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# Bonds- YTM, coupon rate, interest rate risk

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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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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))