Question

Suppose that an investor with a 3-year investment horizon is considering buying an 8-year 6% coupon bond selling at par (semi-annual coupon payments). The investor expects that she can reinvest the coupon payments at an annual interest rate of 7% and that at the end of the investment horizon all bonds will be selling to offer a YTM of 9%.

How much is the coupons & interest earned on reinvesting these coupon by the end of 3-yr?

What is the sale price of the bond by the end of 3 year?

What is the (annualized) expected holding period return for this bond?

Round your answer to 2 decimal places.

Answer 1

Given,

Coupon rate (C)= 6% paid semi annually

It is assumed that Face value (F)= $1,000

Therefore, annual coupon= F*C/2 = 1000*6%/2= $30

Number of coupon payments over 3 year horizon= 3*2= 6

Also given, Interest rate on reinvestment of coupon= 7%

Coupon and interest earned on reinvesting these coupon, over 3 years= $196.50 calculated using FV function of Excel as follows:

Sale price of the bond at the end of 3 years= $881.31 calculated using PV function of Excel as follows:

Annualized expected holding period return = [(P₁-P₀+C)/P₀]*100/3

Where P₁= Selling price, P₀= Investment price and C= Coupon with interest on reinvestment

Substituting the values,

Annualized expected holding period return = [(881.31-1000+196.50)/1000]*100/3= 2.59%