Please provide all your work on the calculations.

Except where otherwise specified, all interest rates are stated as annual rates.

7a. Obtain weekly prices for a stock of your choice for the 5-year period March 1, 2007 through March 1, 2017. The stock must have traded continuously for the entire 5-year period. (Use the adjusted closing prices from the âhistorical priceâ section for the stock from yahoo finance.) The prices must be submitted as part of the exam answers. Assuming the risk free interest rate is between 0.6875% and 1.3125% (but not 1%).

b. Calculate continuously compounded returns on the stock for each week during the last five years.

c. Determine the average weekly return on the stock.

d. Determine the standard deviation of weekly stock returns.

e. Calculate the average annual return and annual standard deviation for the stock.

f. Using the answers to e and assuming each period during of the year has length .00001 (that is, there are 100,000 sub-periods during the year), find a âuâ and âdâ that can be used in a binary model to estimate the periodic upward and downward movement of the stock price.

g. Select as a strike price an even dollar amount approximately 5% higher than the stockâs current market price and determine how many upward stock price movements must occur in the next 9 months in order for a call option to be in the money.

h. Solve for p and p* for a call option on this stock.

i. Use the general binomial model (without constructing a lattice) to determine the price of a 9-month call option for this stock with the strike price selected in part g.

beigewasp747

1. Which of the following is true?

The corporation model can be used to value divisions and firms that do not pay dividends.
The discounted dividend model can be used to value divisions and firms that do not pay dividends.
For the discounted dividend model, a firm's weighted average cost of capital is used as the discount rate.
For the corporate valuation model, a firm's cost of equity is used as the discount rate.

Question 2.2. Which of the following is false?

For the constant growth model to hold, a firm's cost of equity needs to be smaller than its constant dividend growth rate (i.e., rs < g).
For the constant growth model to hold, a firm's cost of equity needs to be greater than its constant dividend growth rate (i.e., rs > g).
From the constant growth model, if the constant dividend growth rate is equal to zero, a firm's share price is equal to the constant dividend divided by the cost of equity (i.e., g=0).
If a company's constant dividend growth rate is negative, the formula for the constant growth model cannot be applied.

Question 3.3. From the discussion of a firm's capital budgeting problem in chapter 11, which of the following is false? (Points : 3.5)

The net present value method (NPV) assumes that cash flows are reinvested at the weighted average cost of capital (WACC).
The internal rate of return method (IRR) assumes that cash flows are reinvested at the internal rate of return.
The modified internal rate of return method (MIRR) assumes that cash flows are reinvested at the weighted average cost of cpaital.
For mutually exclusive projects, if there is a conflict between NPV and IRR, the project with the highest IRR is chosen.
The IRR is independent of a firm's weighted average cost of capital.

Question 4.4. Which of the following is true? (

As a firm's dividend payout ratio increases, the firm's WACC decreases.
The WACC only represents the "hurdle rate" for a typical project with average risk. Therefore, the project's WACC should be adjusted to reflect the project's risk.
Firms with riskier projects generally have a lower WACC.
Holding all else constant, an increase in the target debt ratio tends to lower the WACC.

Question 5.5. Which of the following is false?

If interest rates rise, the price of the bond will rise and its YTM (yield to maturity) will fall.
Short-term bond prices are less sensitive than long-term bond prices to interest rate changes.
Companies are not likely to call bonds unless interest rates have declined significantly. Thus, the call provision is valuable to firms but detrimental to long term investors.
On balance, bonds that have a sinking fund are regarded as being safer than those without such a provision.

Question 6.6. Which of the following is not true? (Points : 3.5)

According to SML (security market line), the risk premium on a high-beta stock would increase more than that on a low-beta stock.
If beta < 1.0, the security is less risky than average.
According to the Security Market Line (SML), in general, a companyâs expected return will double when its beta doubles.
According to the Security Market Line (SML), if a portfolio of real world stocks has a beta of zero, the required rate of return for the portfolio is equal to the risk-free rate.

Question 7.7. P&G Industries bonds have a maturity of 15 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 10 years at $1,125, and currently sell at a price of $1,105. What is their nominal annual yield to call?

6.87%.
7.37%.
11.05%.
8.32%.

Question 8.8. Which of the following is not the flaw (weakness) of the discounted payback method? (Points : 3.5)

It does not tells us by how much the project should increase shareholder wealth, or by how much a project yields over the cost of capital; it merely tells us when we recover our investment.
It ignores cash flows occurring after the payback period.
It ignores the time value of money, that is, dollars received in different years are all given the same weight.

Question 9.9. Jermey Lin has $52,500 invested a stock with a beta of 0.80 and another $47,500 invested in a stock with a beta of 3.2. If these are the only two investments in his portfolio, what is his portfolio's beta?

1.56.
1.82.
2.00.
1.94

Question 10.10. According to CAPM, if the required rate of the return of Stock A obtained from the security market line (SML) is less than the expected rate of the return of stock A from the capital market transaction, then stock A is

fairly priced.
undervalued.
overvalued.

Question 11.11. Determine the yield-to-call (to nearest 0.1 of a percent) of an LTV bond with a 12 percent coupon, that pays interest annually. The bond can be called in 5 years, has a call premium of $114, and is currently selling for $912.50. The bond has a face value of $1,000.

14.58%.
13.92%.
16.34%.
12.17%.

Question 12.12. Project M costs $1,000, its expected cash inflows are $500 per year for 3 years, and its WACC is 11%. What is the project's NPV? (Points : 3.5)

$259.57.
$221.86.
$195.23.
$257.35.

Question 13.13. Project J costs $1,025, its expected cash inflows are $425 per year for 3 years, and its WACC is 10%. What is the project's IRR?

12.58%.
10.82%.
11.76%.
9.64%.

Question 14.14. Project X costs $6,750, its expected cash inflows are $1250 per year for 10 years, and its WACC is 10%. What is the project's payback?(Note, the regular payback is asked in this question, not the discounted payback.) (Points : 3.5)

5.40 years.
10 years.
4.58 years.
6.12 years.

Question 15.15. Project S costs $800, its expected cash inflows are $350 per year for 3 years, and its WACC is 7%. What is the project's MIRR?

13.97%.
12.04%.
14.93%.
9.15%.

Question 16.16. Project Y costs $650, its expected cash inflows are $500 per year for 5 years, and its WACC is 10%. What is the project's discounted payback?

1.47 years.
1.24 years.
1.62 years.
1.15 years.

1. Which of the following is true?

The corporation model can be used to value divisions and firms that do not pay dividends.
The discounted dividend model can be used to value divisions and firms that do not pay dividends.
For the discounted dividend model, a firm's weighted average cost of capital is used as the discount rate.
For the corporate valuation model, a firm's cost of equity is used as the discount rate.

Question 2.2. Which of the following is false?

For the constant growth model to hold, a firm's cost of equity needs to be smaller than its constant dividend growth rate (i.e., rs < g).
For the constant growth model to hold, a firm's cost of equity needs to be greater than its constant dividend growth rate (i.e., rs > g).
From the constant growth model, if the constant dividend growth rate is equal to zero, a firm's share price is equal to the constant dividend divided by the cost of equity (i.e., g=0).
If a company's constant dividend growth rate is negative, the formula for the constant growth model cannot be applied.

Question 3.3. From the discussion of a firm's capital budgeting problem in chapter 11, which of the following is false?

The net present value method (NPV) assumes that cash flows are reinvested at the weighted average cost of capital (WACC).
The internal rate of return method (IRR) assumes that cash flows are reinvested at the internal rate of return.
The modified internal rate of return method (MIRR) assumes that cash flows are reinvested at the weighted average cost of cpaital.
For mutually exclusive projects, if there is a conflict between NPV and IRR, the project with the highest IRR is chosen.
The IRR is independent of a firm's weighted average cost of capital.

Question 4.4. Which of the following is true? (Points : 3.5)

As a firm's dividend payout ratio increases, the firm's WACC decreases.
The WACC only represents the "hurdle rate" for a typical project with average risk. Therefore, the project's WACC should be adjusted to reflect the project's risk.
Firms with riskier projects generally have a lower WACC.
Holding all else constant, an increase in the target debt ratio tends to lower the WACC.

Question 5.5. Which of the following is false? (Points : 3.5)

If interest rates rise, the price of the bond will rise and its YTM (yield to maturity) will fall.
Short-term bond prices are less sensitive than long-term bond prices to interest rate changes.
Companies are not likely to call bonds unless interest rates have declined significantly. Thus, the call provision is valuable to firms but detrimental to long term investors.
On balance, bonds that have a sinking fund are regarded as being safer than those without such a provision.

Question 6.6. Which of the following is not true? (Points : 3.5)

According to SML (security market line), the risk premium on a high-beta stock would increase more than that on a low-beta stock.
If beta < 1.0, the security is less risky than average.
According to the Security Market Line (SML), in general, a companyâs expected return will double when its beta doubles.
According to the Security Market Line (SML), if a portfolio of real world stocks has a beta of zero, the required rate of return for the portfolio is equal to the risk-free rate.

Question 7.7. P&G Industries bonds have a maturity of 15 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 10 years at $1,125, and currently sell at a price of $1,105. What is their nominal annual yield to call? (Points : 3.5)

6.87%.
7.37%.
11.05%.
8.32%.

Question 8.8. Which of the following is not the flaw (weakness) of the discounted payback method? (Points : 3.5)

It does not tells us by how much the project should increase shareholder wealth, or by how much a project yields over the cost of capital; it merely tells us when we recover our investment.
It ignores cash flows occurring after the payback period.
It ignores the time value of money, that is, dollars received in different years are all given the same weight.

Question 9.9. Jermey Lin has $52,500 invested a stock with a beta of 0.80 and another $47,500 invested in a stock with a beta of 3.2. If these are the only two investments in his portfolio, what is his portfolio's beta? (Points : 3.5)

1.56.
1.82.
2.00.
1.94

Question 10.10. According to CAPM, if the required rate of the return of Stock A obtained from the security market line (SML) is less than the expected rate of the return of stock A from the capital market transaction, then stock A is (

fairly priced.
undervalued.
overvalued.

Question 11.11. Determine the yield-to-call (to nearest 0.1 of a percent) of an LTV bond with a 12 percent coupon, that pays interest annually. The bond can be called in 5 years, has a call premium of $114, and is currently selling for $912.50. The bond has a face value of $1,000. (Points : 3.5)

14.58%.
13.92%.
16.34%.
12.17%.

Question 12.12. Project M costs $1,000, its expected cash inflows are $500 per year for 3 years, and its WACC is 11%. What is the project's NPV?

$259.57.
$221.86.
$195.23.
$257.35.

Question 13.13. Project J costs $1,025, its expected cash inflows are $425 per year for 3 years, and its WACC is 10%. What is the project's IRR? (

12.58%.
10.82%.
11.76%.
9.64%.

Question 14.14. Project X costs $6,750, its expected cash inflows are $1250 per year for 10 years, and its WACC is 10%. What is the project's payback?(Note, the regular payback is asked in this question, not the discounted payback.) (Points : 3.5)

5.40 years.
10 years.
4.58 years.
6.12 years.

Question 15.15. Project S costs $800, its expected cash inflows are $350 per year for 3 years, and its WACC is 7%. What is the project's MIRR? (

13.97%.
12.04%.
14.93%.
9.15%.

Question 16.16. Project Y costs $650, its expected cash inflows are $500 per year for 5 years, and its WACC is 10%. What is the project's discounted payback?

1.47 years.
1.24 years.
1.62 years.
1.15 years.

Instructions: Use the formula below to compute the problems: âPlease Read the question carefully.â

K_d = Yield (1 â T)

1. Telecom Systems can issue debt yielding 8 percent. The company is in a 35 percent bracket. What is its after-tax cost of debt?

2. After-tax cost of debt: Royal Jewelers Inc., has an aftertax cost of debt of 6 percent. With a tax rate of 40 percent, what can you assume the yield on the debt is?

3.

Cash flow: Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $50,000, and that it has a 30 percent tax bracket. Compute its cash flow using the format below.

Earnings before depreciation and taxes _____

Depreciation _____

Earnings before taxes _____

Taxes @ 30% _____

Earnings after taxes _____

Depreciation _____

4.

Cost of preferred stock: Medco Corporation can sell preferred stock for $80 with an estimated flotation cost of $3. It is anticipated the preferred stock will pay $6 per share in dividends.

a. Compute the cost of preferred stock for Medco Corp.

b. Do we need to make a tax adjustment for the issuing firm?

5. Cost of preferred stock: The Meredith Corporation issued $100 par value preferred stock 10 years ago. The stock provided an 8 percent yield at the time of issue. The preferred stock is now selling for $75. What is the current yield or cost of the preferred stock? (Disregard flotation costs.)

6. Costs of retained earnings and new common stock: Barton Electronics wants you to calculate its cost of common stock. During the next 12 months, the company expects to pay dividends (D₁) of $1.20 per share, and the current price of its common stock is $30 per share. The expected growth rate is 9 percent.

a. Compute the cost of retained earnings (K_e). Use Formula 11-6.

b. If a $2 flotation cost is involved, compute the cost of new common stock (K_n). Use Formula 11-7.

7. A firm's cost of preferred stock is equal to the preferred dividend divided by market price plus the dividend growth rate (K_p= D/P_o+ g).

8. The coefficient of variation, calculated as the standard deviation of expected returns divided by the expected return, is a standardized measure of the risk per unit of expected return.

a. True

b. False

9. The standard deviation is a better measure of risk than the coefficient of variation if the expected returns of the securities being compared differ significantly.

a. True

b. False

10. The CAPM is built on historic conditions, although in most cases we use expected future data in applying it. Because betas used in the CAPM are calculated using expected future data, they are not subject to changes in future volatility. This is one of the strengths of the CAPM.

a. True

b. False

11. You have the following data on three stocks:

Stock	Standard Deviation	Beta
A	20%	0.59
B	10%	0.61
C	12%	1.29

If you are a strict risk minimizer, you would choose Stock if it is to be held in isolation and Stock if it is to be held as part of a well-diversified portfolio.

a. A; A.

b. A; B.

c. B; A.

d. C; A.

e. C; B.

12. A portfolioâs risk is measured by the weighted average of the standard deviations of the securities in the portfolio. It is this aspect of portfolios that allows investors to combine stocks and thus reduce the riskiness of their portfolios.

a. True

b. False

13. You are considering two bonds. Bond A has a 9% annual coupon while Bond B has a 6% annual coupon. Both bonds have a 7% yield to maturity, and the YTM is expected to remain constant. Which of the following statements is CORRECT?

a. The price of Bond B will decrease over time, but the price of Bond A will increase over time.

b. The prices of both bonds will remain unchanged.

c. The price of Bond A will decrease over time, but the price of Bond B will increase over time.

d. The prices of both bonds will increase by 7% per year.

e. The prices of both bonds will increase over time, but the price of Bond A will increase at a faster rate.

14. A 12-year bond has an annual coupon of 9%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 7%. Which of the following statements is CORRECT?

a. If market interest rates decline, the price of the bond will also decline.

b. The bond is currently selling at a price below its par value.

c. If market interest rates remain unchanged, the bondâs price one year from now will be lower than it is today.

d. The bond should currently be selling at its par value.

e. If market interest rates remain unchanged, the bondâs price one year from now will be higher than it is today.

15. Suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

a. 5.14%

b. 5.42%

c. 5.70%

d. 5.99%

e. 6.28%

16. Suppose 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year. What is the real risk-free rate of return, r*? Disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average.

a. 3.80%

b. 3.99%

c. 4.19%

d. 4.40%

e. 4.62%

17. Assume that interest rates on 20-year Treasury and corporate bonds are as follows:

T-bond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18%

The differences in these rates were probably caused primarily by:

a. Tax effects.

b. Default and liquidity risk differences.

c. Maturity risk differences.

d. Inflation differences.

e. Real risk-free rate differences.

18. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.

b. The discount rate increases.

c. The riskiness of the investmentâs cash flows decreases.

d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.

e. The discount rate decreases.

19. Assume that inflation is expected to decline steadily in the future, but that the real risk-free rate, r*, will remain constant. Which of the following statements is CORRECT, other things held constant?

a. If the pure expectations theory holds, the Treasury yield curve must be downward sloping.

b. If the pure expectations theory holds, the corporate yield curve must be downward sloping.

c. If there is a positive maturity risk premium, the Treasury yield curve must be upward sloping.

d. If inflation is expected to decline, there can be no maturity risk premium.

e. The expectations theory cannot hold if inflation is decreasing.

20. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

a. True

b. False

FIN 302 Lecture Notes - Lecture 17: Weighted Arithmetic Mean, Standard Deviation

FIN 302 Full Course Notes

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