHead s stock? (4 points) nswer: using the constant growth model the price is: $2*1.05/( ) = $42. (b) You anticipate that GreenHead Inc. s industry will go through major changes in exactly 10 years from now. These changes will not impact the dividend payments described earlier but will result in an increase in the firm s systematic risk. Specifically, the cost of capital will remain at 10% over the next 10 years but then will increase to 20% indefinitely. What is the value of GreenHead s stock? (5 points) nswer: The present value of the first 10 dividends is: 2*1.05/( ) 1/ * 2* /( ) = $

4 to this we need to add the present value of the remaining dividends beyond year 10: 1/ * 2* /( ) = $8.79 Therefore, the overall value of the stock now is: $ (c) GreenHead Inc. s CO considers moving some of the firm s manufacturing facilities overseas to Italy and rename the firm TestaVerde Inc. She assumes that the cost of capital will remain unchanged at 10% indefinitely. Since part of the production plants and sales will be overseas dividends will now fluctuate yearly as follows: Beginning next year dividends will be paid as follows: next year s dividend will equal $2 and will grow at a rate of 6% biannually, for ever. Beginning two years from today the dividend will equal $3 and will grow at a 5% biannually, forever. What will the value of the firm s stock be if the company decided to adopt the CO s plan? (4 points) nswer: We can discount the value of dividends on odd and even years and then add to find the share price. First, the effective cost of capital over any two-year period is = 1.21 or 21%. On even years we find that: P even = 3/( ) = $ On odd years we similarly find the present value as follows: P odd = 1.1 * [2/( )] = By moving the manufacturing facilities the resulting share value will be $ Question 3: (Portfolio nalysis, 12 points) sset has an expected return of 18% and a standard deviation of 38%. sset B has an expected return of 14% and a standard deviation of 21%. (a) How much should you invest in asset and asset B in order to obtain an expected return of 17%? (3 points) nswer: We need to invest 25% of our wealth in asset B and 75% in asset. 17% w*14% (1 w)*18% w 25% 4

5 (b) ssume you can borrow and lend at the risk-free rate of 8%. If you can combine an investment in the risk-free rate with only one of these assets, which of these assets ( or B) offers a better investment opportunity? xplain why. (4 points) nswer: We can compare the Sharpe ratio for each asset as: Sharpe( ) r r f rb rf Sharpe( B) B 0.21 Since asset B has a greater Sharpe ratio, it offers a better investment opportunity. (c) Now assume that you can still lend at a rate of 8% but the borrowing rate is higher at 10%. s in the previous section (b), you can combine borrowing or lending with only one of assets or B. Which of these assets would you select if your goal is to create a portfolio with an expected return equal to 16%? xplain why, showing exactly how you would form the desired portfolio. (5 points) nswer: Since the borrowing rate is higher than the lending rate the Sharpe ratio changes as we switch from lending to borrowing. Given that the target expected return is 16% we need to determine which asset to combine with lending at 8% or borrowing at 12%. Since the target expected return is higher than asset B s expected return we know that we will need to borrow in this case so we need to set the weights as follows: (1-w)10 + w14 = 16 w=1.5 or 150%. The resulting portfolio s standard deviation is equal to w*21% or 31.5%. Since the target expected return is lower than asset s expected return we lend in this case and we need to set the weights as follows: (1-w)8 + w18 = 16 w=0.8 or 80%. The resulting portfolio s standard deviation is equal to w*38% or 30.4%. We therefore choose asset since the portfolio s standard deviation is lower (30.4% < 31.5%). 5

6 Question 4: (CPM, 20 points) Stock has a beta equal to 1 and stock B has a beta equal to 1.5. The expected market return is 11% and the risk-free return is 5%. (a) ssuming the CPM model is correct, what is the expected return of stock B? (2 points) nswer: The expected return is 5+1.5*(11-5) = 14%. (b) Construct a portfolio with a beta equal to zero using stock and stock B. (3 points) nswer: We need to solve the following equation: 0 = w*1 + (1-w)*1.5. The asset weights are 300% long in stock and short 200% in stock B. (c) ssuming the CPM model is correct, what is the expected return on the portfolio in part (b)? (2 point) nswer: It is just equal to the risk-free return, 5%. (d) ssume that Stock B s return has a covariance of with the market return. First, determine the covariance of stock s return with the market return. Second, determine the correlation between stock s return and the market return? If this is not possible, explain why. Third, assuming that the firm specific risks of stock and B are uncorrelated determine whether the covariance between stock and stock B is positive, negative or zero? If this is not possible, explain why. (7 points) nswer: First, M 2 M cov 1 cov Second, we cannot compute the correlation of stock s returns and the market without knowing the standard deviation of Stock s returns. Third, the covariance between stock and B is positive. ny covariation is caused by return comovement with the market or due to firm specific covariation (say if they firms are in the same industry). However, the covariation due to firm specific risk is 6

7 assumed to be zero. Therefore, the only source of joint covariation is possibly due to market related comovement. Since both firms have a positive betas with the market that means that they will both have a positive joint covariation. (e) In addition to assets and B described above you are told that the expected return on MISRBL PNTHRS, Inc. shares is 0% and its beta is ssuming that the CPM is the correct asset-pricing model, does the market correctly price this firm? If your answer is yes then proceed to the next question. Otherwise, first explain whether it is over/under valued and then how would you take advantage of the mispricing. You can form arbitrage portfolio buy buying or selling MISRBL PNTHRS, Inc. as well as the riskfree rate and the market portfolio. (6 points) nswer: PNTHRS s Inc. expected return is 0% while the CPM predicts that the expected return ought to be *( ) = 3.5%. Hence, its expected return is too low - it is overpriced! Trading strategy: Sell this firm's share and buy a portfolio with the same beta. We can use the Market portfolio and T-bills. Find the weight w on the market such that: = (1-w)*0 + w*1 w = Hence the weights are 125% on T-bills and -25% on the market. The gain in expected return terms is 3.5%. Question 6: (Leverage, 10 points) The company Noboro has a tradition of financing all their operations with equity offerings. They have no debt in their capital structure. The expected return on their equity is currently 12%, the share price is $25 per share, and the company has 20 million shares outstanding. The expected return on the market portfolio is 14%. The risk free rate of interest is currently 6%. The new management of Noboro has decided to break with the company's tradition and finance 25% of their operations with debt. This would still give the company a credit rating, and the expected return on this debt would equal the risk free rate. The company would issue debt and use all the proceeds to repurchase some of their shares after relevering. a) (2 points) What is Noboro's equity beta before taking on debt? 7

8 nswer: The beta of Noboro's equity from the CPM is: 0.12 = beta*( ) beta = b) (2 points) What is the equity beta after the company has repurchased the shares and issued debt? What is the expected return on equity now? How has this affected the company's cost of capital (the WCC ))? nswer: Using the fact that the WCC has not changed we know that it is still equal to 12%. The new capital structure is now based on 25% in debt and 75% in equity so: 0.12 = 0.25* *(r nobore ) (r nobore ) = So the equity earns the same rate as the market, i. e. 14%. The beta of the equity is now The cost of capital is still 12%. c) (2 points) What is the dollar amount of debt the company has to issue? How many shares does it have to repurchase? What is the stock price after such a recapitalization? nswer: The company has a total market capitalization value of 20m*$25=$500 million, hence it has to issue 0.25*500=$125 million of debt. It has to repurchase 5 million shares. The share price remains unchanged at 375m/15m=$25. d) (2 points) Before undertaking any debt issue, Noboro has discussed the matter at length with the institutional shareholders of the company. They strongly suggest that Noboro increase its leverage so that the expected return on equity is 2% p.a. above the expected return on the market portfolio, that is, 16%. Is the planned recapitalization sufficient to achieve this goal? If not, determine how much debt (as a percentage of the value of the company and in dollars) Noboro should issue for the recapitalization in order to satisfy the institutional investors. Be specific whether you refer to the total debt they need to issue, or the additional debt they need to issue on top of what is already planned. ssume that at the new level of debt the debt will still be risk-free. nswer: In order to outperform the market by 2% they have to increase leverage even further to have an equity beta of Then they have to increase the debt/equity ratio so that: 8

9 D D D This gives: 2 / 3, hence D/V=40% D Given that the firm s value is $500 million, Noboro should issue a total of $200 million of debt, $75 million in addition to what was originally planned. e) For the next section assume that Noboro is still unlevered. (2 points) The treasurer of Noboro makes a presentation to the board to promote the following plan. She argues that Noboro needs to acquire additional production facilities with a cost of $250 million. The new facilities will have identical systematic risk as the current assets of Noboro. Her plan is to issue $125million in debt and another $125million in equity. What is the asset beta of Noboro now (all assets combined)? What is the expected return on equity now if the debt is still risk free? The beta of the assets remains unchanged as the old and new assets have the same expected return. The expected return on the assets is therefore still 12%. If the debt is risk free we have the return on the equity as: D 125 r r r rd 0.12 * , or 13.2%

FINANCE 100 Corporate Finance

FINANCE 100 Corporate Finance FINNCE 100 Corporate Finance Professor Roberts Solutions to Sample Quiz # NME: SECTION: Question Maimum Student Score Question 1 50 Question 50 TOTL 100 Instructions: You may bring one 8.511 inch sheet