Question

Calculate YTM – Assume a bond will mature in 20 years.  
A. Calculate the YTM for a bond with a price of $874 and annual payment of $70.  
B. Calculate the price at the end of year 10. Calculate the price at the end of year 19. Explain the results.

No excel! Must use formulas.

Answer 1

20 year maturity bond

No of periods = 20 years

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

$874 = $70 / (1 + YTM)¹ + $70 / (1 + YTM)² + ...+ $70 / (1 + YTM)²⁰ + $1000 / (1 + YTM)²⁰

Using Texas Instruments BA 2 Plus Calculator

SET N = 20, FV = 1000, PMT = 70, PV = -874

CPT I/Y = 8.31

YTM = I/Y = 8.31%

Price at the end of year 10

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

Bond Price = $70 / (1 + 8.31%)¹ + $70 / (1 + 8.31%)² + ...+ $70 / (1 + 8.31%)¹⁰ + $1000 / (1 + 8.31%)¹⁰

Using PVIFA = (1 - (1 + Interest rate)^{- no of periods} / interest rate to value coupons

Bond Price = $70 * (1 - (1 + 8.31%)^-10) / (8.31%) + $1000 / (1 + 8.31%)¹⁰

Bond Price = $463.21 + $450.11

Bond Price = $913.31

Price at the end of year 19

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

Bond Price = $70 / (1 + 8.31%)¹ + $1000 / (1 + 8.31%)¹

Bond Price = $64.63 + $923.28

Bond Price = $987.91

The bond is trading at a discount as the bond nears maturity the price of the bond moves closer to the Par value. This explains the difference in the prices at year 10 & year 19. At year 19 the price is closer to the Par value. At year 10 th price is far away from the Par value.