Question

An investor must choose between two bonds:

Bond A pays $100 annual interest and has a market value of $870. It has 12 years to maturity.

Bond B pays $70 annual interest and has a market value of $850. It has six years to maturity.

Assume the par value of the bonds is $1,000.

A drawback of current yield is that it does not consider the total life of the bond. For example, the approximate yield to maturity on Bond A is 12.02 percent.

What is the approximate yield to maturity on Bond B?

The exact yield to maturity?

(Use the approximation formula to compute the approximate yield to maturity and use the calculator method to compute the exact yield to maturity. Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)

Answer 1

Answer a.

Bond B:

Face Value, F = $1,000
Current Price, P = $850
Annual Interest, C = $70
Period, n = 6 years

Approximated YTM = [C + (F - P) / n] / [(F + P) / 2]
Approximated YTM = [$70 + ($1,000 - $850) / 6] / [($1,000 + $850) / 2]
Approximated YTM = $95 / $925
Approximated YTM = 0.1027 or 10.27%

Answer b.

Bond B:

Let Annual YTM be i%

$850 = $70 * PVIFA(i%, 6) + $1,000 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -850
PMT = 70
FV = 1000

I = 10.49%

Exact YTM = 10.49%