Question

Last year, Timberlake EarPhones, Inc. issued a 20-year bond at par(Bond(L)) and a 10-year bond at par (Bond(S)). Both bonds were issued at par; both bonds have a coupon rate of 8 percent, paid semiannually, and both bonds have a face values of $1,000. The yield to maturity on both bonds is now 4 percent. What are the current market prices of Bond(L) and Bond(S)? How much are the percentage changes in bond (L) and Bond(S) since they were issued? What bond pricing principle explains the difference?

Answer 1

Bond L:

Current market price of Bond L = $ 1,000 x 8 % x 1/2 x [ { 1 - ( 1 / 1.02 ) ³⁸ } / 0.02 ] + $ 1,000 x ( 1 / 1.02 ) ³⁸ = $ 40 x 26.44064 + $ 1,000 x 0.47119 = $ 1,528.82

Percentage change in price = $ (1,528.82 - 1,000 ) / $ 1,000 * 100 = + 52.88 %

Bond S:

Current market price of Bond S = $ 40 x [ { 1 - ( 1 / 1.02 ) ¹⁸} / 0.02 ] + $ 1,000 x ( 1 / 1.02 ) ¹⁸ = $ 40 x 14.99203 + $ 1,000 x 0.70016 = $ 1,299.84.

Percentage change in price = $ ( 1,299.84 - 1,000) / $ 1,000 * 100 = + 29.98 %

Longer the term to maturity of a bond, greater is the sensitivity in bond price to changes in yield to maturity.