Question

An investor considers the purchase of a 3 year bond with a 7% coupon rate, with interest paid annually. Assuming the sequence of spot rates shown below answer the following questions.

A. The present value of the bond's final cash flow is:

B. The yield to maturity of this bond is

Time to maturity: Spot rate:

1 3%

2 5%

3 7%

Answer 1

Assuming that Face value = $1000

Coupon rate = 7% then =1000*7% =$70

years = 3

Spot rate:

Year 1 = 3%

Year 2 = 5%

Year 3 = 7%

then

The present value of the bond = 70 / (1.03) + 70 / (1.05)² + (1000+70) / (1.07)³

= 67.96 + 63.49 + 873.44

= 1004.89

The present value of the bond's year 3 cashflow = 873.44

The yield to maturity of this bond =[ C + (Face value - present value / n) ] / (Face value + present value)/2

= [70 + (1000-1004.89)/ 3] / (1000+1004.89)/ 2

=6.82%