Question

A 30-year maturity bond has a 7% coupon rate, paid annually. It sells today for \(867.42. A 20-year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for\)879.50. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 8% and that 15-year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6%. Which bond offers the higher expected rate of return over the five-year period?

Short answer

Answer

The 30-year bond offers the higher expected return i.e. 8.22% against 20-year bond which gives 7.76% return.

Step-by-step solution

Step by Step SolutionStep 1: Given information

Maturity of the 30-year bond falls to 25 years, so n=25

The yield is forecast i = 8%.

PMT = 70

FV = 1000

The price forecast = $893.25

Calculation of total proceeds, five year return and annual return

The total payment accumulation of five coupon payments after five years at a 6% interest rate= $394.60.

So total proceeds: $394.60 + $893.25 = $1,287.85

The five-year return = ($1,287.85/867.42) – 1 = 1.48469 – 1 = 48.469%

The annual rate of return = (1.48469)(1/5) –1 = 0.0822 = 8.22%

Calculation of total proceeds five year return and annual return

Maturity of the 20-year bond falls to 15 years, so n=15

The yield is forecast i = 7.5%.

PMT = 65

FV = 1000

The price forecast = $911.73

The total payment accumulation of five coupon payments after five years at a 6% interest rate= $366.41.

So total proceeds: $366.41 + $911.73 = $1,278.14

The five-year return = ($1,278.14/$879.50) – 1 = 1.45326 – 1 = 45.326%

The annual rate of return = 1.45326(1/5) – 1 = 0.0776 = 7.76%

So 30-year bond offers the higher expected return i.e. 8.22% against 20-year bond which gives 7.76% return.