Question

1 - (Bond Valuations Relationships) A bond of a Corporation pays $100 in annual interest with a $1000 par value. The bonds mature in 15 years the markets required yield to maturity on a comparable risk bond as 8%. (A) calculate the value of the bond (B) how does the value change if the markets required to yield to maturity on a comparable risk bond (i) increases to 14% or (ii) decreases to 4%

Answer 1

Answer A.

Face Value = $1,000
Annual Coupon = $100
Time to Maturity = 15

Annual Interest Rate = 8%

Price of Bond = $100 * PVIFA(8%, 15) + $1,000 * PVIF(8%, 15)
Price of Bond = $100 * (1 - (1/1.08)^15) / 0.08 + $1,000 * (1/1.08)^15
Price of Bond = $100 * 8.55948 + $1,000 * 0.31524
Price of Bond = $1,171.19

Answer B-1.

Annual Interest Rate = 14%

Price of Bond = $100 * PVIFA(14%, 15) + $1,000 * PVIF(14%, 15)
Price of Bond = $100 * (1 - (1/1.14)^15) / 0.14 + $1,000 * (1/1.14)^15
Price of Bond = $100 * 6.14217 + $1,000 * 0.14010
Price of Bond = $754.32

Percentage Change in Price = ($754.32 - $1,171.19) / $1,171.19
Percentage Change in Price = -35.59%

Answer B-2.

Annual Interest Rate = 4%

Price of Bond = $100 * PVIFA(4%, 15) + $1,000 * PVIF(4%, 15)
Price of Bond = $100 * (1 - (1/1.04)^15) / 0.04 + $1,000 * (1/1.04)^15
Price of Bond = $100 * 11.11839 + $1,000 * 0.55526
Price of Bond = $1,667.10

Percentage Change in Price = ($1,667.10 - $1,171.19) / $1,171.19
Percentage Change in Price = 42.34%