Question

Suppose a semiannual bond was issued several years ago when the interest rate was 7%. The bond’s annual coupon rate was thus set at 7%. With 8 years left in bond’s life, the interest rate is 6% per year until the end of maturity. (Show your calculations but do not use excel or financial calculator for it.)

A. What is the price of the bond 8 years prior to expiration?        

B. What will be the bond’s price six years prior to maturity?         

C. An investor purchases the bond eight years prior to maturity and sells the bond six years prior to maturity. What is the total return of the investor from investing into the bond? What conclusion can you draw from the return?

Answer 1

Let us assume that the face value of the bond is $100

Coupon rate of Bond = 7%

Coupon frequency = semi-annual

Coupon = face value * coupon rate/2 = 100*7%/2 = 100*3.5% = $3.5

Annual interest rate = 6%

Semi-annual interest rate = 6%/2 = 3%

A.

Remaining maturity of the bond = 8 years = 16 semi-annual periods

Price of the bond can be calculated using the PV of an ordinary annuity plus PV of the face value

Where Price is the price of the bond

C = Coupon = $3.5

i = Semi-annual interest rate = 3%

n = Remaining maturity of the bond = 16 semi-annual periods

FV = face value = $100

Price = $43.963857 + $62.316694 = $106.2806

B.

Remaining maturity of the bond = 6 years = 12 semi-annual periods

Price of the bond can be calculated using the PV of an ordinary annuity plus PV of the face value

Where Price is the price of the bond

C = Coupon = $3.5

i = Semi-annual interest rate = 3%

n = Remaining maturity of the bond = 12 semi-annual periods

FV = face value = $100

Price = $34.839014 + $70.137988 = $104.9770

C.

Investor purchases the bond eight years prior to maturity and sells it six years prior to maturity

Let investor buy the bond at time t= 0

At t= 0 investor buys the bond for $106.2806

At t= 0.5 investor gets a coupon of $3.5

At t= 1 investor gets a coupon of $3.5

At t= 1.5 investor gets a coupon of $3.5

At t= 2 investor gets a coupon of $3.5 and Sells the bond for $104.9770 = $3.5 + $104.9770 = $108.4770

The cash flows are shown below. The total return of the investor can be calculated using IRR function in spreadsheet.

IRR ( cashflow amounts, rate guess)

The total return of the investor = IRR = 3%

This is sem-annual return

Total annual return of the investor = 3% *2 = 6%

From this we can see that the investor has received the market interest rate