Question

Bond value and timelong -Changing required returns  Personal Finance Problem   Lynn Parsons is considering investing in either of two outstanding bonds. The bonds both have ​$1 000 par values and 14​% coupon interest rates and pay annual interest. Bond A has exactly 8 years to​ maturity, and bond B has 18 years to maturity.  

a.  Calculate the present value of bond A if the required rate of return​ is: (1) 11​%, ​(2) 14​%, and​ (3) 17​%.

b.  Calculate the present value of bond B if the required rate of return​ is: (1) 11​%, ​(2) 14​%, and​ (3) 17​%.

c. From your findings in parts a and b​, discuss the relationship between time to maturity and changing required returns.

d.  If Lynn wanted to minimize interest rate​ risk, which bond should she​ purchase? ​ Why?

Answer 1

Answer a.

Bond A:

Face Value = $1,000

Annual Coupon Rate = 14%
Annual Coupon = 14% * $1,000
Annual Coupon = $140

Time to Maturity = 8 years

If interest rate is 11%:

Price of Bond = $140 * PVIFA(11%, 8) + $1,000 * PVIF(11%, 8)
Price of Bond = $140 * (1 - (1/1.11)^8) / 0.11 + $1,000 / 1.11^8
Price of Bond = $1,154.38

If interest rate is 14%:

Price of Bond = $140 * PVIFA(14%, 8) + $1,000 * PVIF(14%, 8)
Price of Bond = $140 * (1 - (1/1.14)^8) / 0.14 + $1,000 / 1.14^8
Price of Bond = $1,000.00

If interest rate is 17%:

Price of Bond = $140 * PVIFA(17%, 8) + $1,000 * PVIF(17%, 8)
Price of Bond = $140 * (1 - (1/1.17)^8) / 0.17 + $1,000 / 1.17^8
Price of Bond = $873.79

Answer b.

Bond B:

Face Value = $1,000

Annual Coupon Rate = 14%
Annual Coupon = 14% * $1,000
Annual Coupon = $140

Time to Maturity = 18 years

If interest rate is 11%:

Price of Bond = $140 * PVIFA(11%, 18) + $1,000 * PVIF(11%, 18)
Price of Bond = $140 * (1 - (1/1.11)^18) / 0.11 + $1,000 / 1.11^18
Price of Bond = $1,231.05

If interest rate is 14%:

Price of Bond = $140 * PVIFA(14%, 18) + $1,000 * PVIF(14%, 18)
Price of Bond = $140 * (1 - (1/1.14)^18) / 0.14 + $1,000 / 1.14^18
Price of Bond = $1,000.00

If interest rate is 17%:

Price of Bond = $140 * PVIFA(17%, 18) + $1,000 * PVIF(17%, 18)
Price of Bond = $140 * (1 - (1/1.17)^18) / 0.17 + $1,000 / 1.17^18
Price of Bond = $833.98

Answer c.

Price of bond will fluctuate more with the change in required return when time to maturity is high.

Answer d.

Long-term bonds have higher interest rate risk than short-term bonds. So, Lynn should purchase Bond A.