Performance measurement : Questions

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Kathleen Merritt
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1 Performance measurement : Questions 1. Cacor fund manager promises you Cac40 return + 0,1%. Can we say that the fund beats the market? 2. If one observes time-series correlation in a fund s returns, does that mean that the fund beats the market? 3. What are the characteristics of a portfolio which has the highest Sharpe ratio? 4. Are high management fees a sign of the quality of the fund s management? 5. Give the definition of active management risk. 6. Give the definition of active management return. 1 Lex Diapo Suite Menu < Retour

2 Cost of capital : Questions 1. If the firm does not pay out dividends, is equity less costly debt? 2. Does an increase in cost of debt necessarily increase firm s cost of capital? Justify your reasoning. 3. Cost of capital follows a U-shaped curve with respect to cost of debt. True or false? 4. If market capitalization of a company goes down, everything else constant cost of debt goes up. Yes or no? 5. A company has issued debt at 8 % 2 years ago Currently, the company is negotiating an identical debt at 4%. Is company s cost of debt 8% or de 4%? 6. If the company s stock price has gone up significantly, its cost of capital has: i) gone up, ii) gone down, iii) not been affected, iv) it is not possible to answer 7. Is self-financing cheaper than equity financing? 2 Lex Diapo Suite Menu < Retour

3 Investment decisions: Questions 1. Do companies have to self-finance replacement investments? 2. Do companies invest only when their net income is positive? 3. Does an investment earning a return higher than cost of capital create value? For whom? 4. NPVs of projects A and B are 101 and 10O, respectively. Should the company prefer A over B regardless of the cost of investment? Even if project A costs 3 times that of B? 5. Two projects have the same NPV. First project has a life time of three years and the second one 6 years. Which project should the company choose? Discuss. 3 Lex Suite < Retour

4 Decomposition (16-3) Decompose shareholders required return on equity into its economic and financial risk premium components. Solution Shareholders required return on equity is the sum of tree components 1.Risk-free rate R f,0 2. Economic risk premium ( R U,1 ) R f, 0 3. Financial risk premium which is the compensation for deferrred consumption; ~ E ( R ) E( ) L,1 R U,1 4 Lex Diapo Suite Menu < Retour ~ If the company is levered, this third component is also justified by riskaversion. ~ Sum of the three components is equal to: ( ) ~ E as a result of investors risk-aversion; E R L,1 Remember: E ~ ~ ( R ) = R + [ E( R ) R ] L,1 f,0 U,1 f,0 1 1 L

5 Capital structure and beta (16-4) A company s capital is financed by 35% equity and 65% debt. Its stock beta, estimated based on last 5 years market data, is If the risk-free rate is 7.8% and price of risk is 8.3%, calculate required return on shareholders equity. 2. Calculate its asset beta. 3. Calculate the return which will help the company to evaluate projects of similar risk with its current operations. 4. Repeat the same calculations, this time assuming that company s debt beta is Lex Diapo Suite Menu < Retour

6 Multi-activity company and beta (16-5) A multi-activity company X has 3 divisions with following weights: Division % of X s value Mechanics 50% Electronics 30% Aeronautics 20% In each of its divisions, the company faces competition. The characteristics of representative competitors in each industry is given below: Compan y Equity β A : Meca B : Elec C : Aero X? D/(D+E) Furthermore, the debt of companies A, B, and C are riskless, the risk-free rate is 7% expected return on the market is 15% 6 Lex Diapo Suite Menu < Retour

7 Multi-activity company and beta (Questions) 1. Calculate each division s asset beta. 2. What is company X s equity beta? 3. What is company X s cost of capital? 4. What is the cost of capital of each division? 5. Same questions, this time assuming companies A, B, and C each has debt beta of Lex Diapo Suite Menu < Retour

8 Cost of capital with comparable companies (16-7), exam june 2006 In 1989, General Motors is looking at the possibility of acquiring Hughes aircraft corporation. GM plans to evaluate Hughes by taking weighted average of two comparable companies, Lockheed et Northrop. Furthermore, Hughes corporation expects to distribute a dividend of $300 m in 1990, which is expected to grow at a rate of 5%. GM s expected return is 15,2% and market risk premium is 6%. 1. Why doesn t GM use its own beta to estimate Hughes cost of capital? 2. Calculate Hughes cost of capital. 3. Calculate Hughes value. Beta Debt/equity GM 1,20 0,4 Lockheed 0,90 0,9 Northrop 0,85 0,7 8 Lex Suite < Retour

9 Investment with equity financing A project has the return characteristics presented in the below table. The risk-free rate is 9% and the company is planning to finance the project via equity financing State Probability Project Market Return Return 1 0,25-20% -8% 2 0,50 +16% +14% 3 0,25 +52% +28% Questions : 1. What is the cost of capital for the project? 2. Should shareholders accept/reject the project? N. Mourgues (1993, Economica, p. 121) 9 Lex Diapo Suite Menu < Retour

10 Investment decision (16-1) Equity beta of company X is 1.2. For each 100 worth of shares the company has 50 worth of debt. The risk-free rate is 5%. Expected market return is 15% Questions : 1. What is the cost of capital? 2. The company has a potential project with an expected return of 12%. Should the company accept the project? 10 Lex Diapo Suite Menu < Retour

11 Mutually exclusive (16-2)(exam June 2000) A company has to choose between two mutually exclusive projects A and B. The time the decision taken is denoted by 0. Both projects require an initial investment of 1500 at time 0, and will earn a sure cash flow of 1500 at time 1 (one year later). On top of the sure cash flows, the projects are expected to earn the following random cash flows depending on the state of the economy : State of the economy Proba bility Cash flow Rm Firm Project A Project B Very good 1/ % 40% Average 1/ % 10% Below 1/ % 0% average Very bad 1/ % -5% continued 11 Lex Diapo Suite Menu < Retour

12 continued The risk-free rate is4%. Rm stands for the expected return on the market portfolio. The last column in the table presents return on shareholders equity. The company is levered and pays 10% interest on its debt. The principal and interest to be paid next year is 2000, and the value of debt is recorded as 1818 on the balance sheet of the company. The debt is assumed to be risk-free. Shareholders equity comprises 500 shares with nominal value 10 per share. Price per share in the stock market is 20. Company s P/E ratio estimated by I/B/E/S is 9. Assume that taxes do not play any role on company s financial and investmend decisions. 1. What is the company s debt ratio? (1 point) 2. Calculate the return and risk (volatility and beta) of both projects (2 points) 3. What is the company s cost of capital according to CAPM? (2 points) 4. What is the company s cost of capital according to CAPM, assuming that the company can finance the projects by borrowing 2000 at 5% (1 point) 5. What is the shareholders required return on equity? (1 point) 6. Which decision does the company take: Invest or don t invest? If invest, which project?(2 points) 7. What is the relationship between equity beta of the company and its leverage? 8. What would the equity beta be if it is measured using weekly returns of the company observed in the stock market? (1 point) 9. If you measure equity beta using monthly returns what would the company s equity beta be? (1 point) 12 Lex Diapo Suite Menu < Retour

13 Capital structure and NPV (16-6) A company is fully equity financed. Its equity beta is 1. The risk-free rate is 10%. Expected return on the market is 15%. 1. What is the required return by shareholders on a project whith similar risk to company s current activities? 2. If the project s beta is 1.6, what is the required return on the project? 3. The above project requires an initial investment of 10 millions and is expected to generate 2.3 millions per year over the next 10 year. a. Calculate its NPV using company s required rate of return. b. Calculate its NPV adjusting for the proper risk of the project. 13 Lex Diapo Suite Menu < Retour

Decomposition (16-3)

Decomposition (16-3) Decompose shareholders required return on equity into its economic and financial risk premium components. Solution Shareholders required return on equity is the sum of tree components