Question

What is the yield to maturity of a nine-year bond that pays a coupon rate of 11% per year, has a $1,000 par value, and is currently priced at $1,175? Assume annual coupon payments.

a. 11.10%

b. 8.2%

c 9.20%

d.13%

Answer 1

F ace Value of Bond = $1000

Annual Coupon payment = $1000*11%

= $110

No of years to maturity(n) = 9

Current Bond Price = $1175

As the price of Bond is higher than the face value of bond, the Yield to maturity(YTM) will be less than the Coupon Rate as Price and YTM have inverse relationship.

Taking YTM as 8%

$Price = \frac{CouponPayment}{(1+YTM)^{1}}+\frac{CouponPayment}{(1+YTM)^{2}}+.....+\frac{CouponPayment}{(1+YTM)^{n}}+\frac{FaceValue}{(1+YTM)^{n}}$

$Price = \frac{110}{(1+0.08)^{1}}+\frac{110}{(1+0.08)^{2}}+.....+\frac{110}{(1+0.08)^{9}}+\frac{1000}{(1+0.08)^{9}}$

Price = $ 687.159+ $500.25

Price = $1187.41

As at YTM@5%, Price is closer to Current price. Thus taking another YTM closer at 9%

$Price = \frac{CouponPayment}{(1+YTM)^{1}}+\frac{CouponPayment}{(1+YTM)^{2}}+.....+\frac{CouponPayment}{(1+YTM)^{n}}+\frac{FaceValue}{(1+YTM)^{n}}$

$Price = \frac{110}{(1+0.09)^{1}}+\frac{110}{(1+0.09)^{2}}+.....+\frac{110}{(1+0.09)^{9}}+\frac{1000}{(1+0.09)^{9}}$

Price = $ 659.472 + $460.43

Price = $1119.90

Calculating YTM:-

$YTM =LowerRate +\frac{Price_{LR}-SellingPrice}{Price_{LR}-Price_{HR}}*(HigherRate-LowerRate)$

$YTM =8 +\frac{1187.41-1175}{1187.41-1119.90}*(9-8)$67.51

YTM = 8.18%

So, Effective YTM is 8.2%

Option B

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