EC3010 Corporate Finance Answers PDF

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Tommaso Gabrieli

2011

Corporate Finance - Final Exam City University London Instructions Answer all questions in Part A and any two of the four questions of Part B. Each question in Part A is worth 2.5 marks and each question in Part B is worth 37.5 marks. In Part A only choose one answer ( A, B, C or D) and write this answer in your answer book; there is no negative mark if you do not select the right answer.

Part A 1. The reason that Proposition I of the Modigliani and Miller Theorem does not hold in the presence of corporate taxes is : A) Levered firms pay lower taxes when compared with identical un–levered firms B) Bondholders require higher rates of return compared with stockholders C) Bondholders require lower rates of return compared with stockholders D) Dividends are no longer relevant with taxes 2. The Modigliani and Miller theory with taxes implies that firms should issue maximum debt. In practice, this is not true because of the following reason(s): (1) Debt is more risky than equity (2) The risk of bankruptcy and its attendance costs increase with debt (3) The risk of financial distress implies that future cash flows are discounted at a higher rate A) Only reason 1 is valid B) Only reason 2 is valid C) Only reason 3 is valid D) Only reasons 2 and 3 are valid 3. In order for the Capital Asset Pricing Model (CAPM) to hold, it is necessary that: (1) Investors have the same preferences (2) Investors have homogeneous beliefs (3) Financial markets have negligible transaction costs A) Only reason 1 is valid B) Only reason 2 is valid 1

C) Only reason 3 is valid D) Only reasons 2 and 3 are valid 4. Investments A and B both offer an expected rate of return of 6% and are perfectly positively correlated. If the standard deviation of A is 5% and that of B is 3%, then risk-averse investors would: A) Only hold A B) Only hold B C) Hold both A and B D) Need more information to answer 5. Both stock X and stock Y have a standard deviation of 10. If you invest 50% of the funds in stock X and 50% in stock Y, what is the standard deviation of the portfolio? A) 10 B) 7.5 C) 5 D) Need more information to answer. 6. Security i has an expected return of 8% and a beta equal to 4. The risk-free rate on the market is 3%. If the Capital Asset Pricing Model (CAPM) holds the mean return of the market portfolio is: A) 3.25% B) 4.25% C) 5.25% D) None of the above 7. Assume you are evaluating a stock and have a two factor model. Factor 1 embodies the changes in the rate of inflation and the risk premium related to this factor is 0.5%. Factor 2 reflects the percentage growth in real GDP and the risk premium related to this factor is 1%. The average rate of return on an asset with a beta equal to 0 is 2%. The stock you are evaluating has b1 = 1.00 and b2 = 1.5. If there is no arbitrage opportunity, what is the expected return on your stock according to the Arbitrage Pricing Theory (APT)? A) 3% B) 4% C) 5% D) None of the above 8. A firm has an investment budget of 100 and is considering two possible projects. Project A has an initial cost of 75 and project B has an initial cost of 20. Project A has higher Net Present Value (NPV) but lower Profitability Index (PI) than project B. In which project should the firm invest? A) Only A 2

B) Only B C) A combination of A and B D) Need more information to answer

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9. The opportunity cost of capital for a risky project is A) The expected rate of return of a government security having the same maturity as the project B) The expected rate of return of a well diversified portfolio of common stocks C) The expected rate of return of a portfolio of securities with similar risks as the project D) None of the above 10. Agency problems are at the core of the recent banking crises. Which of the following situations can be described as an agency problem? (1) Managers took excessive risks given shareholders’ preferences (2) Managers were using the wrong models to quantify risk but did not know it (3) Managers of government-owned banks may still have different objects from shareholders A) Only 1 and 2 B) Only 2 and 3 C) Only 1 and 3 D) All of them Answers: 1A, 2D, 3D, 4B, 5D, 6B, 7B, 8D, 9C, 10C Go to the next page for Part B

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Part B 1. The expected return of the S&P500 is 8% and has a standard deviation of 80% per year. The expected return of IBM is unknown, but it has a covariance with the S&P500 of 0.5. The expected return of MS is unknown, but it has a covariance with the S&P500 of 0.3. The risk free rate is 3% per year. (a) Using the Capital Asset Pricing Model (CAPM), Compute the expected return and standard deviations of IBM and MS. [9 marks] (b)Assume that the standard deviation of IBM and MS is respectively equal to 120% and 80% of the S&P500 standard deviation. In a mean-variance diagram draw S&P500, the risk-free asset, IBM, MS and the capital market line. Which portfolio should rational investors hold, according to the theory? [9 marks] (c) Consider now a one-factor model for the returns of IBM and MS, where the expected returns of the securities and the risk free rate are those found in answer (a), the factor betas of IBM and MS are respectively 3 and 2, the expected value of the common factor F˜1 is 1% and the expected value of specific factors ǫI BM and ǫI BM is zero. How much should be invested in each of the stocks to design the pure factor portfolio (the portfolio with beta=1)? Write the factor equation of the pure factor portfolio. [9 marks] (d) Using the pure factor portfolio found in (c) find the tracking portfolio for DELL, whose expected return is assumed to be given by the factor equationR˜DELL = 0.02 + 2 F˜1 . Show that an arbitrage opportunity does exist and explain briefly how you could take advantage of it. [10.5 marks] Answer: IBM ,rmarket ) = (00.5 = 0.781. (a)bIBM = CovV(rar(r .8)2 mar ket ) r IBM = rf + bI BM (r market − rf ) = 0.03 + 0.781(0.08 − 0.03) = 6.9%. (rM S ,rmarket ) bM S = Cov = 0.469. = (00.3 .8)2 V ar(rmarket ) r M S = rf + bM S (r market − rf ) = 0.03 + 0.469(0.08 − 0.03) = 5.3%. (b) Both IBM and MS lie below the capital market line. IBM must lie to the right of the Market portfolio (here S&P500), while MS to the left. Any rational investor should hold a combination of the risk-free and the market portfolio, depending on the preference for risk. (c)According to the one factor model r˜IBM = 6.9% − 3% + 3F˜1 , r˜M S = 5.3% − 2% + ˜ 2F1 . In order to construct the pure factor portfolio put weights x and 1-x on the two stocks such that 3x + 2(1 − x) = 1, therefore xI BM = −1, xM S = 2. The constant of the pure factor portfolio is equal to r p1 = −3.9% + 2 ∗ 3.3% = 2.7%. It follows the factor equation of the pure factor portfolio: R˜p1 = 2.7% + F˜1 . (d) Expected return for the pure factor portfolio: 2.7%+1%=3.7%. Risk premium for the pure factor portfolio: λ1 = 3.7% − 3% = 0.7%. Expected return of the tracking portfolio for DELL: r T = 3% + 2 ∗ 0.7% = 4.4%. Expected return of DELL: r DELL = 0.02 + 2 ∗ 1% = 3% 5

An arbitrage opportunity exists because this expected return of 4.4% differs from the 3% expected return of the tracked security. The arbitrage opportunity requires that we purchase the high expected return stock (i.e., the tracking portfolio) and short DELL [This is enough as an explanation]. More specifically, this is achieved by going long on the pure factor portfolio constructed from IBM and MS. For every dollar short on DELL, short 1$ of IBM and buy 2$ of MS. Such a position has no factor risk, costs nothing today, and generates $0.044 -$0.03 = $0.014 in the future for every dollar of DELL shorted. This is an arbitrage that can be scaled to any degree. 2. A company is considering investing in the following projects, A, B, C, D, E. The opportunity cost of capital is 7% for each project. The projects’ cash flows are as follows: Period 0 A -£55,000 B -£55,000 C -£15,000 A -£10,000 A -£5,000

Period 1 £15,000 £10,000 £5,000 £5,000 £2,000

Period 2 £20,000 £20,000 £10,000 £5,000 £2,000

Period 3 £20,000 £20,000 £10,000 £7,000 £5,000

(a) Which projects are profitable? If the firm can only choose one project, which should it choose? [9 marks] (b) If the firm has an investment budget of 25,000 and projects cannot be replicated, which projects should the firm undertake? How would the previous answer change if projects can be replicated? [9 marks] (c) For which projects the internal rate of return (IRR) is greater than 5%? [9 marks] (d) Using a precise numerical explanation based on the data from the table, describe two possible arbitrage opportunities that can be used to finance the projects above: (i) borrowing at a fixed interest rate and (ii) short selling stocks in the firm. [10.5 marks] Answer: (a) NP VA = −55 + 15/(1.07) + 20/(1.07)2 + +20/(1.07)3 = −6.72. NP VB is also negative as the period cash-flows are smaller or equal to those of A. By computation NP VC = 6.14, N P VD = 4.44, NP VE = 2.52. By NPV computations it is immediate to find profitability indexes: P IC = 1.41, P ID = 1.44, P IE = 1.5. Only C,D,E are profitable. Firm should choose C as it has the highest NPV. (b) With a budget of 25,000 the firm can invest in C and D and maximize sum of NPV. If projects are replicable the firm should invest in 5 projects E as it is the project with the highest PI. (c) C,D,E have IRR¿0.05 as the their NPV is positive with cost of capital = 7%. It can be computed that also for cost of capital = 5% N P VA < 0, therefore both A and 6

B have IRR¡5%. (d) One arbitrage opportunity consists in short selling stocks in the company and use the cash flow from sale to invest in the project. If the return on the company stocks is lower than the IRR of the project, such strategy edges against possible losses from the project and gives a non negative expected profit. Another arbitrage opportunity consists in borrowing at some fixed interest rate and use the cash flow from sale to re-pay the debt. If the interest rate on debt is lower than the IRR, such strategy gives a non negative expected profit. Full marks awarded for complete answers, preferably with numerical examples. 3. A recently established company needs to raise external capital. (a) State the Modigliani-Miller Theorem.[9 marks] (b) Show that, under certain conditions, the value of the firm will be the same if the company issues debt. [9 marks] (c) Assume that the firm started with 5 millions of equity (500,000 outstanding shares with unitary price of 10$) and zero debt. The firm changes to a new capital structure with 2.5 millions of equity and 2.5 millions of debt by repurchasing 250,000 shares and issuing debt. Describe how an investor could offset the change and recreate the same payoffs that would have obtained under the old capital structure. [10 marks] (d) Assume that the firm goes back to the old capital structure re-issuing shares and buying back own debt. Describe how an investor who prefers the new capital structure could offset this change. [9.5 marks] Answer: (a)The MM theorem states that the capital structure of the firm is irrelevant in the absence of arbitrage opportunities, taxes, costs of bankruptcy and financial distress, information problems and transaction costs. (b) For instance, one can show that two companies that are identical (have the same cash flows) except for their capital structure, one being all-equity financed and the other having some debt, should have the same value. Suppose that the current value of the unleveraged firm is VU and the values of the debt, equity and total of the leveraged firm is D + E = VL . If VU < VL = D + E, there would be an arbitrage opportunity. One could construct a portfolio consisting in a short position of a certain percentage of U and a long position (of the same percentage) of the debt and the equity of L. This portfolio will yield (for sure) gains in the present and all the future cash flows would be 0. Reversing the strategy, one can show that VL cannot be lower than VU . (c) An investor can re-create the original capital structure selling half of his own shares and using the cash to buy debt. In this way the investor maintains the same fraction of outstanding shares and hence the same earnings before interests and taxes. In other words the investor re-creates a debt/equity ratio of zero in his own portfolio. (d) An investor can maintain the new capital structure by borrowing and doubling his own shares. In this way the investor maintains the same fraction of outstanding shares and 7

hence the same earnings before interests and taxes. In other words the investor maintains a debt/equity ratio of 1 in his own portfolio. 4. In the recent crisis the distress of many banks and financial institutions can be essentially attributed to the following reasons: (i) The wrong valuation of the risk of some securities (ii) Very high levels of debt (leveraging or gearing) (iii) Bonus schemes rewarding short term revenues Discuss the previous proposition explaining the following important results of corporate finance: (a) Portfolios promising high returns should also bear high risks. [9 marks] (b) High levels of debt increase the volatility of earnings. [9 marks] (c) Bonus schemes rewarding short term gains are unlikely to solve the agency problems. Likewise, the government intervention that saved distressed financial institution may increase the moral hazard problem. [9.5 marks] (d) A market driven process of debt restructuring of distressed companies may re-correct the miss-pricing of risk. [10 marks] Answer: (a) Refer to the fundamental result of CAPM. (b) Refer to the implications of gearing. (c) Refer to the agency theory and the concept of moral hazard. (d) Refer to Modigliani Miller Theory with bankruptcy costs and case studies on debt restructuring process.

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