Question

8. A $1000 treasury bond expires in 5 years. It pays semi-annually at a coupon rate of 10.5%. If the market price of this bond is 1078.80, what is the YTM?

Answer 1

No of periods = 5 years * 2 = 10 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (10.5% / 2) * $1000

Coupon per period = $52.5

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

$1078.80 = $52.5 / (1 + YTM / 2)¹ + $52.5 / (1 + YTM / 2)² + ...+ $52.5 / (1 + YTM / 2)¹⁰ + $1000 / (1 + YTM / 2)¹⁰

Using Texas Instruments BA 2 plus Calculator

SET N = 10, PMT = 52.5, FV = 1000, PV = -1078.80

CPT ---> I/Y = 4.2656

YTM = 2 * I/Y

YTM = 2 * 4.2656

YTM = 8.53%