Question

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?

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 -

$P = \frac{C}{1+r}+ \frac{C}{(1+r)^2}+\frac{C}{(1+r)^2}....+\frac{C}{(1+r)^n}+\frac{F}{(1+r)^n}$

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

$P = \frac{C}{1+r}+ \frac{F}{1+r}\Rightarrow 1080 = \frac{117+1300}{1+r}$

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

b)

n = 1

P = ?

F = 1500

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

r = 5% = 0.05

Therefore

$P = \frac{C}{1+r}+ \frac{F}{1+r}\Rightarrow P = \frac{90+1500}{1+0.05}$$= \frac{1590}{1.05} = 1514.29$

c)

Par value = face value = F = 900

n = 2

r = 14% = 0.14

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

Therefore

$P = \frac{C}{1+r}+\frac{C}{(1+r)^2}+ \frac{F}{1+r}\Rightarrow P = \frac{90}{1+0.14} + \frac{90}{(1+0.14)^2} + \frac{900}{(1+0.14)^2}$

$P = \frac{90}{1.14} + \frac{90}{1.14^2} + \frac{900}{1.14^2} = 78.95+69.25+692.52 = 840.72$