Decomposition (16-3)

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1 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 This third component is also justified by R E L,1 R U,1 Sum of the three components is equal to: E ~ E as a result of investors risk-aversion; shareholders risk-aversion. ~ R L,1 Remember: E ~ R R E R L,1 f,0 ~ U,1 R f,0 1 1 L 1 Lex Diapo Suite Menu <

2 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 <

3 Capital structure and beta (solution) 1. Shareholders required return on equity is given by CAPM: E( Ri ) R f i[ E( Rm ) R f ] 7.8% % 10.79% 2. The company is levered. therefore shareholders also bear financial risk. We know that Thus. 1 L U U 1 1 L U D E 3 Lex Diapo Suite Menu <

4 Capital structure and beta (solution) 2. Shareholders required return on equity can be decomposed as follows : D E( Ri ) R f U[ E( Rm ) R f ] U [ E( Rm ) R f ] E economicrisk premium financial risk premium % % % 1.05% % Asset beta is related with economic risk of the company and thus corresponds to unlevered equity beta, u in previous question, which is Lex Diapo Suite Menu <

5 Capital structure and beta (solution) 3. Required return on a project with similar risk to the company s current projects is given by weighted average cost of capital (WACC). It can be calculated in two ways: a. Weighted average of differents sources of capital. Cost of capital corresponds weighted average of cost of equity, E(R i ) calculated in question 1, and cost of debt which is the risk free-rate R f. Thus we have: WACC % % 8.85% b. Required return on assets. or return relevant to economic risk: E( R ) R [ E( R ) R ] a f U m f 8.85% 5 Lex Suite <

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: Company Equity D/(D+E) A : Meca B : Elec C : Aero X? 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 <

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 <

8 Multi-activity company and beta (Solutions) 1. Equity betas correspond to betas of companies A, B, and C. To obtain asset betas, we should calculate the beta of an unlevered company (as if the company had no debt): 1 D L U U 1 1 L E MECA U ELEC U (1 L (1 L MECA ELEC ) ) MECA L ELEC L 0, AERO U (1 L AERO ) AERO L Company X can be viewed as a portfolio of 3 assets (divisions). Therefore, its equity beta is: X E 50% % % Equity beta X U 50% % % Asset beta Assuming no debt 8 Lex Diapo Suite Menu <

9 Multi-activity company and beta (Solutions) 3. Cost of capital is the return required by shareholders in order to tie up their capital into the company s assets Using security market line : WACC 7% % % 4. Taking into account the divisons, we have : WACC MECA 7% % 11.48% WACC ELEC 7% 1.288% 17.24% WACC AERO 7% % 12.76% 9 Lex Diapo Suite Menu <

10 Cost of capital with comparable companies (16-7), exam june 2004, 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 and Northrop. Furthermore, Hughes Corp. 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 Lockheed Northrop Lex Suite <

11 Comparables. solution 1. The acquirer (GM) and the target (Hughes) are in different industries (with different risks, different assets). Thus, the economic risk of two companies is not comparable. 2. Shareholders required return on equity can be calculated via observed risk (beta) and return on debt. We know that: 1 D L U U 1 1 L E Thus Lockheed U Northrop 1 U Shareholders expected return on GM (15.2%) and market risk premium (6%). helps us to evaluate the risk free rate: 11 Lex Suite <

12 Comparables (corrigé. suite) R R f f E ~ R 8% GM GM MRP Cost of capital is obtained by using SML. For Lockheed, this is % ( *6) and for Northrop it is 11% (8+0.5*6). Thus, the weighted average is %. 3. Using Gordon s dividend discount model and assuming infinite life for the company gives: V=300/( )= million USD 12 Lex Suite <

13 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 % -8% % +14% % +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) 13 Lex Diapo Suite Menu <

14 E(P)=0.25*(-20)+0.5* *52=16% E(M)= 0.25*(-8)+0.5* *28=12% Var(P)=0.25*(-20-16) *(16-16) *(52-16) 2 =648 Var(M)=0.25*(-8-12) *(14-12) *(28-12) 2 =166 Cov(P,M)=0.25*((-20-16)*(-8-12))+0.5*((16-16)*(14-12) +0.25*((52-16)*(28-12))=324 Β P =Cov(P,M)/Var(M)=324/166= Lex Suite <

15 Investment with equity financing(solution) Project Market E( R ) 16% 12% s( R ) 25.45% 12.88% Cov(R i,r m ) 324 i % 14.85% Shareholders required return on equity : E( R ) = 9% [12% - 9%]=14.85% 1.95 Project s expected return = 16% > 14.85% Accept the project. 15 Lex Diapo Suite Menu <

16 Investment with equity financing(solution) To calculate cost of capital (assuming the projects is of similar risk to that of company s ongoing projects), first we need to find the risk (beta) of the project: State Probability Return on Project Market 1 0,25-20% -8% 2 0,50 16% 14% 3 0,25 52% 28% Expected return 16% 12% Variance of returns 6,48% 1,66% Standard deviation of returns 25,46% 12,88% Covariance of returns with the market 3,24% Beta 1,95 The company has no debt, thus U et L are equal, hence cost of capital is 9% x (12% - 9%) = 14.85% 16 Lex Suite <

17 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? 17 Lex Diapo Suite Menu <

18 U Investment decision (correction) The beta of unlevered company is : L Cost of capital is: E L 1, 2 1 0, 8 R L R ER 1 L U,1,0 1 5% 3 or alternatively: E f L,1 18 Lex Diapo Suite Menu < 1 3 5% % 5% 1 13% 17% 5% % 5% 13% R U, 1 The company should not take the project as its expected return is less than shareholders required rate of return (cost of capital).

19 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 expenditure 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 average 1/ % 0% Very bad 1/ % -5% continued 19 Lex Diapo Suite Menu <

20 continued The risk-free rate is 4%. 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 and the value of debt is recorded as 1818 on the balance sheet of the company. The debt is assumed to be risk-free in the market. Shareholders equity comprises 500 shares with nominal value of 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 investment 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) 20 Lex Diapo Suite Menu <

21 Mutually exclusive (solution) State of economy Probability Cash flow Rm Project A Project B Very good 0, % Average 0, % Below average 0, % Very bad 0, % Investment Return 0,25 26,67% 33,33% 30% 0,25 26,67% 26,67% 15% 0,25 20,00% 13,33% 0% 0,25-6,67% -13,33% -2% Pi Xi 6,67% 8,33% 7,50% 6,67% 6,67% 3,75% 5,00% 3,33% 0,00% -1,67% -3,33% -0,50% 21 Lex Diapo Suite <

22 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. 22 Lex Diapo Suite Menu <

23 Capital structure and NPV (solution) 1. The required return on the project could be found using CAPM. Because the project is of similar risk, one can use company s equity beta (given that it is unlevered) and find 10% + 1*(15% - 10%) = 15% 2. If the project s beta is 1.6, then E(R) = 10% + 1.6*(15% - 10%) = 18% 3. For the given cash flows: 10 t1 2.3 (1WACC ) a. Assuming company s risk, cash flows should be discounted at 15%, implies an NPV of 1.54 millions b. Assuming project s specific risk, cash flows should be discounted at 18%, implies an NPV of million Lex Diapo Suite Menu <

Performance measurement : Questions

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