Question

3. BOND VALUATION

a) An investor has two bonds in his portfolio that have a face value of RM1000 and pay a 10% annual coupon. Bond L matures in 15years, while Bond S matures in 1 year.

b) What will the value of each bond be if the going interest rate is 15%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

c) Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

Answer 1

Answer a.

Bond L:

Face Value = RM1,000

Annual Coupon Rate = 10%
Annual Coupon = 10% * RM1,000
Annual Coupon = RM100

Time to Maturity = 15 years

If interest rate is 15%:

Price of Bond = RM100 * PVIFA(15%, 15) + RM1,000 * PVIF(15%, 15)
Price of Bond = RM100 * (1 - (1/1.15)^15) / 0.15 + RM1,000 / 1.15^15
Price of Bond = RM707.63

If interest rate is 8%:

Price of Bond = RM100 * PVIFA(8%, 15) + RM1,000 * PVIF(8%, 15)
Price of Bond = RM100 * (1 - (1/1.08)^15) / 0.08 + RM1,000 / 1.08^15
Price of Bond = RM1,171.19

If interest rate is 12%:

Price of Bond = RM100 * PVIFA(12%, 15) + RM1,000 * PVIF(12%, 15)
Price of Bond = RM100 * (1 - (1/1.12)^15) / 0.12 + RM1,000 / 1.12^15
Price of Bond = RM863.78

Bond S:

Face Value = RM1,000

Annual Coupon Rate = 10%
Annual Coupon = 10% * RM1,000
Annual Coupon = RM100

Time to Maturity = 1 year

If interest rate is 15%:

Price of Bond = RM100 * PVIF(15%, 1) + RM1,000 * PVIF(15%, 1)
Price of Bond = RM100 / 1.15 + RM1,000 / 1.15
Price of Bond = RM956.52

If interest rate is 8%:

Price of Bond = RM100 * PVIF(8%, 1) + RM1,000 * PVIF(8%, 1)
Price of Bond = RM100 / 1.08 + RM1,000 / 1.08
Price of Bond = RM1,018.52

If interest rate is 12%:

Price of Bond = RM100 * PVIF(12%, 1) + RM1,000 * PVIF(12%, 1)
Price of Bond = RM100 / 1.12 + RM1,000 / 1.12
Price of Bond = RM982.14

Answer b.

Long-term bonds have higher interest rate risk than do short-term bonds.