Question

Question: A 30-year maturity, 8% coupon bond paying coupons semi-annually is callable in five years at a call price of \(1,100. The bond currently sells at a yield to maturity of 7% (3.5% per half-year):

a. What is the yield to call?

b. What is the yield to call if the call price is only \)1,050?

c. What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years?

Short answer

Answer

a. Yield to call is 3.368% semi-annually, 6.736% annually

b.Yield to call is 2.976% semi-annually, 5.952% annually

c. Yield to call is 3.031% semi-annually, 6.062% annually

Step-by-step solution

Calculation of Yield to call

Given [n = 60; i = 3.5; FV = 1000; PMT = 40]

Therefore the bond sells for $1,124.72 based on the 3.5% yield to maturity:

Given, now [n = 10; PV = 1124.72; FV = 1100; PMT = 40]

Therefore, yield to call is 3.368% semi-annually, 6.736% annually:

Calculation of Yield to call when call price is $1050

In this scenario, FV = $1050

Therefore yield to call is 2.976% semi-annually, 5.952% annually.

With a lower call price, the yield to call is lower.

Calculation of Yield to call when call price is $1100 but bond can be called in two years

In this case, given [n = 4; PV = 1124.72 ; FV = 1100; PMT = 40]

Hence, Yield to call is 3.031% semi-annually, 6.062% annually: