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I have a couple Yield to Maturity practice questions I'm working on out of my textbook....

I have a couple Yield to Maturity practice questions I'm working on out of my textbook. Any help appreciated!

a.) Suppose that a bond has one year to maturity. What is the yield to maturity on the bond if it was bought for $1080 and has a $1300 face value with a coupon rate of 9%?

b.) Consider a coupon bond with a face value of $1500, one year to maturity, and a coupon rate of 6%. With a yield to maturity of 5%, what price will the bond sell for?

c.) If a coupon bond has two years to maturity, a coupon rate of 10%, a par value of $900, and a yield to maturity of 14%. What price will the coupon bond sell for?

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Answer #1

Yield to maturity is defined as the effective yield of a bond based on its current price in the market. It is the best measure of the return rate. It can be calculated as -

P = rac{C}{1+r}+ rac{C}{(1+r)^2}+rac{C}{(1+r)^2}....+rac{C}{(1+r)^n}+rac{F}{(1+r)^n}

where

C = annual coupon payment (in dollars, not a percent = coupon rate * face value

n = number of years to maturity

r = YTM

P = price of the bond

F= face value of the bomd

a)

n = 1

P = 1080

F = 1300

C = 0.09* 1300 = 117 (Assuming annual coupon rate of 9%)

Therefore

1080+r 117 1300 1+1+r 14 1080_117-

1 + r-1417/1080 1.312 r= 1.312-1 = 0.312 31.2%

b)

n = 1

P = ?

F = 1500

C = 0.06* 1500 = 90 (Assuming annual coupon rate of 6%)

r = 5% = 0.05

Therefore

901500 1 +0.05 1+1+r1590-1514.29 1.05

c)

Par value = face value = F = 900

n = 2

r = 14% = 0.14

C = 10% of 900 = 0.1*900 = 90

Therefore

90 90 900 10.14 (1 0.14)2 (10.14)2

90 90 1.14 1 1.142 78.95 69.25 + 692.52 = 840.72

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