# Computing the expected interest rates

1. Yearly rates are 4%, 5%, 6%, 7%, and 8% for the next five years. Please compute and explain the expected interest rate for both the three and four-year bonds if we show the liquidity premiums to be 1.25%, 1%, .75%, .5%, and 0%.

2. Yearly rates are 4%, 5%, 6%, 7%, and 8% for the next five years. Please compute and explain the expected interest rate for both the three and four-year bonds during the period.

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1.

Yearly rate for year 1=is1=4%

Yearly rate for year 2=is2=5%

Yearly rate for year 3=is3=6%

Yearly rate for year 4=is4=7%

Yearly rate for year 5=is5=8%

Expected interest rate for 3-year bond=ie3=?

Pure expectation theory suggests that

(1+ie3)^3=(1+is1)*(1+is2)*(1+is3)

(1+ie3)^3=(1+4%)*(1+5%)*(1+6%) =1.15752

ie3=(1.15752)^(1/3)-1=5.00%

Liquidity premium for three year=ilp3=0.75%

Market expectation theory in combination ...

#### Solution Summary

Solution describes the methodology to calculate the expected interest rate for the given three and four year bonds.

Calculating returns for stock and bonds - Set of 14 problems:

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.

Bid-Ask Spread:

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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