Question

Markus is considering investing in either of two outstanding bonds. The bonds both have N$5,000 par values and 8% coupon interest rates and pay interest twice a year. Bond A has exactly 10 years to maturity and bond B has 20 years to maturity. Show your calculations in full. a. Calculate the value of bond A if required return is 5%. Show your calculations in full. b. Calculate the value of bond B if the required return is 3.5%. Show your calculations in full. c. Which bond would you recommend to Markus to buy if he wishes to minimise interest rate risk? Support your answer.

Answer 1

a)

Bond A

No of periods = 10 years * 2 = 20 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (8% / 2) * N$5000

Coupon per period = N$200

Let us compute the Bond A price

Bond Price = Coupon / (1 + YTM / 2)^period + Par value / (1 + YTM / 2)^period

Bond Price = N$200 / (1 + 5% / 2)¹ + N$200 / (1 + 5% / 2)² + ...+ N$200 / (1 + 5% / 2)²⁰ + N$5000 / (1 + 5% / 2)²⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = N$200 * (1 - (1 + 5% / 2)^-20) / (5% / 2) + N$5000 / (1 + 5% / 2)²⁰

Bond Price = N$3117.83 + N$3051.35

Bond Price = N$6169.19

b)

Bond B

No of periods = 20 years * 2 = 40 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (8% / 2) * N$5000

Coupon per period = N$200

Let us compute the Bond B price

Bond Price = Coupon / (1 + YTM / 2)^period + Par value / (1 + YTM / 2)^period

Bond Price = N$200 / (1 + 3.5% / 2)¹ + N$200 / (1 + 3.5% / 2)² + ...+ N$200 / (1 + 3.5% / 2)⁴⁰ + N$5000 / (1 + 3.5% / 2)⁴⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = N$200 * (1 - (1 + 3.5% / 2)^-40) / (3.5% / 2) + N$5000 / (1 + 3.5% / 2)⁴⁰

Bond Price = N$5718.85 + N$2498.00

Bond Price = N$8216.85

c)

I would recommend Bond A to Markus to minimise interest rate risk since it has a shorter maturity compared to Bond B.