# Bonds- YTM, coupon rate, interest rate risk

1. Skitman Corp. issued 12-year bonds 2 years ago at a coupon rate of 9.2 percent. The bonds make semiannual payments. If these bonds currently sell for 104 percent of par value, what is the YTM?

2. Interpreting Bond Yields: Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond then? The YTM?

3. Interest Rate Risk: Bond J is a 4 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have eight years to maturity, make semiannual payments, and have a YTM of 7 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

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#### Solution Preview

The answers are in the attached file.

1. Skitman Corp. issued 12-year bonds 2 years ago at a coupon rate of 9.2 percent. The bonds make semiannual payments. If these bonds currently sell for 104 percent of par value, what is the YTM?

Yield to maturity

Yield to maturity can be calculated using Excel worksheet function RATE

Data

No of years to maturity= 10 =12-2

Coupon rate= 9.20%

Face value= $1,000

Frequency = S Semi annual coupon payments

Redemption value = $1,000

Price of the bond= $1,040.00 =104%*1000

Interest payment per year= $92.00 =9.2% x 1000

Interest payment per period= $46.00 =92/2

No of Periods =n= 20 =2x10

Yield= 8.60% (Using EXCEL Function RATE)

=2x RATE(20,46,-1040,1000)

We multiply by 2 as the rate calculated is for semiannual period

We can also use approximation formula:

Coupon @ 9% = 92

Par /Face value= 1000

Redemption value= $1,000

Maturity= 10 years

Price= $1,040.00

Therefore , yield= 8.63% =(92+(1000-1040)/10)/(0.5*(1000+1040))

Answer: YTM= 8.60%

2. Interpreting Bond Yields: Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is ...

#### Solution Summary

Calculates YTM, coupon rate and interprets the interest rate risk of lower-coupon bonds.

Corporate Finance: Bond value, YTM, stock worth, growth rate, interest rate risk, beta

Problems:

Number 1:

(Bond valuation) A $1,000 face value bond has a remaining maturity of 8 years and a required return of 7%. The bond's coupon rate is 8%.

What is the fair value of this bond?

Number 2

(Yield to maturity) Smith Industries has a 8.0% bond maturing in 12 years. What is the yield to maturity if the current market price of the bond is:

a. $1,090?

B. $1,000?

C. $890?

Number 3

(Stock valuation) Suppose GE has nonmaturing (perpetual) preferred stock outstanding that pays a $0.50 quarterly dividend and has a required return of 8% APR (2% per quarter). What is the stock worth?

Number 4

(Growth rate) Suppose Cisco has a payout ratio of 45% and an expected return on its future investments of 9%. What is Cisco's expected growth rate?

Number 5

(Cumulative growth rate) Jasper Inc has not paid dividends. They are considering paying a common stock dividend of $0.75 per share next year.

Analysts indicate the required rate of return is 12% and expect the firm will grow the dividend 5%. What is the value of the firm?

Number 6

(Interest-rate risk) Reliant Energy has many bonds trading on the New York Stock Exchange.

Suppose Reliant's bonds have identical coupon rates of 8.5% but that one issue matures in 3 year, one in 9 years, and the third in 12 years.

Assume that a coupon payment was made yesterday

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

Number 7

(Default risk) You buy a very risky bond that promises a 11% coupon and return of the $1,000 principal in 10 years. You pay only $750 for the bond.

a. You receive the coupon payments for four years and the bond defaults.

After liquidating the firm, the bondholders receive a distribution of $250 per bond at the end of 4.5 years. What is the realized return on your investment?

b. 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?

Number 8

Beta and required return

The riskless return is currently 6%, and Jupitaer Co. has estimated the contingent returns given here.

a) Calculate the expected returns on the stock market and on Jupiter Co. stock.

b) What is Jupiter's beta?

c) What is Jupitere's required return according to the CAPM?

Realized Return

State of the market Probability that state occurs stock mkt Jupiter

Stagnant 20% -10% -15%

Slow growth 35% 10% 15%

average growth 30% 15% 25%

rapid growth 15% 25% 35%