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Q-10-321

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Essentials Of Investments
Found in: Page 330
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

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?

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

See the step by step solution

Step by Step Solution

Step 1: 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:

Step 2: 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.

Step 3: 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:

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