Deck 2: Valuation and Financing Decisions in an Ideal Capital Market

Question 1

Using the Binomial Model, find the values of a firm's levered equity (E_L), and the expected return on the equity, r_LE, given the following values: V=100, u=1.3, d=1/u, p=0.7, r_f=5%, X=100, and T=3.

Answer 1

D

Question 2

The expected returns on the debt and equity of a levered firm are r_E=15% and r_D=7%, and the current market value of the debt and equity are E=66 and D=44, respectively.What is the firm's weighted average cost of capital (WACC)?

A)7.8%
B)9.8%
C)11.8%
D)13.8%

Answer 2

11.8%

Question 3

Using the Binomial Model, find the value of a firm's levered equity (E_L) given the following values: V=100, u=1.3, d=1/u, p=0.7, r_f=5%, X=100, and T=3.     EL

A) 32.34
B) 27.34
C) 23.96
D) 18.96

Answer 3

18.96

Question 4

The market value of Delaware East's assets is $100 mn.The firm has one issue of pure-discount debt outstanding which promises to pay $60 mn.in 5 years.If the standard deviation of the firm's assets is 22% and the risk-free rate is 5%, what are the values of the firm's equity and debt, based on the Black-Scholes model?

Question 5

Until now, Delaware East, Inc.has been an all-equity firm; its most recent market equity value was $100 mn., and its cost of equity (and cost of assets) is 15%.Now, the firm decides to increase its leverage by issuing $40 mn.in debt, with the proceeds being used to pay a dividend to shareholders.The cost of the debt is r_D=7%.What is the firm's new cost of equity capital, according to Modigliani and Miller's Proposition II?

A)15.33%
B)18.20%
C)20.33%
D)22.50%

Question 6

Suppose you develop a mutual fund that includes 78 stocks, all with equal weights in the fund's portfolio.The average standard deviation of the stocks is 44%, and the average pair-wise correlation among the stocks is 0.30.What is your estimate of the standard deviation of the fund's portfolio?

A)19.5%
B)24.5%
C)29.5%
D)34.5%

Question 7

Firm XYZ is currently financed entirely with equity.The market value of the firm's assets and equity is V_U=E_U=500, and the expected return on the firm's assets and equity is r_A=r_E=12.5%.Suppose the firm issues debt with a value of D_L= 200, and uses the proceeds to retire equity.The market value of the firm remains the same, V_L=E_L+D_L=500.If the expected return on the debt is r_D=7%, what is the expected return on the firm's levered equity?

A)15.33%
B)18.20%
C) 20.33%
D)23.00%

Question 8

For your retirement fund, you have decided to place 40% of your contributions into a riskfree asset that pays 4% interest per annum, and the remaining 60% of your contributions will be placed in an available stock mutual fund that approximates the holdings of the mythical market portfolio.You expect this fund to provide an average return of r_P=9%, but will expose you to risk, measured in terms of an estimated standard deviation of $\sigma$ _P=20%.What is your estimate of the expected return and standard deviation of your complete portfolio, r_C and $\sigma$ _C, respectively?
$\begin{array}{ll}&1' \mathrm{P} & \sigma_{\mathrm{P}} \\a.&6 \% & 5.9 \% \\b.&6 \% & 20.0 \% \\c.&7 \% & 12.0 \% \\d.&7 \% & 20.0 \%\end{array}$

Question 9

For the equity of Delaware East, $\beta$ =1.25.If the expected return on the market is 15% and the risk-free rate is 5%, what is the expected return on the firm's equity?

A)12.50%
B)15.00%
C)17.50%
D)18.75%

Question 10

The expected returns and standard deviations for stocks A and B are r_A=14% and r_B=19%, respectively, and $\sigma$ _A=23% and $\sigma$ _B=34%, respectively.The correlation of the returns on the two stocks is $\sigma$ _AB=0.3.What is the expected return, r_P, and standard deviation, $\sigma$ _P, of a portfolio with weights of w_A=0.60 and w_B=0.40 in stocks A and B, respectively?
$\begin{array}{ll}&1' \mathrm{P} & \sigma_{\mathrm{P}} \\a.&16 \% & 22.1 \% \\b.&16 \% & 24.8 \% \\c.&17 \% & 22.1 \% \\d.&17 \% & 24.8 \%\end{array}$

Question 11

Which of the following assumptions of an ideal (or perfect) capital market most closely relates to the assumed symmetry of information set shared by all firms and all investors?

A)Capital Markets are frictionless
B)Homogeneous expectations
C)Atomistic competition
D)The firm has a fixed investment program
E)Once chosen, the firm's financing is fixed

Question 12

Suppose you develop a mutual fund that includes 500 NYSE stocks, all with equal weights in the fund's portfolio.The average standard deviation of the stocks is 36%, and the average pair-wise correlation among the stocks is 0.40.What is your estimate of the standard deviation of the fund's portfolio?

A)19.9%
B)22.8%
C)26.2%
D)32.1%

Question 13

Suppose the beta of the stock of Microsoft, Inc.is $\beta$ _msft=1.45.If r_f=4% and r_M=9%, what is the equilibrium expected return on Microsoft stock, r_msft, according to the CAPM? As an analyst of the firms in the high-technology industry, you expect Microsoft to provide a return of 10% over the next year.Comparing your estimate with equilibrium expected return on Microsoft that you just calculated, would you recommend to your investors that they buy Microsoft stock?

A)Yes: Microsoft is underpriced
B)No: Microsoft is overpriced

Question 14

Until now, Delaware East, Inc.has been an all-equity firm; its most recent market equity value was $80 mn., and its cost of equity (and cost of assets) is 15%.Now, the firm decides to increase its leverage by issuing $40 mn.in debt, with the proceeds being used to pay a dividend to shareholders.The cost of the debt is r_D=7%.What is the firm's new cost of equity capital, according to Modigliani and Miller's Proposition II?

A)15.33%
B)18.20%
C) 20.33%
D)23.00%