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# Valuing bond and common stocks

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1.Baron Inc. bonds have a face value of \$1000 and mature in 10 years. The coupon rate is 18%, and coupons are paid semiannually. The yield is 12% compound semiannually. Find the bond's price.

2. Danish Inc. has cumulative preferred stock that pays an annual dividend of \$4.50. If the current price is \$37.50, what is the required return?

3. Alpo expects to pay dividends of \$3.54 at the end of year 1, \$4.18 at the end of year 2, and \$4.93 at the end of year 3. After year 3, dividends are expected to grow at a constant rate of 8% each year. The required return is 18%. What is Alpo's current share price?

4. XXC expects earnings per share to be \$6.00 next period. The retention rate is 60% and the return on equity (ROE) is 20%. The required return is 18%. What is XXC's stock price?

Note- Interest is compounded annually and payments are at year end unless stated otherwise.

#### Solution Preview

1.Baron Inc. bonds have a face value of \$1000 and mature in 10 years. The coupon rate is 18%, and coupons are paid semiannually. The yield is 12% compound semiannually. Find the bond's price.

Face Value=M=\$1000
Coupon rate=18% p.a.
Semi annual coupon rate=18%/2=9%
Semiannual Coupon amount, C=9% of face value=\$1000*9%=\$90
Number of coupon payments left, n=10*2=20
Annual Yield=12%
Semi annual Yield, r=12%/2=6%

Here, we are getting coupon payments on regular periods. It is a case of ordinary annuity with amount C=\$90, discount rate=semi annual yield=6% and number of period=20.

PV of ordinary annuity is given by= C/r*(1-1/(1+r)^n)

PV of maturity ...

#### Solution Summary

There are four problems. Solution to second problem depicts the steps to calculate required rate of return on a preferred stock. Solutions to other problems demonstrate the methodology to estimate the values of a coupon paying bond and common stocks.

\$2.19

## Computation of Bond prices and yields;Basic bond valuation & Common stock value - Constant Growth

1. Bond prices and yields.

Assume that the Christianson Corp. \$1,000-par-value bond has a 5.700% coupon, matured on May 15, 2017, had a current price quote of 97.708, and had a yield to maturity (YTM) of 6.034%.

Given this information, answer the following questions:

a. What was the dollar price of the bond?
b. What is the bond's current yield?
c. Is the bond selling at par, at a discount, or at a premium? Why?
d. Compare the bond's current yield calculated in part b to it's YTM and explain why they differ.

2. Basic bond valuation.

JD Designs Inc. has an outstanding issue of \$1,000-par-value bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date.

a. If bonds of similar risk are currently earning a 10% rate of return, how much should JD Designs Inc. bond sell for today?

b. Describe the two possible reasons why the rate on similar-risk bonds is below the coupon interest rate on the JD Designs Inc bond.

c. If the required return were at 12% instead of 10%, what would the current value of JD Designs' bonds be? Contrast this finding with your findings in part a and discuss.

3. Common stock value - Constant Growth

Darlington Inc. common stock paid a dividend of \$1.20 per share last year. The company expects earnings and dividends to grow at a rate of 5% per year for the foreseeable future.

a. What required rate of return for this stock would result in a price per share of \$28?

b. If Darlington Inc. expects both earnings and dividends to grow at an annual rate of 10%, what required rate of return would result in a price per share of \$28?

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