1. An investor holds two well-diversified portfolios on US securities. The expected return on portfolio A is 12% and the expected return on portfolio B is 8%. The investor identified that the US economy has only one factor (industrial production), and βA= 1 and βB= 0.7. What should be the risk-free rate according to the APT?
2. An investor holds shares of Bank of Montreal. The Canadian stock market can be explained by three sources of systematic risk: short-term interest rates (I), the rate of inflation (P), and industrial production (Y). Short-term interest rates have an associated risk premium of 3%, inflation has an associated risk premium of 7% and industrial production has an associated risk premium of 1%. Each systematic factor has a mean value of zero, so that non-zero factor values represent unexpected surprises from prior expectations.
The excess return for the stock can be described by the following formula:
R = 0.12 + 0.8 I + 0.3 P + 1.1 Y + e
What is the stock's alpha according to the APT? Enter your answer as a decimal number or with the percentage sign.
3. A. If the return on a passive, index-tracking fund is 7.3% and a particular active fund in the same sector returns 8.3%, what should be the return on the average active fund in the same sector, before fees, according to the article "The arithmetic of active management"by William Sharpe?
B. If fees on active funds in that sector are 1% of assets under management (AUM) on average, and are paidannuallyin arrears (at the end of each year), what is the annual return on the average active fund in that sector after fees?
4. There are 10,000 mutual fund managers. 20 claim that they are the best, since their fund beat the relevant index every year for 7 years.
However, you think that markets are efficient and that the average fund manager is as likely to deliver a better performance than the index as to underperform the index, before fees.
a. What is the probability that the average single fund managers beats the index 7 years in a row (before fees)?
b. How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?
5. LightWorks Inc. has a cost of equity of 9%. The firm will pay an annual dividend of $2.1 in one year and its dividends had been expected to grow by 6% per year thereafter. You just heard on the news that LightWorks has changed its growth forecasts and now expects its dividend to grow by 4% per year forever after the first year.
a. What is the changein the intrinsic value of LightWorks (in $)? Choose the right sign.
b. If you tried to sell LightWorks stock immediately after the news broadcast, what price would you most probably get?
6. Minnow Mining Corp.has $170 million of interest-bearing debt, with an average coupon rate of 6.3%.The debt will be kept constantforever.Its average tax rate is 34%.
a. What is the annual interest tax shield (in $ million)?
b. What is the present value of all future annual interest tax shields (in $ million)?
7. Better Home and Garden (BHG) expects an EBIT of $190,000 every year forever. The company currently has no debt, and its unlevered cost of capital is 12%. Its average tax rate is 34%. The company wants to borrow $418,000 to repurchase shares. The debt will have an interest rate of 6.6% and will be kept constant forever.
a. What is the value of the firm without debt?
b. What is the value of the firm with debt?
8. NGB Inc. is evaluating a project that will cost $270,000 initially and will generate free cash flows of $297,000 in one year. The company has no other projects. Its market value of equity is $189,000 and it has borrowed $81,000 at an interest rate of 2%. Assume perfect capital markets.
a. What is the company'scost of levered equity?
b. What is the company'scost of unlevered equity?
9. Fast Inc.has no debt and a WACC of 10%. The company now changes its capital structure to a debt-to-equity ratio of 0.3. The interest rate on debt is 5.7%, the new cost of equity is 10.97% and the tax rate is 25%.
a. What is the company's new WACC?
10. Glacier Inc. has no long-term debt. Its cost of equity is 16% and there are no taxes.
The board of directors decided to change its capital structure such that the debt/equity ratio becomes 1.2. The company can borrow at an interest rate of 8%.
a. What was the WACC before the restructuring?
b. What is the new cost of equity?
c. What is the new WACC (without taxes)?
11. A new firm requires an initial investment of $1,000 and will generate a before-tax gross return of $2,500 after one year. The firm is 20% financed with debt at an expected return of 3%.
The appropriate unlevered after-tax cost of capital is 14% and the marginal income tax rate is 21%.
a. What is the weighted average cost of capital?
b. What is the present value of the cash flows using the weighted average cost of capital?
c. How much debt does the company have (in $)?
d. What is the APV?
12. You've gathered the following information for Holly Corp.:
Current debt-to-equity ratio: 0.6
Current beta: 1.1
Risk-free rate: 2%
Expected return on market portfolio: 8%
Tax rate: 40%
a. What is the current cost of equity?
b. What would be the firm's cost of equity if it didn't have any debt?
13. LVMH currently has a debt-to-capital ratio of 10% and an average tax rate of 34%. LVMH's bonds have a 3% yield to maturity. Using the CAPM, the firm estimates that its cost of equity is 11%.
The firm is considering a new capital structure with a debt-to-capital ratio of 20%.An investment bank has estimated that the yield to maturity on the company's bonds would rise to 6%.
The risk-free rate is 2% and the expected equity market risk premium (MRP) is 7%.
a. What is LVMH's current WACC?
b. What is the beta of LVMH's common stock?
c. What would be the beta if the company didn't have any debt (unlevered beta)?
d. What would be the new beta if the company went ahead with the recapitalization?
e. What would be the new cost of equity after the recapitalization?
f. What would be the new WACCafter the recapitalization?
14. Apollo Inc has a stock price of $56. The company is considering two dividend policies:
- Paying no dividend
- Paying an annual dividend of $4.07
Without dividend payments, the stock price is expected to grow by 4% per year. The capital gains tax is zero and the dividend tax rate is 15%.
a. What total return is necessary for policy 2 (with dividends) to have the sameafter-tax return as policy 1 has currently?
15. A company has had net income of $22 million in its most recent year and wants to distribute 40% of its net income to shareholders through either dividends or stock repurchases. The firm currently has 2 million shares outstanding, trading at $60.
a. What is EPS after adividend payment?
b. What is EPS after astock repurchase?
c. Would shareholders be better off with a stock repurchase compared to a dividend payment (ignore taxes and signalling effects)?
-No, since EPS won't be higher in the future.
-No, since the higher EPS comes at a cost.
-Yes, since the company bought their shares.
-Yes, since it increases EPS.
16. Google has 330 million shares outstanding and the following market value balance sheet (in $ billion):
Assets
|
|
Liabilities & Equity
|
Current assets
|
60
|
Current liablities
|
14
|
Fixed assets
|
39
|
Equity
|
85
|
|
|
|
|
|
|
a. What is the current stock price?
b. Google just decided to pay out $20 billion in dividends. What is the dividend per share?
c. The ex-dividend date is tomorrow. What opening stock price do you expect on the ex-dividend date? Assume perfect capital markets.
d. If Google decided to spend $20 billion on buying back its own shares instead of paying dividends, what would be the stock price?
17. The futures price per troy ounce of gold delivered in 3 months is as follows:
Day
|
Futures price
|
0
|
1,232
|
1
|
1,235
|
2
|
1,229
|
3
|
1,226
|
a. You bought one futures contract on day 0. What is your daily profit on day 1 (in $)?
b. What is your daily profit on day 2 (in $)?
c. What is your daily profit on day 3 (in $)?
d. If the initial margin requirement is 10%, how much money do you have to put into your brokerage account?
e. What is the balance in your margin account at the end of day 1?
f. What is the balance in your margin account at the end of day 2?
g. What is the balance in your margin account at the end of day 3?
18. On June 1, an investor bought one September maturity Treasury-bond futures contract at a price of $121,415 with an initial margin requirement of 15%.
What would be the percentage profit (loss) for the investor if the futures price is $116,424 on August 1?
19. An investor currently holds a bond portfolio worth $32 million. The portfolio has a modified duration of 6 years. The investor decides to hedge their position by selling T-bond futures with a modified duration of 8.4 years. The futures price is $92 per $100 par value, and the contract multiplier is $1,000.
a. What is the price value of a basis point for the bond portfolio (in absolute terms)?
b. What is the price value of a basis point for the futures contract(in absolute terms)?
c. How many T-bond futures does the investor have to sell?
20. Suppose that the current exchange rate is $1.26 per Euro. The Euro yield curve is flat at 2.8% and the U.S yield curve is flat at 3.1%.
a. What should be the 1-year forward exchange rate (in USD per EUR)?
b. What should be the 2-year forward exchange rate (in USD per EUR)?
c. What should be the swap rate on an agreement to exchange currencies over a 2-year period (in USD per EUR)?
21. The following table provides put option data for Ashsteel Inc. (expiration in September). Each contract is for 100 options.
Contract
|
Strike
|
Bid
|
Ask
|
%change
|
ASIUW.X
|
190
|
3.85
|
4
|
3.74
|
ASIUG.X
|
192
|
5.25
|
5.5
|
1.76
|
ASIUM.X
|
195
|
7
|
7.5
|
6.24
|
ASIUK.X
|
200
|
11.05
|
11.55
|
5.64
|
a. How many contracts do you need to buy to obtain the right to sell 1,100 shares?
b. How much would it cost to obtain the right to sell 1,100 shares for $195 each?
c. Which put contract of the 4 above is selling at the lowest price?
-ASIUK.X
-ASIUM.X
-ASIUG.X
-ASIUW.X
d. Which put contract of the 4 above is selling at the highest price?
-ASIUK.X
-ASIUG.X
-ASIUW.X
-ASIUM.X
22. Two months ago, you bought a put option on Apple stock with a strike price of $148, which expires today.
a. What is the payoff if the stock price is $158 today?
b. What is the payoff if the stock price is $138 today?
23. Two months ago, you sold a call option on Apple stock with a strike price of $138, which expires today.
a. What is the payoff if the stock price is $147 today?
b. What is the payoff if the stock price is $129 today?
24. A European call option on Google stock costs $32. It expires in 0.5 years and has a strike price of $850. Google does not pay dividends and its stock price is $860. The risk-free rate is 0.7% (EAR).
a. What should be the price of aput option with the same strike price and expiration date?
26. A put option on a stock with a current price of $76 has a strike price of $89.
What is the intrinsic value of the option?
a. What is the intrinsic value of the option?