# TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III

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1 TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II III Instructions 1. Only one problem should be treated on each sheet of paper and only one side of the sheet should be used. 2. The solutions folder must be handed in before you leave (even if it contains no solution sheets). 3. State on the folder the number of solution sheets that it contains. About the test 1. Aids allowed: - Calculator (all admitted, but empty memory). - Dictionary to English language if necessary, free of notes and calculations. No other aids are allowed. 2. At each problem is stated the number of points that a correct solution is given. To pass the test the total points should be 18 or higher. 3. It is important that the solution method and arguments leading to a conclusion are clearly stated. Answers without motivation are not accepted WRITE AS CLEARLY AND DISTINCTLY AS POSSIBLE! GOOD LUCK! 1

2 TPPE17 Corporate Finance 2(5) Problem 1 (10 points) a) Explain the following concepts: i. Arbitrage (1 pts.) ii. The Law of One Price (1 pts.) b) Explain why maximizing the NPV is the correct decision rule in comparison to the IRR. (3pts.) c) The inherent conflict (dysfunctionality) of Corporate Governance in typical large public firm (2pts.) d) You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is \$2356 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.375% (APR). How much do you owe on the mortgage today? (3 pts.) Problem 2 (10 points) Problem 2 (10 points) A. Explain the following concepts: i. Systematic and unsystematic risk (1pts.) ii. Sharp Ratio (1pts.) B. Write down the assumptions of the CAPM. Explain the efficient portfolio and the capital market line. (Draw necessary diagrams and equations to justify of your answer) (12=3pts.) A. Using the following information, estimate the Year Stock A -10% 20% 5% -5% 2% 9% Stock B 21% 30% 7% -3% -8% 25% i. the average return and volatility for each stock, ii. the covariance between the stocks, and the correlation between these two stocks and interpret the result. (1112=5 pts.) 2

3 TPPE17 Corporate Finance 3(5) Problem 3 (10 points) a) Explain the following concepts: i. Direct and Indirect Bankruptcy costs (2 pts.) b) What are the assumptions underlying the Modigliani-Miller theorem? Mathematically derive the MM1 Proposition in the presence of corporate taxes and show that value of the levered firm is equal to the value of the unlevered firm plus present value of the tax shield. (12=3pts.) c) The valuation model of a growing firm seems to validate the theory of dividend policy irrelevance. Explain this model and show how it ignores dividend policy. Prove that dividend policy is irrelevant at a discount rate of 12 percent, if a firm with two million shares decides to trade-off dividend between two periods by paying 20 percent less in the current period as against the policy of constant \$50m in all periods. (3 pts.) d) Your firm is considering a \$150 million investment to launch a new product line. The project is expected to generate a free cash flow of \$20 million per year, and its unlevered cost of capital is 10%. To fund the investment, your firm will take on \$100 million in permanent debt. Suppose the marginal corporate tax rate is 35%. Ignoring issuance costs, what is the NPV of the investment? (2 pts.) Problem 4 (10 points) a) Explain the following concepts: I. American and European option (1pts.) II. Convertible security and convertible bond (1 pts.) III. Put-call parity (1pts.) IV. Assumption of the Black-Scholes option pricing model. (2 pts.) V. Rebecca is interested in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of \$100 and expires in 90 days. The current price of Up stock is \$120, and the stock has a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year. a. Using the Black-Scholes formula, compute the price of the call. b. Use put-call parity to compute the price of the put with the same strike and expiration date (2.52.5=5pts.) 3

4 TPPE17 Corporate Finance 4(5) ANSWER Problem 1 (10 points) Explain the following concepts: (a) Arbitrage (1 pts.) and The Law of One Price (1 pts.) Arbitrage: The practice of buying and selling equivalent goods in different markets to take advantage of a price difference. An arbitrage opportunity occurs when it is possible to make a profit without taking any risk or making any investment. A competitive market in which there are no arbitrage opportunities. Law of One Price: If equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets. In a normal market, the NPV of buying or selling a security is zero. (b) Explain why maximizing the NPV is the correct decision rule in comparison to the IRR. (3pts.) Sometimes firms must decide among mutually exclusive projects. The manager must rank the projects and choose the best one. In this case, NPV again yields the correct decision. Suppose a project with a positive NPV is being compared with another project that is identical in all respects, except that the size is double. Then the larger project will have an NPV that is double that of the first, meaning it is clearly the better project. However, the IRRs for the two projects will be the same. Hence IRR cannot be used to evaluate mutually exclusive projects of different scales. By the same token, IRR cannot be used consistently to evaluate two projects with different timing or different risk. One improvement of IRR is included here. The incremental IRR investment rule applies the IRR rule to the difference between the cash flows of the two mutually exclusive alternatives. This approach will give the same answer as NPV. However, incremental IRR still has some problems. First, the incremental IRR could not exist, or there could be several. The fact that the incremental IRR exceeds the cost of capital does not imply that the NPV of either project is positive. In addition, it is sometimes difficult to keep track of which project is the incremental project. (c) The inherent conflict (dysfunctionality) of Corporate Governance in typical large public firm (2pts.) The dysfunctionality of corporate governance such as - a lack of transparency and of managerial accountability: investors are imperfectly informed of managers actions - a level of compensation that is not always related to performance - accounting manipulations - managerial accountability, - corporate governance failures. (d)you have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is \$2356 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.375% (APR). How much do you owe on the mortgage today? (3 pts.) Hints: 4

5 TPPE17 Corporate Finance 5(5) Timeline: ,356 2,356 2,356 To find out what is owed, compute the PV of the remaining payments using the loan interest rate to compute the discount rate: Discount Rate = = % 12 2, PV = 1 ( ) 304 = \$354, Problem 2 (10 points) A. Explain the following concepts: (a) Systematic and unsystematic risk (1pts.) and Sharp Ratio (1pts.) Usually stock prices fluctuate due to two types of news. Firm specific: news about the company itself. The risk associated is then called firm-specific, unsystematic or diversifiable. Market-wide: news about the whole economy, affecting the whole market. The risk associated is then called systematic, undiversifiable. If firms are only affected by firm-specific risk, then it is possible to reduce the risk significantly through diversification, adding more and more stocks in the portfolio, so that returns offset each other. Therefore no compensation is needed for that. In reality firms are linked to both types of risk. The point is, only systematic risk must be compensated, since it is the only risk that cannot be canceled away through diversification. Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio. The portfolio with the highest Sharpe ratio is the portfolio where the line with the risk-free investment is tangent to the efficient frontier of risky investments. The portfolio that generates this tangent line is known as the tangent portfolio. (B) Write down the assumptions of the CAPM. Explain the efficient portfolio and the capital market line. (Draw necessary diagrams and equations to justify of your answer) (12=3pts.) Answer: Seminar Lecture Note CAPM and last Lecture Note 5

6 TPPE17 Corporate Finance 6(5) (C) Using the following information, estimate the Year Stock A -10% 20% 5% -5% 2% 9% Stock B 21% 30% 7% -3% -8% 25% Hints: a. i) the average return and volatility for each stock, ii) the covariance between the stocks, and iii) the correlation between these two stocks and interpret the result. (1112=5 pts.) R R A B = = 3.5% = 6 = 12% 2 ( ) 2 2 ( ) ( ) 2 2 ( ) ( ) 1 Variance of A = ( ) = Volatility of A = SD( R A ) = Variance of A = = 10.60% 2 2 ( ) ( ) Variance of B = ( ) ( ) ( ) ( ) = Volatility of B = SD( R B ) = Variance of B = = 15.65% b. ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 1 Covariance = = 0.104% c. Correlation Covariance = SD(R )SD(R ) A = 6.27% B 6

7 TPPE17 Corporate Finance 7(5) Problem 3 (10 points) (A) Explain the following concepts: (a) Direct and Indirect Bankruptcy costs (2 pts.) The costs of bankruptcy: _ Direct costs. Administrative and legal costs. _ Indirect costs. They are much larger than direct costs: (1). The perception on the part of customers that the.rm is in trouble. Customers may stop purchasing the product or service. (2). Suppliers start demanding stricter terms as protection against default, leading to an increase in working capital. 3. Firms may find it diddicult to raise fresh capital (equity and debt) leading to the rejection of good investment projects. _ Indirect costs are higher for: 1. Firms selling durable products with long lives that require replacement parts and services. (ex a computer manufacturer) 2. Firms selling goods and services where quality is an important atttribute (ex if a car maker is in trouble its customers may be uncertain of the quality of its cars) 3. Firms producing products whose value to customer depends on services and complementary products supplied by independent.rms (If Apple computer gets into trouble, companies producing software for its computers may stop producing.) 4. Firms that sell products that require continuous service (A manufacturer of copying machines is more accepted than a furniture manufacturer.) (B) What are the assumptions underlying the Modigliani-Miller theorem? Mathematically derive the MM1 Proposition in the presence of corporate taxes and show that value of the levered firm is equal to the value of the unlevered firm plus present value of the tax shield. (12=3pts.) Note: Seminar-2 note (Both assumption and Derivation). (C) The valuation model of a growing firm seems to validate the theory of dividend policy irrelevance. Explain this model and show how it ignores dividend policy. Prove that dividend policy is irrelevant at a discount rate of 12 percent, if a firm with two million shares decides to trade-off dividend between two periods by paying 20 percent less in the current period as against the policy of constant \$50m in all periods. (3 pts.) Presentation and analysis of a valuation model for a growing firm, such as; V 0 = EBIT(1-t c )/(1k u) I t (r t - k u )/k u (1k u ) t=2 In this model, growth is driven by constant differential between return on investment and cost of capital ((r t - k u )). The components of this model need to be carefully explained. It does not contain any factor that depicts the influence of dividend policy on value of the firm. The relevant factors contributing to value of the firm are; 7

8 TPPE17 Corporate Finance 8(5) -return on investment -cost of capital The information provided can be used to prove that dividend policy is irrelevant. With constant amount of dividend payout the value of firm and equity are; Value of firm: V F = DIV 0 DIV 1 /(1r) = 50 50/1.12 = \$94.643m Value of equity: V E =94.643/2 = \$47.32 With the trade-off in dividend payout the value of the firm and equity are; Value of firm: V F = DIV 0 DIV 1 /(1r) = /1.12 = \$94.643m Value of equity: V E =94.643/2 = \$47.32 The values remain the same, indicating that dividend policy is irrelevant. (D) Your firm is considering a \$150 million investment to launch a new product line. The project is expected to generate a free cash flow of \$20 million per year, and its unlevered cost of capital is 10%. To fund the investment, your firm will take on \$100 million in permanent debt. Suppose the marginal corporate tax rate is 35%. Ignoring issuance costs, what is the NPV of the investment? (2 pts.) With permanent debt the APV method is simplest. NPV(unlevered) = / 0.10 = \$50 million. PV(ITS) = t c D = 35% 100 = \$35 million. Thus, the NPV with leverage is APV = NPV PV(ITS) = = \$85 million. Problem 4 (10 points) Explain the following concepts: Q: American and European option (1pts.) American Option: Options that allow their holders to exercise the option on any date up to, and including, the expiration date. European Option: Options that allow their holders to exercise the option only on the expiration date. The names American and European have nothing to do with the location where the options are traded. Q: Convertible security and convertible bond (1 pts.) A Convertible Security is a bond or a preferred stock that is convertible into a specified number of shares of common stock at the option of the holder. This provides the convertible holder a fixed return (interest or dividend) and the option to exchange a bond or preferred stock for common stock. The option allows the company to sell convertible securities at a lower yield than it would have to pay on a straight bond or preferred stock issue. A convertible bond is a bond which can be converted before maturity into a predetermined number of shares of the issuing company. Basically it is like a normal bond with an embedded warrant which represents a call option on the stock. Q: Put-call parity (1pts.) The relationship between value of the stock(s), the bond, the call and put option is known as Put- Call Parity. Consider the two different ways to construct portfolio insurance. Purchase the stock and a put Purchase a bond and a call Because both positions provide exactly the same payoff, the Law of One Price requires that they must have the same price. Therefore, SP=PV(K)C 8

9 TPPE17 Corporate Finance 9(5) Where K is the strike price of the option (the price you want to ensure that the stock will not drop below), C is the call price, P is the put price, and S is the stock price. Rearranging the terms gives an expression for the price of a European call option for a non-dividend-paying stock. C=PS-PV(K) This relationship between the value of the stock, the bond, and call and put options is known as Q: Assumption of the Black-Scholes option pricing model. (2 pts.) Black-Scholes Option Pricing Model: A technique for pricing European-style options when the stock can be traded continuously. It can be derived from the Binomial Option Pricing Model by allowing the length of each period to shrink to zero and letting the number of periods grow infinitely large. Assumption: The short selling of securities with full use of proceeds is permitted There are no transaction costs or taxes. All securities are perfectly divisible There are no dividends during the life of the derivative There are no riskless arbitrage opportunities. Securitiy trading is continuous The risk-free rate of interest, r, is constant and the same for all maturities. Q: Rebecca is interested in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of \$100 and expires in 90 days. The current price of Up stock is \$120, and the stock has a standard deviation of 40% per year. The risk-free interest rate is 6.18% per year. (a) Using the Black-Scholes formula, compute the price of the call. (b) Use put-call parity to compute the price of the put with the same strike and expiration date (2.52.5=5pts.) Note: a. Using the Black-Sholes formula: ln / 365 PV(K) = 100 / (1.0638) = , d1 = = / = d 2 = / 365 = C = S N ( d1 ) PV ( K) N ( d2 ) = = \$23.29 b. Using put-call parity: P = C PV ( K) S = = \$1.78 9

10 TPPE17 Corporate Finance 10(5) THE CUMULATIVE NORMAL DISTRIBUTION Table gives N(x). To obtain N(-x) use N(-x) = 1-N(x). Use interpolation, e.g. N(0.6278) = N(0.62)0.78*(N(0.63)-N(0.62))= x ,0 0,5000 0,5040 0,5080 0,5120 0,5160 0,5199 0,5239 0,5279 0,5319 0,5359 0,1 0,5398 0,5438 0,5478 0,5517 0,5557 0,5596 0,5636 0,5675 0,5714 0,5753 0,2 0,5793 0,5832 0,5871 0,5910 0,5948 0,5987 0,6026 0,6064 0,6103 0,6141 0,3 0,6179 0,6217 0,6255 0,6293 0,6331 0,6368 0,6406 0,6443 0,6480 0,6517 0,4 0,6554 0,6591 0,6628 0,6664 0,6700 0,6736 0,6772 0,6808 0,6844 0,6879 0,5 0,6915 0,6950 0,6985 0,7019 0,7054 0,7088 0,7123 0,7157 0,7190 0,7224 0,6 0,7257 0,7291 0,7324 0,7357 0,7389 0,7422 0,7454 0,7486 0,7517 0,7549 0,7 0,7580 0,7611 0,7642 0,7673 0,7704 0,7734 0,7764 0,7794 0,7823 0,7852 0,8 0,7881 0,7910 0,7939 0,7967 0,7995 0,8023 0,8051 0,8078 0,8106 0,8133 0,9 0,8159 0,8186 0,8212 0,8238 0,8264 0,8289 0,8315 0,8340 0,8365 0,8389 1,0 0,8413 0,8438 0,8461 0,8485 0,8508 0,8531 0,8554 0,8577 0,8599 0,8621 1,1 0,8643 0,8665 0,8686 0,8708 0,8729 0,8749 0,8770 0,8790 0,8810 0,8830 1,2 0,8849 0,8869 0,8888 0,8907 0,8925 0,8944 0,8962 0,8980 0,8997 0,9015 1,3 0,9032 0,9049 0,9066 0,9082 0,9099 0,9115 0,9131 0,9147 0,9162 0,9177 1,4 0,9192 0,9207 0,9222 0,9236 0,9251 0,9265 0,9279 0,9292 0,9306 0,9319 1,5 0,9332 0,9345 0,9357 0,9370 0,9382 0,9394 0,9406 0,9418 0,9429 0,9441 1,6 0,9452 0,9463 0,9474 0,9484 0,9495 0,9505 0,9515 0,9525 0,9535 0,9545 1,7 0,9554 0,9564 0,9573 0,9582 0,9591 0,9599 0,9608 0,9616 0,9625 0,9633 1,8 0,9641 0,9649 0,9656 0,9664 0,9671 0,9678 0,9686 0,9693 0,9699 0,9706 1,9 0,9713 0,9719 0,9726 0,9732 0,9738 0,9744 0,9750 0,9756 0,9761 0,9767 2,0 0,9772 0,9778 0,9783 0,9788 0,9793 0,9798 0,9803 0,9808 0,9812 0,9817 2,1 0,9821 0,9826 0,9830 0,9834 0,9838 0,9842 0,9846 0,9850 0,9854 0,9857 2,2 0,9861 0,9864 0,9868 0,9871 0,9875 0,9878 0,9881 0,9884 0,9887 0,9890 2,3 0,9893 0,9896 0,9898 0,9901 0,9904 0,9906 0,9909 0,9911 0,9913 0,9916 2,4 0,9918 0,9920 0,9922 0,9925 0,9927 0,9929 0,9931 0,9932 0,9934 0,9936 2,5 0,9938 0,9940 0,9941 0,9943 0,9945 0,9946 0,9948 0,9949 0,9951 0,9952 2,6 0,9953 0,9955 0,9956 0,9957 0,9959 0,9960 0,9961 0,9962 0,9963 0,9964 2,7 0,9965 0,9966 0,9967 0,9968 0,9969 0,9970 0,9971 0,9972 0,9973 0,9974 2,8 0,9974 0,9975 0,9976 0,9977 0,9977 0,9978 0,9979 0,9979 0,9980 0,9981 2,9 0,9981 0,9982 0,9982 0,9983 0,9984 0,9984 0,9985 0,9985 0,9986 0,9986 3,0 0,9987 0,9987 0,9987 0,9988 0,9988 0,9989 0,9989 0,9989 0,9990 0,9990 3,1 0,9990 0,9991 0,9991 0,9991 0,9992 0,9992 0,9992 0,9992 0,9993 0,9993 3,2 0,9993 0,9993 0,9994 0,9994 0,9994 0,9994 0,9994 0,9995 0,9995 0,9995 3,3 0,9995 0,9995 0,9995 0,9996 0,9996 0,9996 0,9996 0,9996 0,9996 0,9997 3,4 0,9997 0,9997 0,9997 0,9997 0,9997 0,9997 0,9997 0,9997 0,9997 0,9998 3,5 0,9998 0,9998 0,9998 0,9998 0,9998 0,9998 0,9998 0,9998 0,9998 0,9998 3,6 0,9998 0,9998 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 3,7 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 3,8 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 0,9999 3,9 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 4,0 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,

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