Unformatted text preview: Helpful Formulas Inflation formula: rreal rnominal i 1 i Price to earnings ratio P0 P0 1 EPS r P0 PVGO Naïve diversification formula: Var Portfolio 1 1 Avg .Var 1 Avg .Cov where Avg .Var n n Var 1 n i T Miles/Ezzell Formula for WACC 1 rA D WACC r A TC rD DE 1 rD of debt) PV (TS ) DL rD TC 1 r A r A g 1 rD Present value of tax shield (constant growth of cash flows g and constant proportion Relation between equity beta and debt beta with taxes Constant Amount: E A 1 DL 1 TC DL 1 TC D . EL EL Constant proportion (annual rebalancing): E A 1 TC rD TC rD DL DL 1 D 1 E L 1 rD E L 1 rD D D Constant proportion (continuous rebalancing): E A 1 L D L EL EL Market / book value for fully equity financed firm (constant ROE) P BVPS 1 PB r PB ROE Common Assumptions 1. The market risk premium is positive 2. The nominal and real interest rate are positive 3. The forward rate f t indicates the forward rate between date t‐1 and t 4. The spot rate rt indicates the annualized interest rate (annual compounding) between date 0 and date t 5. mm means million 6. bn means billion Page 2 of 15 Part 1: Multiple Choice Instructions: Only one answer is (exactly) correct. Clearly mark the answer on the Scantron Sheet 882‐E (questions 1‐19) Use common sense to rule out incorrect answers Every questions counts 5 points Questions are ordered according to topics in the class 1. Convert a 10% APR with quarterly compounding into an APR with semi‐annual compounding! a. 10% b. 20% c. 10.125% d. 5% e. 9.975% 2. What is the effective annual rate on a loan if you are quoted a 12% APR (with monthly compounding)? a. 12.6825% b. 12% c. 11.935% d. 1% e. 0.83% 3. You know the following spot rates: r1 5% and r2 7% . What is the yield to maturity on a two year zero coupon bond with face value $100? a. 5% b. 7% c. 7.0583% d. 6.9494% e. 12.35% 4. You know the following rates: r1 5% and f 2 7% . What is the two‐year discount factor? a. 0.88 b. 1.1235 c. 1.12 d. 6.9494% e. 0.8901 Page 3 of 15 5. A 10 year zero‐coupon bond trades at 60. A ten year bond with a 5% coupon (paid annually) sells at 95. The face value of each bond is 100. What is the 10 year spot rate? a. 21% b. 1.64% c. 66.67% d. 5.24% e. ‐33.33% 6. The yield to maturity on a 2 year bond with semi‐annual coupon payments of $2.5 on a face value of $100 is 5% (APR with semiannual compounding). What is the price of the bond? a. $91.14 b. $100.04 c. $102.5 d. $100 e. $97.56 7. The forward rate f 3 is 5% and the forward rate f 4 is 6%. How much does an investment of $1 that will be made at date 2 grow to until date 4 (if you secure investment terms today)? a. Cannot say with this information b. 1.11 c. 0.11 d. 1.113 e. 0.113 8. The real interest rate is 10%. The inflation rate is 2%. What is the nominal interest rate? a. 8% b. 7.843% c. 12% d. 10% e. 12.2% 9. One apple costs $1 today. In times of deflation (negative inflation) prices are decreasing. Say inflation =‐1%. Suppose you want to buy 100 apples next year. How much do you need to save today if the nominal interest rate is 1%? a. $101 b. $99.01 c. $98.02 d. $99 e. $100 Page 4 of 15 10. A project has two IRR’s of 2% and 8%. Which statement is generally true? a. All projects with a hurdle rate between 2% and 8% have positive NPV b. All projects with a hurdle rate of less than 2% or greater than 8% have positive NPV c. The information is not sufficient to make an investment choice d. The NPV for a hurdle rate of 2% or 8% is positive e. The NPV for a hurdle rate of 2% or 8% is negative 11. The equity beta of firm 1 is 0.1. The equity beta of firm 2 is 0.2. Which statement is true in general? a. The assets of both firms must have different risk b. The expected return on firm 2 is twice as high as of firm 1 c. Both firms have a lower equity volatility than the market d. Firm 2 may have a lower expected return than firm 1 e. The expected excess return of firm 2 is twice as high as of firm 1 12. The P/E ratio (using next period’s earnings) of firm ABC is 10. Next period’s net earnings are $10mm. The number of shares outstanding is 1,000. What is the value of the firm? a. $100bn b. $100mm c. $10mm d. $1mm e. $1,000 13. The average multiple “market value of assets over Sales”, i.e. MVA / Sales , in industry X is 2. Using the comparable method what should be the value of equity of a specific firm in this industry if sales are $1bn and the firm’s debt accounts for 40% of the market value of assets? a. $2bn b. $1bn c. $800mm d. $1.2bn e. Cannot tell 14. The market cap rate is 15%. ROE is 20%. What is the value of the stock if next period’s dividend is $100 and expected dividend growth is 5% forever? a. $666.67 b. $1,000 c. $200 d. $333.33 e. $2,000 Page 5 of 15 15. Which stock has the highest equity beta (no taxes)? a. Volatility of Equity: 30%, Asset beta = 0.5, debt financing % of assets: 25% b. Volatility of Equity: 40%, Asset beta = 1, debt financing % of assets: 10% c. Volatility of Equity: 25%, Asset beta = 2, debt financing % of assets: 0% d. Volatility of Equity: 35%, Asset beta = 1.5, debt financing % of assets: 90% e. Volatility of Equity: 45%, Asset beta = 0.5, debt financing % of assets: 1% 16. Suppose you buy $100 worth of stock 1 and sell short $100 worth of the market portfolio. The expected market excess return is 8%. Stock 1 has a beta of 1.5. What is the expected $ profit on your portfolio after one year? a. $4 b. $8 c. $0, since you should not be able to beat the market d. Cannot tell without the risk‐free rate e. $12 17. Firm A has issued riskless debt of $1,000. It will keep this level forever. Firm B has issued riskless debt of $2,000 and keeps this level forever. Cash flows and the underlying assets of the firms are unrelated. The present value of firm 1’s tax shield is $300. What is the present value of the tax shield for firm 2? a. $300 b. $600 c. $450 d. Cannot tell without knowing the cash flows of the firm e. Cannot tell without knowing the beta of the underlying assets 18. One machine is bought for $400 and lasts for four years. The scrap value of the machine is zero. The interest rate is 5%. The tax rate is 35%. What is the present value of tax shields (coming from the depreciation) assuming straight‐line depreciation? a. $124.11 b. $400 c. $140 d. $35 e. $100 19. The expected return on equity is 20%. The expected return on debt is 10%. 50% of the assets are financed with debt. Debt will be rebalanced annually to ensure a fixed proportion of debt. The beta of assets is 1.5. The tax rate is 35%. What is the WACC? a. Cannot tell with this information b. 20% c. 15% d. 6.5% e. 13.25% Page 6 of 15 SHORT CONCEPT QUESTIONS Instructions: Answers must fit in the space provided. Irrelevant material will draw a penalty. If I do not ask for explanations, you do not need to explain! Every questions counts 6 points Questions are ordered according to topics in the class Question 1): Name 2 key differences between common stock (equity) and bonds! Question 2 a): What happens to prices of securities if expected returns increase? Question 2 b): Which securities will be more affected in their price if expected returns change? Securities whose payoffs occur far out in the future (long‐term securities) or whose payoffs occur sooner (short‐term securities)? (One sentence/bullet explanation is required) Question 3: Two almost identical firms in the timber industry decide to use different contracting standards. Firm 1 uses long‐run (10 years) nominal contracts whereas firm 2 uses short‐run contracts (1 year) with their customers. These contracts fully determine nominal revenue. Which firm will be most likely relatively better off if future inflation turns out to be significantly lower than expected? (Short explanation is required) Question: 4a) Explain the relation between IRR and yield to maturity! Question 4b): Can there be multiple yields to maturity for a standard coupon bond? Why? Page 7 of 15 Question 5: Two projects have the same (positive) NPV. Project 1 has high cash inflows early on whereas project 2 has high cash inflows out in the future. Which project would be chosen if the payback period method is applied? Explain shortly! Question 6: Name two reasons for a high P/E ratio of a firm! Question 7: Is this a sensible statement? “I am not going to sell this stock because the current market price is way below the price that I bought the stock at.” Why? Question 8 a): Write down the CAPM formula and explain each term (one bullet for each term). Give a realistic number for each term (annualized values)! Question 8b) Draw a qualitative graph of expected returns of stocks (Y‐Axis) against beta (X‐Axis). Assume rF = 10% and the expected market return is 20%. What is the slope of the line? Do all stocks have to lie on that line? Do realized returns have to lie on that line as well? Page 8 of 15 Question 9: Can a risky security be priced such that the current price is greater than the expected value of repayments in the future? In other words, could you think of a case in which you pay more than $1 today for something that pays (on average) $1 tomorrow. If yes, how can you interpret this security? If no explain why! Question 10: A publicly traded firm is 100% equity financed and has a beta 0.5. Suppose you want to make a $50 investment with a beta of 1. How can you achieve this using personal debt and the stock of this firm? Ignore taxes! Question 11: A firm produces expected cash flows of $1,000 forever. Due to a change in the business model, the all‐equity firm will change its beta from old 1 to new 0.5 after period 5 (period 6 cash flow has a different beta than period 5 cash flow). How would you (conceptually) account for the beta change when you value the company, i.e. what elements of the valuation equation will be affected by this? Your answer should not depend on the particular numbers I provided! Page 9 of 15 1. Loans (20 Points) You are considering the purchase of a shiny new convertible! The dealer is desperate to sell the car, and offers you a choice of two deals: Buy the car at its full price, $20,000, but finance it at the below market interest rate of 1% (EAR). In this case, you’d put down $5,000 in cash today, and borrow the rest of the purchase price from the dealer. The loan would require you to make equal payments at the end of each of the next 5 years (i.e. the payments would be 1, 2, 3, 4 and 5 years from today). Pay cash, but get the car for a discount of 15% off list price (i.e., $17,000). Assume you have plenty of cash in the bank, earning an interest rate of 8% per year. a. How big is each payment on the car loan? [5] b. What is the remaining balance on the loan immediately after you make the payment 3 years from today? [5] c. Assuming you are definitely going to buy the car, which option should you choose? [10] Page 10 of 15 2. CAPM (20 Points) All the answers to this question refer to the following plot that indicates the trade off between expected return and standard deviation of investments in an economy in which the CAPM holds exactly. To make things easy, can mark the points with the question number (e.g., a “b” marks the risk free rate). You might need to draw extra lines/curves. 0.20 0.15 0.10 0.05 0.1 0.2 0.3 0.4 a) Label the axes. [2] b) The risk free rate is 5%. Mark it on the plot. [2] c) Mark the market portfolio (you will need to make it clear on the plot why you chose one particular point). [3] d) Mark the efficient frontier (of all assets, including the risk free asset). [3] e) Mark an efficient portfolio that consists of a positive weight in risk free and risky securities. [2] f) Mark an efficient portfolio that consists of levered position in risky stocks. i.e. a portfolio where you buy stocks on margin. [2] g) Mark the portfolio of only risky assets that has the lowest standard deviation of all portfolios of risky assets. [3] h) What is the correlation of the portfolio in e) and the market portfolio? Answer below [3] Page 11 of 15 3. Pricing of Securities (20 Points) There are two securities trading in a competitive market. One period from now, security A will pay off $1,000 in good times and $500 in bad times. It has a price today of $600. Next period security B pays off $1,000 in bad times and $500 in good times and has a price of $700. The likelihood of good times and bad times is the same. a) What is the expected return of security A? [5] b) What is the expected return of security B? [5] c) Explain why the expected returns of the securities differ. Your answer must fit in the space provided. [5] d) Can you provide bounds on the risk‐free rate? (Extra credit question) [5] Page 12 of 15 4. Firm Valuation and NPV (20 Points) Your firm has outstanding 20,000 shares of common stock, each trading at $25. $500,000 worth of riskless debt. You plan to keep adjusting your debt/equity ratio every year in the future to keep it always the same as it is today. The beta of your firm’s equity is 2.1, the risk‐free interest rate is 5%, the risk premium on the market is 8%, and the firm faces a tax rate of 30%. Suddenly you learn about a new investment opportunity (in the same industry you’re currently in): You can buy 100% of the equity in Weeblesoft for $800,000. Weeblesoft is currently financed 100% with equity. You forecast that its (before tax) free cash flow next year will be $100,000, and that this will grow at 3% per year forever. Calculate the NPV of the acquisition. Should you make it? (Note: Calculate the NPV including the tax benefits of any debt you would issue in making this purchase, assuming you use the same debt‐equity ratio for the purchase as for the existing firm). Page 13 of 15 5. Options (15 Points) On the SAME plot, graph the value of following financial securities as a function of the price of General Electric (GE) stock. Label each plot with the question number. Please make this clear what the label refers to ‐‐‐ if you need to use different color or styles (lines, dashes, dots, etc) to make this clear then do so. a) GE European call option on the expiration day with a strike of $50. [5] b) A short position in a GE European put option on the expiration day with a strike of $50. [5] c) The stock itself, that is, GE, on the expiration day of the above two options. [5] Page 14 of 15 EXTRA CREDIT Question 1: Explain: The expected return on assets is just the weighted average of the expected return on debt and the expected return on equity. As leverage increases, the expected return on equity increases and the expected return on debt remains constant (as long as debt is risk‐free) or increases as well. If both components of assets (equity and debt) are (weakly) increasing in leverage, how is it possible that the expected return on assets remains constant? See also the picture below. Ignore taxes! [4] Leverage and Expected Returns 120% 100% 80% 60% 40% 20% 0% Expected Return D Expected Return E Expected Return A 0 500000 1000000 1500000
Face Value Zero Coupon Bond Question 2: Plot a standard efficient frontier of only risky securities (similar to CAPM question). Now assume that the lending rate is lower than the borrowing rate. Mark the set of efficient portfolios (with borrowing/lending and risky assets)? [10] Page 15 of 15 ...
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