Corporate Finance Final Exam
The following scenario applies to the next three questions.
A firm has three projects (S = short; M = medium; L = long), each with an opportunity cost of capital of 8% per annum and one initial investment at time t=0.
- Project S has one cash inflow of 695.52 at time t=1.
- Project M has two cash inflows of 182.38 each at times t=1 and t=2.
- Project L has three cash inflows of 502.16 each at times t=1, t=2, and t=3.
Projects S and M have the same IRR.
Projects S and L have the same NPV.
The IRR of Project L is 9.0% per annum.
Question 1: Initial investment
What is the initial investment of Project L?
A. 1012.64
B. 1054.78
C. 1061.92
D. 1104.70
E. 1271.11
Question 2: Net present value
What is the net present value of Project S?
A. 21
B. 22
C. 23
D. 24
E. 25
Question 3: Internal rate of return
What is the internal rate of return of Project M?
A. 10% per annum
B. 11% per annum
C. 12% per annum
D. 13% per annum
E. 14% per annum
Question 4: Refinancing
A firm's cost of debt capital rD depends on its debt-to-value ratio D/V as rD = 10% × (1 + D/V). The corporate tax rate Tc = 35%. At a 50% debt-to-value ratio, the firm's WACC is 11%.
What is the firm's WACC at a 30% debt-to-value ratio?
A. 11.26%
B. 12.26%
C. 13.26%
D. 14.26%
E. 15.26%
Question 5: Option prices
The price of a European call option that expires in six months and has a strike price of $85 is $13. The underlying stock price is $80, and the risk-free interest rate is 12.9% per annum.
What is the price of a European put option that expires in six months with a strike price of $85?
A. $9
B. $10
C. $11
D. $12
E. $13
The following scenario applies to the next two questions.
- The risk-free rate is 6.5% per annum and the market risk premium is 7% per annum.
- A firm with 20,000 shares of stock trading at $100 a share and no debt has a CAPM beta of 90%.
- The corporate tax rate is zero, costs of bankruptcy are zero, and capital markets have no imperfections.
- The firm issues $300,000 of debt and pays $300,000 as a one-time dividend to shareholders.
- The firm's cost of debt capital rD for the $300,000 of debt is 8.5% per annum.
- The firm's assets and projects do not change.
Question 6: Return on assets
After the refinancing, what is the return on assets rA?
A. 11.75%
B. 12.05%
C. 12.80%
D. 13.45%
E. 14.15%
Question 7: Beta of equity
After the refinancing, what is the beta of equity βE?
A. 83.19%
B. 91.27%
C. 94.96%
D. 102.38%
E. 116.33%
Question 8: Measures of performance
Which of the following is false regarding executive stock options vs accounting measures of performance?
A. Accounting measures are based on absolute performance; stock options are based on performance relative to investors' expectations.
B. Accounting measures are appropriate only for senior managers whose performance affects the firm's reported results; stock options induce better performance by all managers.
C. Accounting profits are partly controlled by managers, who might cut maintenance or staff training to raise near-term earnings; stock options depend on investors' expectations of long-run earnings.
D. Accounting earnings and rates of return can be biased measures of true profitability if they fail to adjust for the cost of equity capital; stock returns include investors' expectations of the required return on capital.
E. Investments with positive rates of return but negative NPVs increase earnings but reduce stock prices.
The following scenario applies to the next two questions.
- The common stock of firm ABC is trading at 80 a share with 1 million shares outstanding.
- A rights issue allows investors to buy one new share at 56 a share for each five shares held.
Assume no other items influence the stock price except the rights issue.
Question 9: Rights issue and new stock price
What is the stock price after the rights are exercised?
A. 75.00
B. 76.00
C. 77.00
D. 78.00
E. 79.00
Question 10: Value of a right
What is the value of a right to buy one new share?
A. 15.00
B. 17.50
C. 20.00
D. 22.50
E. 25.00
Question 11: Debt tax shields
A firm has fixed (that is, does not vary with the value of the project) perpetual debt with a par value of 450, an annual coupon rate of 8%, and a yield to maturity of 6%. If the corporate tax rate is 20%, what is the present value of the debt tax shields?
A. 104
B. 110
C. 112
D. 120
E. 125
The following scenario for the dividend growth model applies to the next four questions.
- The risk-free rate is 6%, the market risk premium is 12%, and a firm's CAPM β is 0.750.
- In 20X6, the firm's after-tax earnings per share are 7.00, and its payout ratio is 80% each year.
- Earnings are expected to grow indefinitely at a constant rate.
- The firm's ROE = ratio of earnings to book value of equity = 18%.
Question 12: Dividend growth model earnings per share What is the firm's growth rate of earnings per share?
A. 3.6%
B. 5.7%
C. 8.4%
D. 11.0%
E. 13.8%
Question 13: Dividend growth model stock price
What is the firm's stock price right after the dividend payment in 20X6?
A. 50.891
B. 52.735
C. 54.807
D. 55.500
E. 57.554
Question 14: Dividend growth model no growth stock price
What would the firm's stock price be after the dividend payment in 20X6 if it paid all earnings as dividends in 20X7 and subsequent years?
A. 48.347
B. 50.031
C. 51.248
D. 52.857
E. 55.636
Question 15: Dividend growth model present value of growth opportunities
What is the firm's present value of growth opportunities (PVGO) right after the dividend payment in 20X6?
A. 1.918
B. 2.545
C. 2.643
D. 2.704
E. 3.559
Question 16: One year project
A firm undertakes a one year project with the following attributes.
- The initial investment is 100,000.
- The project provides an expected return of 115,000 at the end of the year.
- The opportunity cost of capital is 16%
- The return on debt rD is 4%
- The debt to value ratio (D/V) is 20%
- The corporate tax rate is 25%.
What is the adjusted present value of the project?
A. -670
B. -572
C. -478
D. -362
E. -266
Question 17: Efficient market hypothesis
The efficient market hypothesis assumes that which of the following may be modeled as a random variable drawn from a statistical distribution?
A. Ratios of successive stock prices
B. The annual income from a stock
C. Stockholder dividends received each year
D. Logarithms of stock prices
E. The expected volatility of the stock price
Question 18: Value of equity
A firm has $400,000 of debt and $800,000 of equity.
The risk-free rate is 4% per annum and the yield on the debt is 6% per annum.
Which of the following would raise the value of the equity?
A. Limited liability of shareholders is abrogated by new state statutes.
B. The debt is exchanged for secured loans on the firm's assets with a 6% yield to maturity.
C. The risk-free rate increases, the yield on the debt increases, and the value of the debt decreases.
D. The firm's debt matures and the principal is repaid.
E. Costs of bankruptcy increase as litigation becomes more complex.
Question 19: Efficient frontier
Five stocks are trading with the following expected returns and standard deviations.
|
|
A
|
B
|
C
|
D
|
E
|
|
Expected Return
|
11.7%
|
15.5%
|
17.2%
|
18.2%
|
20.2%
|
|
Standard Deviation
|
15.2%
|
22.2%
|
26.7%
|
30.2%
|
35.2%
|
Investors can hold any combination of these stocks, such as 50% of Stock A and 50% of Stock B.
Which stock is not on the efficient frontier?
A. Stock A
B. Stock B
C. Stock C
D. Stock D
E. Stock E
Question 20: Sharpe ratio
Five stocks are trading with the following expected returns and standard deviations.
|
|
A
|
B
|
C
|
D
|
E
|
|
Expected Return
|
10.5%
|
12.0%
|
14.0%
|
15.0%
|
16.0%
|
|
Standard Deviation
|
12.0%
|
15.0%
|
22.5%
|
26.0%
|
29.0%
|
If investors can borrow and lend at the risk-free rate of 5%, which stock has the highest Sharpe ratio?
A. Stock A
B. Stock B
C. Stock C
D. Stock D
E. Stock E
Question 21: Expected returns
- The ratio of Stock XYZ's expected return to Stock ABC's expected return is 1.40
- Stock XYZ has a CAPM beta of 1.183
- The market risk premium is three times the annual risk-free rate.
What is Stock ABC's CAPM beta?
A. 0.71
B. 0.73
C. 0.75
D. 0.77
E. 0.79
Question 22: Investing principles
If the CAPM is correct, all investors have the same assumptions for expected returns, co-variances, and standard deviations and they can all borrow and lend at the risk-free rate, which of the following is true?
A. All stocks lie on the securities market line.
B. All stocks lie on the efficient frontier.
C. Stocks with the same standard deviations have the same expected returns.
D. All investors have the same proportions of risk-free assets and risky assets.
E. Risk averse investors choose low beta stocks; risk tolerant investors choose high beta stocks.
Question 23: Debt to value ratio and WACC
The risk-free rate is 7% per annum, the market risk premium is 6%, and the tax rate is 35%.
- A firm's equity has a CAPM β of 1.167.
- The firm's debt yields 8.0% per annum.
If the debt to value ratio is 34.1%, what is the after-tax weighted average cost of capital (WACC)?
A. 9.0%
B. 9.5%
C. 10.0%
D. 10.5%
E. 11.0%
The following scenario on optimal portfolios applies to the next three questions.
The market has only two risky securities, with expected returns, standard deviations, and market values of
|
|
Expected Return
|
Standard Deviation
|
Market Value
|
|
Stock Y
|
7.5%
|
30%
|
60 million
|
|
Stock Z
|
11.5%
|
45%
|
40 million
|
The correlation of stocks Y and Z is 89.0432%. Risk-free bonds yield 7%. An investor who can borrow or lend at the risk-free rate forms an optimal portfolio of risk-free bonds and risky securities.
Question 24: Market portfolio of risky assets
What is the standard deviation of the market portfolio of risky securities?
A. 32%
B. 33%
C. 34%
D. 35%
E. 36%
Question 25: Expected return of optimal portfolio
If the investor forms an optimal portfolio with a standard deviation of 20.4878%, what is the expected return on this portfolio?
A. 7.1%
B. 7.2%
C. 7.3%
D. 7.4%
E. 7.5%
Question 26: Standard deviation of optimal portfolio
If the investor forms an optimal portfolio with an expected return of 10.6220%, what is the standard deviation of this portfolio?
A. 45%
B. 46%
C. 47%
D. 48%
E. 49%
The following scenario applies to the next three questions.
A project lasting 4 years has an initial investment of Z at time t=0 and expected net after-tax cash inflows of
|
time t =
|
1
|
2
|
3
|
4
|
|
cash inflow
|
6.26
|
56.00
|
144.31
|
82.49
|
For its book accounting statements, the firm writes off the initial investment by straight line depreciation over four years: ¼ × Z at times t = 1, 2, 3, and 4. The initial investment has no salvage value after the project ends.
The firm has no non-cash accounting income or expenses besides depreciation of the initial investment, so the accounting income each year equals the cash inflow minus the depreciation of the initial investment.
The IRR of the project equals its opportunity cost of capital of 13% per annum.
Question 27: Book value return on investment
What is the book value return on investment in year 2 (from time t=1 to time t=2)?
A. 2%
B. 3%
C. 4%
D. 6%
E. 7%
Question 28: Economic depreciation
What is the economic depreciation in year 4 (from time t=3 to time t=4)?
A. 71
B. 73
C. 75
D. 77
E. 79
Question 29: Economic income
What is the economic income in year 3 (from time t=2 to time t=3)?
A. 23
B. 24
C. 25
D. 26
E. 28
Question 30: Option gain or loss
Three month European call and put options on ABC stock sell at an exercise price (strike price) of $90. The stock price volatility is 35%, and the risk-free interest rate is 5.55% per annum, compounded annually.
On January 1, an investor buys 100 call options and sells 100 put options. The options expire on April 1.
On February 1, the stock price is the same as it was on January 1, the risk-free interest rate has not changed, and the stock price volatility has not changed. The only difference is that the options have two months left to expiration instead of three months.
What is the gain (positive) or loss (negative) on the investor's portfolio during January?
A. -$60
B. -$40
C. -$20
D. +$40
E. +$60
The following scenario applies to the next two questions.
39,000 outstanding shares trade at 60.00 per share. Earnings per share are 10.00, and the target payout ratio is 51%. Assume that dividend announcements do not reveal anything about the firm's prospects.
Question 31: Share repurchase
The firm intended to pay a dividend = earnings per share × the target payout ratio. The firm cancels the dividend and announces it will use the money to repurchase shares. How many shares will the firm purchase?
A. 2,690
B. 2,850
C. 3,008
D. 3,163
E. 3,315
Question 32: New shares
The firm intended to pay a dividend = earnings per share × the target payout ratio. Instead, the firm increases dividends to earnings per share and issues new shares to recoup the extra cash paid out. How many shares will be issued?
A. 2,191
B. 2,534
C. 2,917
D. 3,344
E. 3,822
This scenario of capital structure and betas in perfect capital markets applies to the next two questions.
Assume capital markets are perfect (no corporate income taxes or other imperfections) and the Miller and Modigliani propositions hold.
At a debt-to-equity ratio of 25%, a firm has a debt beta of 10% and an equity beta of 128.75%. The firm issues more debt and repurchases equity to bring its debt-to-equity ratio to 50%, where its debt beta is 19.5%.
Question 33: Beta of assets in perfect capital markets
What is the firm's beta of assets at the debt-to-equity ratio of 50%?
A. 101%
B. 103%
C. 105%
D. 107%
E. 109%
Question 34: Beta of equity in perfect capital markets
What is the firm's beta of equity at the debt-to-equity ratio of 50%?
A. 131%
B. 135%
C. 137%
D. 138%
E. 139%
Question 35: Capital market imperfections
The Miller and Modigliani propositions apply to perfect capital markets.
Which of the following is not an imperfection in capital markets?
A. Corporate income taxes
B. Costs of bankruptcy and financial distress
C. Information asymmetry between managers and shareholders
D. Differences between the cost of debt capital rD and the cost of equity capital rE
E. Effects of debt on incentives for managers
Question 36: Abnormal Returns
The abnormal return equation says that the expected rate of return on stock S is rs = α + β × rm, where rm is the rate of return on the overall market. Monthly rates of return for stock ABC show a β of 1.050 and an α of -0.2% per month. At what market rate of return rm per month is the expected rate of return for Stock ABC equal to rm?
A. -4.00%
B. -1.33%
C. -0.80%
D. +1.33%
E. +4.00%
Question 37: NPV
A project has an initial investment of $100,000 at time t=0 years and one cash inflow at time t=2 years.
The opportunity cost of capital is 10% per annum and the internal rate of return of the project is 12.18% per annum. What is the NPV of the project?
A. $2,500
B. $2,800
C. $3,000
D. $3,300
E. $4,000
Question 38: Risk-neutral probability
- A stock is trading at $100.
- Over the next six months, the stock price will increase 20% or decrease 20%.
- Six month European put and call options trade with exercise prices of $110.
- The risk-free interest rate is 16% per annum compounded semi-annually, or 8% each six months.
- The stock has a CAPM beta of 1.000, and the market risk premium is 8%.
What is the risk-neutral probability of an increase in the stock price over the next six months?
A. 60.0%
B. 62.5%
C. 66.7%
D. 70%
E. 90%
Question 39: Option delta
- A stock is trading at $100.
- Over the next six months, the stock price will increase 20% or decrease 20%.
- Six month European put and call options trade with exercise prices of $110.
- The risk-free interest rate is 16% per annum compounded semi-annually, or 8% each six months.
- The stock has a CAPM beta of 1.000, and the market risk premium is 8%.
What is the delta of the put option?
A. -87%
B. -80%
C. -75%
D. -66%
E. -63%
Question 40: Replicating portfolio
- A stock is trading at $100.
- Over the next six months, the stock price will increase 20% or decrease 20%.
- Six month European put and call options trade with exercise prices of $110.
- The risk-free interest rate is 16% per annum compounded semi-annually, or 8% each six months.
- The stock has a CAPM beta of 1.000, and the market risk premium is 8%.
An investor creates a replicating portfolio for the put option consisting of $Z of cash (risk-free bonds) plus delta shares of stock. What is $Z? (Note that the put option delta is negative.)
A. $78.57
B. $79.33
C. $83.33
D. $85.71
E. $86.54
Question 41: Option price
- A stock is trading at $100.
- Over the next six months, the stock price will increase 20% or decrease 20%.
- Six month European put and call options trade with exercise prices of $110.
- The risk-free interest rate is 16% per annum compounded semi-annually, or 8% each six months.
- The stock has a CAPM beta of 1.000, and the market risk premium is 8%.
What is the price (value) of the put option?
A. $3.57
B. $4.33
C. $8.33
D. $10.71
E. $11.54
Question 42: Option Combinations
An investor enters into the following transactions for six month options on Stock ABC:
- Sells one call option at an exercise price of $40.
- Sells one call option at an exercise price of $60.
- Buys two call options at an exercise price of $50.
The stock price S on the expiration date is between $50 and $60. What is the net payoff to the investor from the four options?
A. 2 × (S - 60)
B. S - 60
C. 0
D. 60 - S
E. 2 × (60 - S)
The following scenario applies to the next two questions.
- Investors can borrow and lend at the risk-free rate of 3% per annum.
- All investors hold a combination of risk-free assets and the market portfolio.
- Investor ABC puts 30% of his money in the market portfolio and the rest in risk-free securities. The expected return of his total portfolio is 13% and its standard deviation is 16%.
- Investor XYZ borrows an amount equal to 20% of his own funds and invests all (both borrowed funds and own funds) in the market portfolio.
Question 43: Expected return
What is the expected return from XYZ's portfolio?
A. 42.0%
B. 42.2%
C. 43.0%
D. 45.5%
E. 47.0%
Question 44: Standard deviation
What is the expected standard deviation of XYZ's portfolio?
A. 47.50%
B. 50.40%
C. 55.25%
D. 60.00%
E. 64.00%
Question 45: Market anomalies
Brealey and Myers discuss several market anomalies: empirical data that seem to contradict the CAPM.
Which of the following results are found in long-term historical analysis of U.S. stock data? (Small firm stocks are commonly known as small cap stocks, or stocks of small firms with low market capitalization. Value stocks have high ratios of book value to market value; growth stocks have low ratios of book value to market value.)
A. High beta portfolios plotted above the market line; low beta portfolios plotted below the market line.
B. Large firm stocks have had higher returns in most years than small firm stocks.
C. Value stocks have provided higher long-run returns than growth stocks.
A. 1 and 2 only
B. 1 and 3 only
C. 2 and 3 only
D. 1, 2, and 3
E. None of A, B, C, or D is true.
Question 46: Put Option
Six month European call and put options are trading on ABC stock at the values shown below.
|
|
Strike Price
|
|
|
$80
|
$85
|
|
call
|
$9
|
$6
|
|
put
|
Z
|
$5
|
The risk-free interest rate is 6% per annum. Find Z.
A. $3.00
B. $3.50
C. $4.00
D. $4.50
E. $5.00
Question 47: Certainty equivalent cash flows
A project has projected cash flows of 100 at time t=1 and 110 at time t=2.
The risk-free rate is 4.8% per annum, market risk premium is 4%, and the project has a CAPM beta of 1.25.
What is the ratio of the certainty equivalent cash flow at time t=2 to the certainty equivalent cash flow at t=1?
A. 1.01
B. 1.02
C. 1.03
D. 1.04
E. 1.05
The following scenario applies to the next three questions on adjusted present values.
The opportunity cost of capital with all equity financing is 12% per annum, and the corporate tax rate is 35%.
A project has an initial investment of 300,000 at time t=0 and perpetual cash inflows of 33,600 per annum at times t=1, 2, 3, .... The project has debt of 82,857 with an interest rate of 8.690% per annum.
Question 48: Tax shields with re-balanced debt
If the debt is continually re-balanced to a constant debt-to-equity ratio, what is the present value of the interest tax shields of the debt?
A. 21
B. 22
C. 23
D. 24
E. 25
Question 49: APV with re-balanced debt
If the debt is continually re-balanced to a constant debt-to-equity ratio, what is the adjusted present value of the project?
A. 1
B. 2
C. 3
D. 4
E. 5
Question 50: APV with fixed debt
If the debt is fixed (not re-balanced to a constant debt-to-equity ratio), what is the adjusted present value of the project?
A. 5
B. 6
C. 7
D. 8
E. 9