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# Stock and bond returns

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Please show all work and complete in excel.

Problem Set #1

Calculating Returns:

1. a) Assume you bought 1000 shares of stock at an initial price of \$25 per share. The stock paid a dividend of \$0.50 per share during the following year, and the share price at the end of the year when you sold it, was \$35. Compute your total dollar return (income) on this investment.

b) In the previous problem, what is the capital gains yield? What is the dividend
yield? What is the total rate of return on the investment?

Geomerric Mean Return:

2. Compute the geometric mean of following annual returns:

Year Return

1 5%

2 -10%

3 12%

4 17%

5 3%

Margins and Margin Returns:

3. You bought 1,000 shares of SNCR at 12.49 per share with 50% margin. Your broker charges 5% annual interest on borrowed funds. At the end of one year, if you sold the sock at:

a) \$14.95/share
b) \$13.91 /share

i) Compute your return on investment for scenarios a) and b) above.

ii) Compute the Margin/Equity % in parts a) and b) above.

Short Sales:

4. You sold short 1000 shares of LEH stock at \$35/share at the end of 3 months. You closed out your positions at the following prices:

a) \$25/share
b) \$35/share
c) \$48/share

Calculate your annual return.

Assume 4% interest receipt on the 50% funds deposited or margin.

Expected returns and Standard Deviations:

5. a) Use the following information on states of the economy and stock returns to calculate the expected return for Dingaling Telephone:

State of Economy Probability of Security Return
State of Economy if State Occurs

Weak Recession 0.20 -10%
Normal 0.40 20%
Boom 0.20 30%
Strong Recession 0.20 -15%

1.00

b) Using the information in the previous question, calculate the standard deviation of return.

6. The bid price of Microsoft stock is \$31.29 and it ask price is \$31.35. Compute its bid-ask % spread.

Nominal Rates:

7. Given: Real interest rate = 3% Inflation rate =4.5,

Compute: a) Approximate nominal interest rate b) Exact nominal interest rate

T-Bill Pricing:

8. Assume a \$10,000 Treasury bill is quoted to pay 5 percent interest over a six-month period:

a) How much interest income would the investor receive?
b) What is the price of the Treasury bill?
c) What is the effective yield?

Bond Pricing:

9. a) Given a 15-year bond that originally sold for \$1,000 with an 8 percent coupon rate, what
would be the price of the bond if interest rates in the marketplace on similar bonds are now 10 percent ? Interest is paid semiannually. %-years have elapsed since the bond issue. Therefore, assume a 10 year time period.

b) What would be the price if interest rates go down to 6 percent? (once again, do a
semi-annual analysis for 10 years)

Yield to Maturity:

10. What is the yield to maturity for a 9 percent coupon-rate bond priced at \$1,040.37? Assume there are five years left to maturity. It is a \$1,000 par value bond. Use the trial-and-error approach with annual discounting.

Constant Growth Models

11. ABC Corporation is currently paying \$2.50 in dividends. Its earnings are expected to grow at a constant rate of 12% for the foreseeable future. If investors require 15% return compute the intrinsic value of ABC stock.

12. XYZ Company is expecting its return on equity to equal 25% and expects to pay 40% of profits as dividends. Its current dividends are \$2.00, and the investors require an 18% return.

a) What is XYZ's expected growth rate?

b) What is XYZ's intrinsic value?

c) If its market price is \$73.50, would you invest in XYZ stock? Explain

Two-stage Growth Model

13. Stock ABC is considered to be a growth stock with a non-constant growth rate of 18% for the next five years, followed by 15% sustainable annual growth from thereafter. ABC's current dividends per share are \$2.10, and its required rate of return is 12%. Calculate its intrinsic value.

Multi-stage Growth Model

14. The following information is available on the ABC stock:
D0 = \$1.50
g1 = 15% for years 1-2
g2 = 12% for years 3-4
g3 = G = 10% for years 5-n

If investors require 14% return compute the price of ABC stock.

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#### Solution Summary

Answer to 14 questions on stock and bond returns

\$2.19

## Finance: Bond Valuation, Dividend Discount Model, Return on Preferred Stock, Valuation, Risk

A 1: (Bond valuation) A \$1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond's coupon rate is 7.4%. What is the fair value of this bond?

A 2: (Dividend discount model) Assume RHM is expected to pay a total cash dividend of \$5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%?

A 3: (Required return for a preferred stock) James River \$3.38 preferred is selling for \$45.25. The preferred dividend is non growing. What is the required return on James River preferred stock?

A 4: (Stock valuation) Suppose Toyota has non maturing (perpetual) preferred stock outstanding that pays a \$1.00 quarterly dividend and has a required return of 12% APR (3% per quarter). What is the stock worth?

B 16: (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl's bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday.
1. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
2. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now?
3. Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond?
4. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer-versus shorter-maturity bonds?

B 18: (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the \$1,000 principal in 10 years. You pay only \$500 for the bond.
1. You receive the coupon payments for three years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of \$150 per bond at the end of 3.5 years. What is the realized return on your investment?
2. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

B 20: (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will begin paying a \$1.00 per share dividend in two years and that the dividend will increase 6% annually thereafter. Bret Kimes, one of James' colleagues at the same firm, is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend will be \$1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%.
1. What value would James estimate for this firm?
2. What value would Bret assign to the Medtrans stock?

Problem: (Beta and required return) The risk less return is currently 6%, and Chicago Gear has estimated the contingent returns given here.
1. Calculate the expected returns on the stock market and on Chicago Gear stock.
2. What is Chicago Gear's beta?
3. What is Chicago Gear's required return according to the CAPM?

Realized Return
State of the Market Probability that State Occurs Stock Market Chicago Gear
Stagnant 0.20 (10%) (15%)
Slow growth 0.35 10 15
Average growth 0.30 15 25
Rapid growth 0.15 25 35

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