1. You find the following quotation for a stock:
Stock (ticker)
|
Div
|
Yld%
|
PE
(ttm)
|
High
(ttm)
|
Low
(ttm)
|
Volume
(100)
|
Last
|
Change
|
AAPL. 2.92. 1.56. 18.17. 207.4 177.14. 28,443. 193.47. 2.85
a. What was the most recent stock price?
b. What was the close price on the day before the one reported in the table?
2. You find the following quotation for a stock (ttm = trailing twelve months)
Stock (ticker)
|
Div
|
Yld%
|
PE
(ttm)
|
High
(ttm)
|
Low
(ttm)
|
Volume
(100)
|
Last
|
Change
|
AAPL. 2.92. 1.56. 18.17. 218.5. 188.24. 25,118. 204.57. 3.32
a. What is the company's market capitalization (in $ million)?
b. How many shares were traded on the report day?
3. Forever 21 is expected to pay an annual dividend of $2.56 per share in one year, which is then expected to grow by 9% per year. The required rate of return is 14%. What is the current stock price?
4. Apple has just paid a quarterly dividend of $3.82. Dividends are expected to grow by 10% for the next 4 quarters, and then grow by 1% thereafter. Apple has a required quarterly return of 5%.
a. What is the expected dividend in four quarters?
b. What is the terminal value in the fourth quarter (P4P4)?
c. What is the value of the stock now?
5. Coca-Cola has expected EPS of $1.2. Its competitors have the following P/E ratios:
a. What is the intrinsic value based on the lowest P/E ratio?
b. What is the intrinsic value based on the highestP/E ratio?
c. What is the intrinsic value based on theaverageP/E ratio?
6. Market orders get executed _____ at _____.
a. whenever the stock price goes above the limit; the current price in the market
b. immediately; the limit price
c. immediately; the current price in the market
d. whenever the stock price goes below the limit; the limit price
7. Which are costs of trading a security?
Check all that apply:
a. Flotation costs
b. The price concession an investor may be forced to make for trading in quantities greater than those associated with the bid-ask quote
c. Dealer's bid-ask spread
d. Broker's commission
8. Calculate the rates of return (holding period returns) for the following stocks:
Stock
|
Beginning price: P
0
|
Ending price: P
1
|
Dividend payment: D
1
|
A
|
22.38
|
17.06
|
2.6
|
B
|
101.74
|
111.92
|
5.25
|
C. 4.25. 5.58 0.14
a. What was the rate of return for stock A?
b. What was the rate of return for stock B?
c. What was the rate of return for stock C?
9. You've recorded the following prices and dividend payments for a stock:
Date
|
Stock pric
eDividend
|
|
1/2
|
20.28
|
|
4/1
|
20.44
|
0.65
|
|
7/1
|
18.86
|
0.65
|
|
10/1
|
20.69
|
0.65
|
|
1/2
|
20.88
|
0.65
|
|
|
|
|
|
|
You bought the stock at on Jan. 2 of the first year and sold it on Jan. 2 of the next year, just after the dividend payment, and reinvested all dividends in the meantime.
What was your realized return over the year?
10. Below are the returns for different asset classes for a particular year:
Asset class
|
Return
|
T-bills
|
1.4%
|
Corporate bonds
|
6.3%
|
Small company stocks
|
15.1%
|
Large company stocks
|
10.7%
|
a. What was the excess return for corporate bonds?
b. What was the excess returnfor small company stocks?
c. What was the excess returnfor largecompany stocks?
11. You bought a share of stock for $100. It is now worth $105 and has just paid an annual dividend of $2 per share.
a. What was the dividend yield?
b. What was the capital gains yield?
c. What was the total rate of return?
12. The risk premium is _____.
Check all that apply:
a. the difference between the expected rate of return on an asset and the risk-free rate
b. normally zero for risky assets
c. the reward for bearing risk
d. normally positive for risky assets
13. Below are the expected returns for different asset classes for next year:
Asset class
|
Exp.return
|
T-bills
|
2.6%
|
Corporate bonds
|
4.9%
|
Small company stocks
|
17.1%
|
Large company stocks
|
13.5%
|
a. What is the risk premium for corporate bonds?
b. What is the risk premium for small company stocks?
c. What is the risk premium for largecompany stocks?
14. A mutual fund delivered the following annual returns over the last 4 years:
Return7% 3% 13%. 6%
a. If you had invested $4,000 at the beginning of the period, what would be the value of your money after 4 years?
b. What was the geometric average return over the 4 years?
15. Tesla stock delivered the following annual returns over 3 years:
Year
|
1
|
2
|
3
|
Rate of return
|
4.6%
|
5.7%
|
1.4%
|
a. What was the arithmetic average return?
16. You've collected the following historical rates of return for stocks A and B:
Year (t)
|
R
A,t
|
R
B,t
|
2016
|
0.02
|
0.02
|
2015
|
0.08
|
0.05
|
2014
|
0.16
|
0.07
|
a. What was the average annual return for stock A
b. What was the average annual return for stock B?
c. What was the standard deviation of returns for stock A?
d. What was the standard deviation of returns for stock B?
17. A portfolio had an annual return of 10% and an annual standard deviation of 27%. Treasury bills yielded 1% during the same period.
What was the Sharpe ratio?
18. In general, an asset with higher expected return _____.
a. is less expensive
b. is more expensive
c. has higher risk
d. has lower risk
19. You've estimated the following expected returns for a stock, depending on the strength of the economy:
State (s)
|
Probability
|
Expected return
|
Recession
|
0.2
|
-0.02
|
Normal
|
0.5
|
0.09
|
Expansion. 0.3. 0.14
a. What is the expected return for the stock?
b. What is the standard deviation of returns for the stock?
20. You've invested the following amounts into a three-stock portfolio:
Stock
|
Investment
|
1
|
$2,000
|
2
|
$12,000
|
3
|
$7,000
|
a. What is the portfolio weight for stock 1?
b. What is the portfolio weight for stock 2?
c. What is the portfolio weight for stock 3?
21. You've assembled the following portfolio:
Stock
|
Expected return
|
Portfolio weight
|
1
|
7.9%
|
30%
|
2
|
11.9%
|
3
|
17.7%
|
|
|
What is the weight for stock 3 if you want to achieve an expected portfolio return of 12%?
22. The table below shows the expected rates of return for three stocks and their weights in some portfolio:
Stock A Stock B Stock C
Portfolio weights 0.5 0.2 0.3
State Probability Expected returns
Recession 0.1 0.06 0.03 0.15
Boom 0.9 0.11 0.05 0.16
a. What is the portfolio return during a recession?
b. What is the expected portfolio return?
c. What is the standard deviation of the portfolio returns?
23. The return on Visa stock has a standard deviation of 26% and the return on Walmartstock has a standard deviation of 14%. Their correlation is 0.57.
a. If you invest 60% in Visa and 40% in Walmart, what is the variance of the portfolio?
b. What is the standard deviation of the portfolio?
24. Why can diversification not eliminate all risk?
a. Some risk factors are specific to particular companies.
b. Common factors affect most stocks in a similar fashion.
c. Some companies in the portfolio may go bankrupt.
d. Risk is inherent to a stock market investment.
25. Unsystematic risk _____.
Check all that apply:
a. affects only a single asset or small group of assets
b. is eliminated in a well-diversified portfolio
c. is measured by standard deviation
d. can be diversified away
26. The efficient frontier _____.
Check all that apply:
a. is strictly monotonic
b. plots the portfolios that are not dominated by some other portfolio
c. is a subset of the investment opportunity set
d. is that part of the feasible set above the minimum variance portfolio
27. You want to invest in either a stock or Treasury bills (the risk-free asset). The stock has an expected return of 9% and a standard deviation of returns of 41%. T-bills have a return of 4%.
a. If you invest 70% in the stock and 30% in T-bills, what is your expected return for the complete portfolio?
b. What is the standard deviation of returns for such a portfolio?
28. The following table shows rates of return for IBM stock and the market portfolio.
Year
|
IBM
|
Market
|
1
|
8%
|
6%
|
2
|
18%
|
11%
|
a. What was the average return on IBM stock?
b. What was the average return on the market portfolio?
c. What was the covariance of returns?
d. What was the variance of returns on the market portfolio?
e. What is the beta of IBM stock?
29. A stock has a beta of 1.9. The risk-free rate is 4%. Assume that the CAPM holds.
a. What is the expected return for the stock if the expected return on the market is 12%?
b. What is the expected return for the stock if the expected market risk premium is 12%?
30. You've assembled the following portfolio:
Stock
|
Beta
|
Portfolio weight
|
1
|
1.5
|
0.2
|
2
|
1.1
|
0.4
|
3
|
0.5
|
0.4
|
a. What is the beta of the portfolio?
31. Cost of capital is also known as the _____.
Check all that apply:
a. market capitalization rate
b. minimum expected return an investment must offer to be attractive
c. appropriate discount rate
d. opportunity cost of investing in real assets instead of financial assets with the same risk
e. required return
32. Which of the following statements is correct for a given company?
a. The WACC is not affected by taxes.
b. The cost of retained earnings exceeds the cost of new common stock.
c. The cost of equity is greater than the cost of debt.
d. The WACC is greater than the cost of equity.
33. Given similar maturities, the (before-tax) cost of debt is also the _____.
Check all that apply:
a. coupon rate on new bonds
b. coupon rate on already outstanding bonds
c. yield to maturity on already outstanding bonds
d. yield to maturity on new bonds
34. The cost of debt is the _____ of the company's bonds.
a. current yield
b. coupon rate
c. yield to maturity
d. price
35. Which are valid methods for finding the cost of equity?
Check all that apply:
a. The perpetuity approach
b. The dividend discount model approach
c. The CAPM or SML approach
d. The YTM approach
36. The Weighted Average Cost of Capital (WACC) is the appropriate discount rate for _____.
Check all that apply:
a. projects that are less risky than average
b. projects that are as risky as the firm as a whole
c. each individual project's cash flows
d. all cash flows for the firm as a whole
37. Which of these factors affecting the WACC can the firm control?
Check all that apply:
a. Tax rates
b. Capital budgeting decision rules
c. Dividend payout ratio
d. Capital structure
e. Investors' risk aversion
38. Amazon has a beta of 0.9. The risk-free rate is 2.3% and the expected return on the S&P500 is 6%.
a. What is Amazon's cost of equity?
b. Now assume that the expected market risk premium is 6%. What is Amazon's cost of equity?
39. A company has a debt-equity ratio of 0.8 and an equity beta 1.1. Its debt is risk free. Ignore taxes.
a. what is the company's asset beta?
b. If the company takes on additional debt so that its debt-equity ratio increases to 1.3, what is the new equity beta?
40. Jackson Holding has just paid an annual dividend of $0.45 per share. Analysts expect the firm's dividends to grow by 2% forever. Its stock price is $35.4.
What is the cost of equity from retained earnings?
41. Tanrun Inc. is expected to pay an annual dividend of $0.45 per share in one year. Analysts expect the firm's dividends to grow by 7% forever. Its stock price is $34.8 and its beta is 1.3. The risk-free rate is 2% and the expected market risk premium is 4.5%.
What is the best guess for the cost of equity?
42. Lugget Corp. has one bond issue outstanding with an annual coupon of 3.4%, a face value of $1,000 and a price of $951.33, which matures in 10 years. The company's tax rate is 25%.
a. What is Lugget's pre-tax cost of debt?
b. What is the company's after-tax cost of debt?
43. Terence Terraforming Inc. has a capital structure of 35% debt and 65% common stock. The expected return on the firm's debt is 4.3% and the expected return on the firm's equity is 10%. The firm's marginal tax rate is 21%.
a. What is the company's weighted average cost of capital?
44. You have collected the following information about a company:
Source of capital
|
Market value
|
Book value
|
After-tax cost
|
Long-term debt
|
100,000
|
100,000
|
0.08
|
Preferred stock
|
60,000
|
72,000
|
0.11
|
Common stock
|
170,000
|
85,000
|
0.18
|
Total. 330,00.
257,000
a.
What is the weighted average cost of capital using market values?
b.
What is the weighted average cost of capitalusing book values?
45. Exavior Inc.'s cash flow from assets during the current year is $100 million, which is expected to grow at a constant rate of 4% in the future. The weighted average cost of capital is 12%.
What is the firm's total corporate value (in $ million)?
46. It is December 2020. You work as a financial analyst forMerck & Co. and are tasked with the due diligence on the proposed acquisition of a biotech startup.You estimated the following cash flows for the startup:
Year
|
Expected cash flow from assets
($ million)
(end of year)
|
2021
|
89.5
|
2022
|
134.25
|
2023
|
174.53
|
2024
|
209.43
|
2025. 230.37
After 2025, cash flows are expected to grow by 2% per year. Based on the riskiness of your industry, you think that your weighted average cost of capital is 18%.
The biotech firm has 5 million shares andbondsworth $120 million outstanding.
a. What is the terminal value, i.e., the present value of all free cash flows from 2026 to infinity expressed in 2025-dollars (in $ million)?
b. What is the total value of the company (in $ million)?
c. What is the value per share of common stock (in $)?
47. Majong Inc.forecasts that it will have the free cash flows shown below. The free cash flows are expected to grow by 4% per year after year 3.
Year
|
1
|
2
|
3
|
CFA ($ million)
|
-20
|
48
|
54
|
The weighted average cost of capital is 14%. The firm has $68 million of debt and 10 million shares outstanding.
a. What is Majong's terminal value (in $ million)?
b. What is the firm value today (in $ million)?
c. What is a good estimate of Majong's price per share?
48. The flotation cost for new equity is 7% and the flotation cost for new debt is 4%. The company has a target debt-equity ratio of 0.9.
a. What are theweighted average flotation costs as a fraction of the amount invested?
b. What would be theweighted average flotation costs as a fraction of the amountinvested if the company used retained earnings to finance the equity portion of the amount invested?
49. Amazon is planning to launch a new version of its home-automation device, the Echo 2. The company has already spent $40 million on research and development and needs another year and $30 million to complete the development. Amazon has chosen to deduct all R&D expenditures as business expenses in the year that they are incurred.
The company also just spent $1.5 million on a market research study and estimated the following sales data:
Years after launch
|
1
|
2
|
Units sold (million)
|
6
|
8
|
Price per unit ($)
|
150
|
120
|
Because of accelerating technological innovation, the Echo 2 will be replaced by a new model after two years. The Echo 2 will reduce free cash flows from the earlier version, the Echo 1, by $29 million per year.
The costs of components and labor are $90 per unit, while salaries and other expenses add upto $10 million in each year the product is sold.
The factory that manufactures the Echo 2 requires a $60 million investment right now and will take one year to complete. The factory has a 5-year tax life after completion and is depreciated straight to zero. It could be sold for $36 million two years after completion. However, Amazon expects to reuse the factory at the end of the project for the Echo 3, thus saving $48 million of the cost for the Echo 3 factory (including all depreciation and tax effects).
To get production up and running, Amazon has to buy components worth $5 million immediately before the launch of the product, and add another $2 million worth of components to its inventory in each of the following two years.
Assume the project is of approximately the same risk as the firm's existing operations. The firm's marginal tax rate is 34%. The following data are current:
Stock:
9 million shares outstanding, price per share is $192, last annual dividend was $14.52 and dividends are expected to grow by 4% per year.
Bonds:
1 bond issue outstanding, book value of $600 million, face value of $1,000, 5% coupon, paid semi-annually, 20 years to maturity, YTM of 7%.
Market:
Treasury bills have a return of 1% and the market risk premium is 8.5%.
a. What is the cost of equity?
b. What is the market value of the bondissue(in $ million)?
c. What is the weighted average cost of capital?
d. What is the annual depreciation (in $ million)?
e. What is the operating cash flow in year 3 (in $ million)?
f. What is the cash flow from assets at the end of year 3 (in $ million)?
g. What is the NPV of this project (in $ million)?