FIN 4424 HW 3&4

An unlevered firm has a value of $200 million. An otherwise identical but leverage firm has $80 million in debt and $120 million in equity. No growth is expected. Assuming a corporate tax rate of 40%, a tax rate on debt income is 25%, and a tax rate on stock income is 15%, what is the value of the levered firm?

$225.6 million vL=vU + (1-(1-Tc)(1-Ts)/(1-Td))*D D=80 vU=200 Tc=40% Td=25% Ts=15%

An unlevered firm's present value of operations is $400 million. An otherwise identical but levered firm has $50 million in debt. Assuming no taxes and bankruptcy costs, what is the present value of operations for the levered firm?

$400 million

An all-equity firm with 200,000 shares outstanding, Antwerther Inc., has $2,000,000 oof EBIT, which is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS). Its tax rate is 25%. The company is considering issuing $5,000,000 of 10.0% bonds and using the proceeds to repurchase stock. The risk free rate is 6.5%, the market risk premium is 5.0%, and the Beta is currently 0.90, but the CFO believes beta would rise to 1.10 if the recapitalization occurs. Assuming that the shares can be repurchased at the price that existed prior to the recapitalization, what would the price be following the recapitalization?

$74.01

E.C. Builders (ECB) has an unlevered value of $1 billion at the end of year 2021. Since year 2022, the firm decided to use debt in their capital structure, what the interest expense and potential financial distress cost in the following table. According to the trade-off theory, what is the levered value at the end of year 2021? (Assume discount rate 12% and Corporate tax rate 35%).

$997 million

Bailey and Sons has a levered beta of 1.10, its capital structure consists of 40% debt and 60% equity, and its tax rate is 25%. What would Bailey's beta be if it used no debt, i.e., what is its unlevered beta?

0.73

WMT has a levered beta of 1.20, its capital structure consists of 30% debt and 70% equity, and its tax rate is 35%. What would WMT's beta be if it used no debt, i.e., what is its unlevered beta?

0.94 Bl=Bu*[1+(1-T) * wD/We] Bl=1.20 D=30% E=70% Bu=0.94

Donald Gilmore has $100,000 invested in a 2-stock portfolio. $35,000 is invested in Stock X and the remainder is invested in Stock Y. X's beta is 1.50 and Y's beta is 0.70. What is the portfolio's beta? a. 0.65 b. 0.72 c. 0.80 d. 0.89 e. 0.98

0.98

Firm ABC uses no debt, it's beta is 1.10, and its tax rate is 40%. However, the CFO is considering moving to a capital structure with 30% debt and 70% equity. If the risk free rate is 5% and the market risk premium is to 6%, by how much would the capital structure shift increase the firms costs of equity?

1.70%

Hazel Morrison, a mutual fund manager, has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. Hazel expects to receive an additional $60 million, which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return?

1.76

Fiske Roofing Supplies' stock has a beta of 1.23, its required return is 11.75%, and the risk-free rate is 4.30%. What is the required rate of return on the market? (Hint: First find the market risk premium.) a. 10.36% b. 10.62% c. 10.88% d. 11.15% e. 11.43%

10.36%

Consider the following information and then calculate the required rate of return for the Universal Investment Fund, which holds 4 stocks. The market's required rate of return is 13.25%, the risk-free rate is 7.00%, and the Fund's assets are as follows: A $20,000 1.50 B $300,000 -0.50 C $500,000 1.25 D $1,000,000 0.75

11.77%

Firm ABC has an unlevered firm value of $50 million. The unlevered cost of equity is 12%. If firm ABC chooses to issue $10 million debt at the cost of debt is 8% and fund the remaining $40 million from equity. What is the cost of equity now with this new capital structure?

13% rE= r0+(r0-rD)*D/E r0= 12% rD= 8% rE= 12%+(12%-8%)*(10/40)

Cartwright Communications is considering making a change to its capital structure to reduce its cost of capital and increase firm value. Right now, Cartwright has a capital structure that consists of 20% debt and 80% equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6% and the market risk premium rM-rRF, is 5%. Currently the company's cost of equity, which is based on CAPM, is 12% and its tax rate is 25%. What would be Cartwright's estimated cost of equity if it were to change its capital structure t 50% debt and 50% equity?

14.84%

Laramie Trucking's CEO is considering a change to the company's capital structure, which currently consists of 25% debt and 75% equity. The CFO believes the firm should use more debt, but the CEO is reluctant to increase the debt ratio. The risk-free rate, rRF, is 5.0%, the market risk premium, RPM, is 6.00%, and the firm's tax rate is 25%. Currently, the cost of equity, rS, is 11.5% as determined by the CAPM. What would be the estimated cost of equity if the firm used 60% debt? (Hint: You must first find the current beta and then the unlevered beta to solve the problem.)

16.05%

Company A has a beta of 0.70, while Company B's beta is 1.20. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. What is the different between A's and B's required rates of return? (Hint: First find the market risk premium, then find the required returns on the stocks.)

3.38%

Assume that your cousin holds just one stock, Eastman Chemical Bonding (ECB), which he thinks has very little risk . You agree that the stock is relatively safe, but you want to demonstrate that his risk would be even lower if he were more diversified. You obtain the following returns data for Wilder's Creations and Buildings (WCB). Both companies have had less variability than most other stocks over the past 5 years. Measured by the standard deviation of returns, by how much would your cousins risk have been reduced if he had held a portfolio consisting of 60% in ECB and the remainder in WCB? (Hint: Use the sample standard deviation formula.) Avg. Return = 15% St. Dev. = 22.64%

3.84%

Suppose the market standard deviation is 25%. What i a portfolio standard deviation if its beta is 1.2?

30%

Sommers Co. issued a bond with a maturity of 10 years, a par value of $1000, and a coupon rate 5% with annual payments. The yield to maturity (YTM) is 7%, What is the bond modified duration?

7.4%

Curtis Corporation's noncallable bonds currently sell for $1,165. They have a 15-year maturity, an annual coupon of $95, and a par value of $1,000. What is their yield to maturity?

7.62%

Field Industries' outstanding bonds have a 25-year maturity and $1,000 par value. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $850. What is the bonds nominal (annual) coupon interest rate?

7.70%

Sommers Co. issued a bond with a maturity of 10 years, a par value of $1000, and a coupon rate 5% with annual payments. The yield to maturity (YTM) is 7%, What is the bond Macaulay duration?

7.9 years

Bloome Co.'s stock has a 25% chance of producing a 30% return, a 50% chance of producing a 12% return, and a 25% chance of producing a −18% return. What is the firm's expected rate of return?

9.00% Use =sumproduct in excel

Freedman Flowers' stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a −28% return. What is the firm's expected rate of return? a. 9.41% b. 9.65% c. 9.90% d. 10.15% e. 10.40%

9.90%

Assume that the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?

An index fund with beta = 1.0 should have a required return of 11%.

A stock with a beta equal to -1.0 has zero systematic (or market) risk.

False

An individual stock's diversifiable risk, which is measured by its beta, can be lowered by adding more stocks to the portfolio in which the stock is held.

False

Even if the correlation between the returns on two securities is +1.0, if the securities are combined in the correct proportions, the resulting 2-asset portfolio will have less risk than either security held alone.

False

For bonds, price sensitivity to a given change in interest rates is generally greater the higher coupon rate.

False

If an investor buys enough stocks, he or she can, through diversification, eliminate all of the market risk inherent in owning stocks, but as a general rule it will not be possible to eliminate all diversifiable risk.

False

Consider the following information for three stocks, A, B, and C. The stock's returns are positively but not perfectly positively correlated with one another, i.e., the correlations are all between 0 and 1. A 10% 20% 1.0 B 10% 10% 1.0 C 12% 12% 1.4 Portfolio AB has half of its funds invested in stock A and half in stock B. Portfolio ABC has one third of its funds invested in each of the three stocks. The risk free rate is 5%, and the market is in equilibrium, so required returns equal expected returns. Which of the following statements is CORRECT?

Portfolio ABC's expected return is 10.66667%.

Charlie and Lucinda each have $50,000 invested in stock portfolios. Charlie's has a beta of 1.2, an expected return of 10.8%, and a standard deviation of 25%. Lucinda's has a beta of 0.8, an expected return of 9.2%, and a standard deviation that is also 25%. The correlation coefficient, r, between Charlie's and Lucinda's portfolios is zero. If Charlie and Lucinda marry and combine their portfolios, which of the following best describes their combined $100,000 portfolio?

The combined portfolio's beta will be equal to a simple weighted average of the betas of the two individual portfolios, 1.0; its expected return will be equal to a simple weighted average of the expected returns of the two individual portfolios, 10.0%; and its standard deviation will be less than the simple average of the two portfolios' standard deviations, 25%.

Other things held constant, which of the following events is most likely too encourage a firm to increase the amount of debt in its capital structure?

The corporate tax rate increases.

Assume that in recent years both expected inflation and the market risk premium (rM − rRF) have declined. Assume also that all stocks have positive betas. Which of the following would be most likely to have occurred as a result of these changes?

The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

Ann has a portfolio of 20 average stocks, and Tom has a portfolio of 2 average stocks. Assume their portfolio betas are the same, which of the following statements is correct?

Tom's portfolio will have more diversifiable risk, the same market risk, and thus more total risk than Ann's portfolio, but the required (and expected) returns will be the same on both portfolios.

"Risk aversion" implies that investors require higher expected returns on riskier than on less risky securities.

True

A firm's capital structure does not affect its calculated free cash flows, because FCF reflects only operating cash flows.

True

Any change in its beta is likely to affect the required rate of return on a stock, which implies that a change in beta will likely have an impact on the stock's price, other things held constant.

True

Bad managerial judgments or unforeseen negative events that happen to a firm are defined as "company-specific," or "unsystematic," events, and their effects on investment risk can in theory be diversified away.

True

Different borrowers have different risks of bankruptcy, and bankruptcy is costly to lenders. Therefore, lenders charge higher rates to borrowers judged to be more at risk of going bankrupt.

True

Diversification will normally reduce the riskiness of the portfolio of stocks.

True

Financial risk refers to the extra risk stockholders bear as a result of using debt as compared with the risk they would bear if no debt were used.

True

For bonds, price sensitivity to a given change in interest rates is generally greater the longer before the bond matures.

True

If a stock's expected return as seen by the marginal investor exceeds this investor's required return, then the investor will buy the stock until its price has risen enough to bring the expected return down to equal the required return.

True

If a stock's market price exceeds its intrinsic value as seen by the marginal investor, then the investor will sell the stock until its price has fallen down to the level of the investor's estimate of the intrinsic value.

True

LeCompte Learning Solutions is considering making a change to its capital structure in hopes of increasing its value. The company's capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table: 0.1 0.9 0.10/0.90 = 0.11 AAA 7.0% 0.2 0.8 0.20/0.80 = 0.25 AA 7.2% 0.3 0.7 0.30/0.70 = 0.43 A 8.0% 0.4 0.6 0.40/0.60 = 0.67 BBB 8.8% 0.5 0.5 0.50/0.50 = 1.00 BB 9.6% The company uses the CAPM to estimate its cost of common equity, rs. The risk-free rate is 5% and the market risk premium is 6%. LeCompte estimates that if it had no debt its beta would be 1.0. (Its "unlevered beta," bU, equals 1.0.) The company's tax rate, T, is 25%. On the basis of this information, what is LeCompte's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure?

ws=0.8; wd=0.2; WACC=10.87%