Final Exam Finance for AEO (Resit) Course: Finance for AEO SubjectCode: 226P05 Date: 8 juli 2008 Length: 2 hours Lecturer: Paul Sengmüller Students are expected to conduct themselves properly during examinations and to obey any instructions given to them by examiners and invigilators. Firm action will be taken in the event that academic fraud is discovered. Instructions There are choices: Choose five out the six questions. Each question is worth 10 points, the maximum score on the exam is 50 points. On question 6, there are five sub-questions: choose four. Answer each question on a separate sheet, clearly marking each sheet with your name and ID number. The exam is closed book, no translation computers are allowed. You may use a Dutch/English dictionary. You are allowed to use a non-graphical calculator. Explain your answers and show your calculations. Partial credit is given for incomplete answers. No credit is given for answers without explanation. Write clearly. 1
Question 1 Uva BV. is is a multinational provider of education services. Currently, Uva s equity beta is 2. Uva has traditionally maintained a 30% debt-to-value ratio. Uva researchers have developed a web-based student control system, which the company is considering developing commercially as a separate division. Management views the risk of this investment as similar to that of another student-technology company, VU NV, which also has an equity beta of 2, but has a fixed debt-to-value ratio of 80%. Uva BV. plans to finance the new division using 10% debt financing (a constant debt-to-value ratio of 10%). The corporate tax rate is 40%, the risk free rate of return is 5% and the market risk premium is 8%. All firms can borrow at the risk free rate and they hold no cash. (That is, the debt cost of capital is 5% and you don t have to worry about net debt.) (a) Calculate both UVA s and VU s equity cost of capital. Use the CAPM: re uva VU, thus re vu = 21% = 5% + 2 8% = 21%. The same calculation holds for (b) Calculate UVA s pre-tax WACC (r U ) and UVA s after-tax WACC (r wacc ) before the new division is added. r U = 0.7 21% + 0.3 5% = 16.2% r wacc = 0.7 21% + 0.3 5% (1 40%) = 15.6% (c) Estimate r U and r wacc of the new division. The return has to be estimated from the unlevered assets of the comparable company (VU) (a) Estimate the return on unlevered assets of VU ( unlever ): r U = 0.2 21% + 0.8 5% = 8.2% This is the r U of the new division (b) Estimate ( lever up ) the return on equity if debt-to-value is 10% (the debt financing of the new division): r E = 8.2% + 0.1 (8.2% 5%) = 8.56% 0.9 (c) Calculate the after-tax WACC of the new division: r wacc = 8.2% 0.1 5% (1 40%) = 8% (d) If the new division is estimated to bring in 3.8 million of free cash flows next year, growing at 1% per year thereafter, what is the maximum UVA 2
should be willing to pay for the new division? Given the way of financing with a fixed D/E ratio, we can use the WACC method using the r wacc from the previous subquestion V L = 3.8 8% 1% = 54.29 This is the maximum Uva should pay for setting up the new division. Question 2 DEF Inc. is a producer of luxury headphones located in a country with a corporate tax rate of 40% and perfect capital markets. Its after-tax weighted average cost of capital is 20%. DEF plans to introduce a new type of Super- DEF headphones. Based on extensive marketing surveys, the sales forecast for Super-DEF is 1000 units per year. Given how quickly tastes change, DEF expects the product will have a two-year life (i.e. sales only in year 1 and 2). It will be sold for 1000 euro each at DEF s stores and will cost 600 euro per unit to manufacture. The only up-front expenses required for this project are a training session for the sales personnel (10,000 euro) and a new office building (300,000 euro, depreciated linearly over three years). Furthermore, only half of the customers will pay at the time of purchase, the other half delays their payment for one year and DEF has one third of sold units as inventory in the same year (note: inventory is valued at manufacturing cost). Assume that the project is of average risk and that DEF maintains a fixed debt-to-value ratio (a) Calculate the unlevered net income of the project in years 0, 1, 2, and 3. (Show all your results in a table that looks like an income statement.) (in thousands) t=0 t=1 t=2 t=3 Sales 0 1000 1000 0 COGS 0 600 600 0 Gross Profit 0 400 400 0 Selling & Admin Exp. 10 0 0 0 Depreciation 0 100 100 100 EBIT -10 300 300-100 Income tax -4 120 120-40 Unlevered NI -6 180 180-60 -Capital Exp. -300 0 0 0 -Change in Accts. rec. 0 500 0-500 -Change in Inventory 0 200 0-200 +Deprecation 0-100 -100-100 =FCF -306-420 280 740 3
(b) Calculate the (unlevered) free cash flows of the the project in each of the years. See previous subquestion (c) Calculate the NPV of the project. Should the company invest? Explain. We can discount using WACC since the project is of average risk and the company maintains a fixed D/E ratio. NPV = 306 + 420 + 280 + 740 = 1.2 1.2 2 1.2 3 428.2. The company should not do the project. (all figures in thousands of euro). (d) How would your answer in (c) change if the firm had to lower its debtto-value ratio because of the project? Explain. The lower D/E (and therefore lower debt/value) ratio would imply that there is less of a tax-shield effect. The after-tax WACC of the project would increase and therefore the project would become even less attractive. Question 3 Suppose ABM AMRO s stock has an expected return of 20% and a volatility of 40%, while Unilever s has an expected return of 15% and a volatility of 10%. Furthermore, assume that the stocks are not correlated. (a) Would there be diversification benefits if you invest in both stocks? Why or why not? Yes, there is a diversification benefit, as long as the stocks aren t perfectly positively correlated. This can best be seen in the formula: σ 2 p = w 2 aσ 2 a + w 2 bσ 2 b + 2w a w b σ a σ b ρ ab If ρ ab = 1 (perfect positive correlation), the formula can be rewritten as σ p = w a σ a + w b σ b : in this case the portfolio volatility is just a linear combination of of the volatility of its components. (b) If there was no risk-free asset in this economy, can you determine the risk-free rate from these two securities? Explain your answer. 4
There is no zero-variance portfolio and therefore we cannot infer the the risk free rate. (c) Suppose that Unilever has a market beta of 0.5 while the market portfolio has an expected return of 18% and a volatility of 15%. What is the correlation between Unilever and the market portfolio? β u = ρu σu σ m and therefore ρ u = β u σ m σu = 0.5 0.15 0.1 = 0.75 (d) If Unilever was on the Security Market Line (SML), what would be the implied risk-free rate if CAPM holds? If Unilever is on the SML, its expected return is equal to the expected return implied by the CAPM: 15% = r f +0.5 (0.18 r f ). Therefore r f = 12% (e) Suppose you have $100,000 in cash, and you decide to borrow another $50,000 (at the implied risk-free rate in (d)) to invest all the money in Unilever. What s your extra realized return due to the leverage if Unilever goes up 20% over the year? The weight of Unilever in your portfolio is 150,000 = 1.5. Your return will 100,000 be R = 150,000 1.2 50,000 1.12 = 24%.The extra return due to leverage will 100,000 therefore be 24% 20% = 4%. Question 4 The following are the current prices (in dollars) of zero-coupon government bonds with face a value of 1000 euro: Maturity 1 year 2 years 3 years 4 years Price 943.4 873.44 863.84 792.1 The following are the current prices (in dollars) and characteristics of three newly issued coupon-paying government bonds with face a value of $1000: Maturity (years) Coupon rate Coupon payment Price schedule Bond 1 3 6% Annual 1010 Bond 2 4 10% Annual 1168.5 Bond 3 2 10% Annual 1055.12 5
(a) Calculate the yield to maturity (YTM) of the zero-coupon bonds. Maturity 1 year 2 years 3 years 4 years YTM 6% 7% 5% 6% (b) Are the prices of the coupon-paying bonds correct given the YTMs of the zero-coupon bonds? Price Correct price Bond 1 1010 1024.68 Bond 2 1168.5 1139.4 Bond 3 1055.12 1055.12 Bonds 1 and 2 are mispriced. (c) Is there an arbitrage opportunity? If so, describe the right arbitrage strategy, assuming that it is possible to short-sell bonds. Bond 1 is undervalued: sell zero coupon bonds, buy bond 1. Bond 2 is overvalued: buy zero coupon bonds, sell bond 2. Question 5 You are an options dealer who deals in non-publicly traded options. One of your clients wants to purchase a one-year European call option on IBM Computer Systems stock with a strike price of $20. Another dealer is willing to write a one-year European put option on IBM stock with a strike price of $20, and sell you the put option for a price of $1.50 per share. IBM pays no dividends. Its stock currently trades for $18 per share, and the risk free interest rate is 6%. (a) Draw a graph of the payoff of the call and the put as a function of the stock price in one year. (b) What is the lowest price you can charge for the option and guarantee yourself a profit? See solutions for example 20.6 from the book 6
Question 6 Answer four of the following five questions: (a) In the context of the CAPM, how is a stock s alpha defined, and what is its interpretation? Explain briefly. The alpha measures the historical performance of a security relative to the expected return predicted by the SML: α i = E[R i] ] r f β i (E[R Mkt ] r f ) If alpha is positive, the stock has performed better than predicted by the CAPM, if alpha is negative, the stock s historical return is below the SML. Thus alpha represents a risk-adjusted performance measure. (b) You are offered a security with perpetual annual payments. It will pay a cash flow of 100 next year and this cash flow will grow at the rate of inflation thereafter. The real interest rate is fixed and equal to 4% per year. How much would you pay for this security? The cash flow is in real terms, therefore we can discount at the real rate of 4%. The security is a constant perpetuity, therefore its value is 100 4% = 2500 (c) How does asymmetric information explain the negative stock price reaction to the announcement of an equity issue? Explain in a few sentences. Because of asymmetric information, managers have more information about the future prospects of the firm than investors and other outsiders. For instance, managers know better when their stock is overvalued, and they have an incentive to issue equity in this case. This means that issuing equity is a negative signal about the true value of the firm from the point of view investors, and the price drops. (d) According to the tradeoff theory of capital structure, all else being equal, which type of firm has a higher optimal debt level: a firm with very volatile cash flows or a firm with very safe, predictable cash flows? Explain briefly. A firms with very volatile cash flows is more likely to become insolvent. If there are costs to being insolvent (costs of financial distress), then firms with more volatile cash flows will have a higher marginal cost from financial distress and take on less debt relative to firms with predictable cash flows. In other words, the optimal level of debt is lower. 7
(e) Give examples of two investment rules other than the NPV rule? Why/why not should they be used? Explain briefly. The IRR rule: (Invest if internal rate of return > cost of capital). Problem: sometimes not unique, multiple IRRs if cash flows change sign, hard to compare for investment projects with different timing and different scale. The payback rule: (Prefer projects that earn their money back faster). Problems: ignores time value of money and does not depend on cost of capital. Both rules should not be used because they are never superior to the NPV rule. 8