Ejercicio de seminario 5, preguntas y respuestas PDF

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FINANCIAL MANAGEMENT I 2015 SEMINAR 5 1.

You are considering how to invest part of your retirement savings. You have decided to put $200,000 into three stocks: 50% of the money in GoldFinger (currently $25/share), 25% of the money in Moosehead (currently $80/share), and the remainder in Venture Associates (currently $2/share). If GoldFinger stock goes up to $30/share, Moosehead stock drops to $60/share, and Venture Associates stock rises to $3 per share, a.

What is the new value of the portfolio?

b.

What return did the portfolio earn?

c.

If you don’t buy or sell shares after the price change, what are your new portfolio weights?

a.

Let ni be the number of share in stock I, then

nG 

200, 000 0.5  4, 000 25

nM 

200,000 0.25  625 80

nV 

200,000  0.25  25,000. 2

The new value of the portfolio is

p  30nG  60nM  3nv

 $232,500. 232, 500 1  16.25% 200, 000

b.

Return 

c.

The portfolio weights are the fraction of value invested in each stock.

nG  30  51.61% 232,500 n  60  16.13% Moosehead: M 232,500 n 3  32.26% Venture: V 232,500 GoldFinger:

2.

Arbor Systems and Gencore stocks both have a volatility of 40%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) + 1, (b) 0.50, (c) 0, (d) −0.50, and (e) −1.0. In which cases is the volatility lower than that of the original stocks? stock vol 40% corr 50-50 Port 1 40.0% 0.5 34.6% 0 28.3% -0.5 20.0% -1 0.0%

Volatility of portfolio is less if the correlation is < 1. 3.

You have $100,000 to invest. You choose to put $150,000 into the market by borrowing $50,000. a.

If the risk-free interest rate is 5% and the market expected return is 10%, what is the expected return of your investment?

4.

b.

If the market volatility is 15%, what is the volatility of your investment?

a.

Er = 5% + 1.5  (10% – 5%) = 12.5%

b.

Vol = 1.5  15% = 22.5%

Assume the risk-free rate is 4%. You are a financial advisor, and must choose one of the funds below to recommend to each of your clients. Whichever fund you recommend, your clients will then combine it with risk-free borrowing and lending depending on their desired level of risk.

Which fund would you recommend without knowing your client’s risk preference? Sharpe ratios of A, B, and C are 0.6, .5, and 1, so you would choose C; it is the best choice no matter what your clients’ risk preferences are. 5.

In addition to risk-free securities, you are currently invested in the Tanglewood Fund, a broad-based fund of stocks and other securities with an expected return of 12% and a volatility of 25%. Currently, the risk-free rate of interest is 4%. Your broker suggests that you add a venture capital fund to your current portfolio. The venture capital fund has an expected return of 20%, a volatility of 80%, and a correlation of 0.2 with the Tanglewood Fund. Calculate the required return and use it to decide whether you should add the venture capital fund to your portfolio.

Required Return= 4%+[(0.8x(0.2)/0.25](12%-4%)=9.12% You should add some of the venture fund to your portfolio because it has an expected return that exceeds the required return.

6.

7.

Suppose the risk-free return is 4% and the market portfolio has an expected return of 10% and a volatility of 16%. Merck & Co. (Ticker: MRK) stock has a 20% volatility and a correlation with the market of 0.06. a.

What is Merck’s beta with respect to the market?

b.

Under the CAPM assumptions, what is its expected return?

a.

MRK  0.06 

b.

E R MRK  0.04 0.075 0.1 0.04  4.45%

0.2  0.075 0.16





You need to estimate the equity cost of capital for XYZ Corp. You have the following data available regarding past returns:

a.

What was XYZ’s average historical return?

b.

Compute the market’s and XYZ’s excess returns for each year. Estimate XYZ’s beta.

c.

Estimate XYZ’s historical alpha.

d.

Suppose the current risk-free rate is 3%, and you expect the market’s return to be 8%. Use the CAPM to estimate an expected return for XYZ Corp.’s stock.

e.

Would you base your estimate of XYZ’s equity cost of capital on your answer in part (a) or in part (d)? How does your answer to part (c) affect your estimate? Explain.

a.

(10% – 45%)/2 = –17.5%

b.

Excess returns: MKT 3%, –38% XYZ 7%, –46% Beta = (7 – ( –46))/(3 – ( –38)) = 1.29

c.

Alpha = intercept = E[Rs – rf] – beta  (E[Rm – rf]) = (7% – 46%)/2 – 1.29  (3% – 38%)/2 = 3.1%

d.

E[R] = 3% + 1.29  (8% – 3%) = 9.45%

e.

Use (d)—CAPM is more reliable than average past returns, which would imply a negative cost of capital in this case! Ignore (c), as alpha is not persistent.

9.

Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin’s equity beta is 0.85, the risk-free rate is 4%, and the market risk premium is 5%. If your firm’s project is all equity financed, estimate its cost of capital. Project beta = 0.85 (using all equity comp) Thus, rp = 4% + 0.85(5%) = 8.25%

10.

Consider the setting of Problem 18. You decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second firm, Thurbinar Design, which is also engaged in a similar line of business. Thurbinar has a stock price of $20 per share, with 15 million shares outstanding. It also has $100 million in outstanding debt, with a yield on the debt of 4.5%. Thurbinar’s equity beta is 1.00. a.

Assume Thurbinar’s debt has a beta of zero. Estimate Thurbinar’s unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar’s unlevered cost of capital.

b.

Estimate Thurbinar’s equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield, and using these results, estimate Thurbinar’s unlevered cost of capital.

a.

E = 20  15 = 300 E + D = 400 Bu = 300/400  1.00 + 100/400  0 = 0.75 Ru = 4% + 0.75(5%) = 7.75%

b.

Re = 4% + 1.0  5% = 9% Ru = 300/400  9% + 100/400  4.5% = 7.875%...