Question

If a bond issuer promises to pay an annual coupon rate of 5% to bond holders and face value of K1000. Find the fair values of the bond if it matures in four years time and yield to maturity is 4% and 3%

Answer 1

We can use the present value formula to calculate the fair value of the bond:

PV = C / (1 + r)^1 + C / (1 + r)^2 + ... + C / (1 + r)^n + FV / (1 + r)^n

where PV is the present value or fair value of the bond, C is the coupon payment, r is the yield to maturity, n is the number of years to maturity, and FV is the face value of the bond.

Plugging in the given values:

Coupon rate = 5%

Face value = K1000

n = 4

At 4% yield to maturity:

r = 4%

PV = 5% x K1000 / (1 + 0.04)^1 + 5% x K1000 / (1 + 0.04)^2 + 5% x K1000 / (1 + 0.04)^3 + 5% x K1000 / (1 + 0.04)^4 + K1000 / (1 + 0.04)^4

PV = K1,066.61

Therefore, the fair value of the bond at 4% yield to maturity is K1,066.61.

At 3% yield to maturity:

r = 3%

PV = 5% x K1000 / (1 + 0.03)^1 + 5% x K1000 / (1 + 0.03)^2 + 5% x K1000 / (1 + 0.03)^3 + 5% x K1000 / (1 + 0.03)^4 + K1000 / (1 + 0.03)^4

PV = K1,093.40

Therefore, the fair value of the bond at 3% yield to maturity is K1,093.40.