# Valuation

1. Yield to Maturity

Calculate the yield to maturity of an 8% coupon bond with 5 years to maturity if the bond sells for $800. The face value of the bond is $1,000.

2. Valuing Stocks with Constant Dividends

A stock pays $2.50 in dividends and has a required rate of return of 12%. Calculate the current price.

What if the required rate of return is 8%

3. Valuing Stocks with Constant Dividend Growth Rates.

A stock pays $2.00 per year in dividends. It is expected to grow at 7% a year.

If your required rate of return is 12% what is the price of the stock.

The growth rate changes to 4%. Now what is the price of the stock?

(required rate of return does not change)

https://brainmass.com/economics/bonds/267960

#### Solution Preview

1. Yield to Maturity

Calculate the yield to maturity of an 8% coupon bond with 5 years to maturity if the bond sells for $800. The face value of the bond is $1,000.

We can determine YTM by using the following formula.

where B is the issued/current price

C is the coupon payment

r is the discount or yield rate

n is the period

Because we need to find the yield to maturity, we need to replace the information given into the equation and calculate for the yield to maturity.

C, which ...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate the yield to maturity of an 8% coupon bond with 5 years to maturity if the bond sells for $800.

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