Question

A 6.50 percent coupon bond with 18 years left to maturity is

offered for sale at $1,035.25. What yield to maturity [interest rate]
is the bond offering? Assume interest payments are paid semi-
annually, and solve using semi-annual compounding. Par value is
$1000.

Answer 1

The equation can be solved using financial calculators or spreadsheet software. In this case, the YTM is approximately 6.17%.

Calculating Yield to Maturity (YTM)

Given:

Coupon rate = 6.50%

Maturity = 18 years

Price = $1,035.25

Par value = $1,000

Payment frequency = Semi-annual (2 times per year)

Steps:

Calculate the semi-annual coupon payment:

Coupon payment = Coupon rate * Par value / Payment frequency

Coupon payment = 0.065 * $1,000 / 2

Coupon payment = $32.50

Calculate the number of semi-annual periods:

Number of periods = Maturity * Payment frequency

Number of periods = 18 years * 2

Number of periods = 36

Use the bond pricing formula to solve for YTM:

Bond Price = PMT * [(1 - (1 + YTM/2)^-N) / (YTM/2)] + Par value / (1 + YTM/2)^N

Where:

PMT is the semi-annual coupon payment

YTM is the yield to maturity (expressed as a semi-annual rate)

N is the number of semi-annual periods

1,035.25 = 32.50 * [(1 - (1 + YTM/2)^-36) / (YTM/2)] + 1,000 / (1 + YTM/2)^36

This equation can be solved using financial calculators or spreadsheet software.

In this case, the YTM is approximately 6.17%.