Question

There is a bond that pays $100 per year interest, with a $1,000 par value. It matures in 15 years. The market required yield to maturity on a comparable bond is 12%.

1. What is the value of the bond?
2. How does the value change if the yield to maturity on a comparable bond increase to 15%? What if it decreases to 8%.
3. Explain the above questions (part b) with the concepts of interest rate risk, premium bonds and discount bonds.
4. Recalculate the answer in b, with the assumption that the bond matures in 5 years (instead of 15 years).
5. Explain the above questions (part d) with the concepts of interest rate risk, premium bonds and discount bonds.

Answer 1

Answer a.

Face Value = $1,000
Annual Coupon = $100
Time to Maturity = 15 years
Annual Return = 12%

Bond Price = $100 * PVIFA(12%, 15) + $1,000 * PVIF(12%, 15)
Bond Price = $100 * (1 - (1/1.12)^15) / 0.12 + $1,000 / 1.12^15
Bond Price = $863.78

Answer b.

If required return is 15%:

Bond Price = $100 * PVIFA(15%, 15) + $1,000 * PVIF(15%, 15)
Bond Price = $100 * (1 - (1/1.15)^15) / 0.15 + $1,000 / 1.15^15
Bond Price = $707.63

If required return is 8%:

Bond Price = $100 * PVIFA(8%, 15) + $1,000 * PVIF(8%, 15)
Bond Price = $100 * (1 - (1/1.08)^15) / 0.08 + $1,000 / 1.08^15
Bond Price = $1,171.19

Answer c.

If required return is higher than the coupon rate, then the bonds will trade a discount.
If required return is less than the coupon rate, then the bonds will trade a premium.
If required return is equal to the coupon rate, then the bonds will trade a par.

Answer d.

Face Value = $1,000
Annual Coupon = $100
Time to Maturity = 5 years

If required return is 12%:

Bond Price = $100 * PVIFA(12%, 5) + $1,000 * PVIF(12%, 5)
Bond Price = $100 * (1 - (1/1.12)^5) / 0.12 + $1,000 / 1.12^5
Bond Price = $927.90

If required return is 15%:

Bond Price = $100 * PVIFA(15%, 5) + $1,000 * PVIF(15%, 5)
Bond Price = $100 * (1 - (1/1.15)^5) / 0.15 + $1,000 / 1.15^5
Bond Price = $832.39

If required return is 8%:

Bond Price = $100 * PVIFA(8%, 5) + $1,000 * PVIF(8%, 5)
Bond Price = $100 * (1 - (1/1.08)^5) / 0.08 + $1,000 / 1.08^5
Bond Price = $1,079.85

Answer e.

Bond with higher time to maturity has higher interest rate risk.