Question

Consider a bond paying a coupon rate of 9% per year semiannually when the market interest rate is only 3.6% per half-year. The bond has six years until maturity.

a. Find the bonds price today and six months from now after the next coupon is paid.

b. What is the total rate of return on the bond? (% per six months)

Answer 1

Solution:

Lets assume Face value of bond = 100$

Given

Coupon rate = 9% semi annual =4.5% Market interest rate = 3.6% Maturity period = 6 years i.e 12 semi annual Years

(A)(1) Caluculation of Price of Bond Today discounted at Market rate i.e 3.6%

Coupon amount Semiannual    = 4.5$(100$x4.5%)

(a)   PVAF for 12 semi annual years @ 3.6%=9.607 x 4.5$ = 43.23$

(b) PVF for 12 semi annual years @3.6%=0.6542 x100 = 65.42$

Price of Bond (a+b) =108.65$ (43.23+65.42)

A(2) Caluculation of Price of Bond Six months from after next Coupon is paid i.e 11 semi annual years

(A)   PVAF for 11 semi annual years @ 3.6% = 8.952 x 4.5 = 40.284$

(B) PVF for 11 semi annual years @3.6% = 0.678 x 100 = 67.8$

  Price of Bond (a+b)   =108.084$(40.284+67.8)

(B) Caluculation of total return on Bond = coupon Rate/ Current Price of Bond

Coupon given = 4.5 % Semiannually From (A)(1) Current price of bond =108.65$

Rate of Return For 6m period = 4.5% x 100/108.65$ x 100 = 4.14 %