Question

Part1. What is the price of a $1,000 par value bond with an 8% coupon rate paid annually, if the bond is priced to yield 8% and has 9 years to maturity? Part 2. What would be the price of the bond if the yield decreased to 6%? Part 3. What would be the price of the bond if the yield rose to 10% and was callable at 110% of par in 4 years? Please specify between parts 1, 2, and 3, Please show work and do not use Excel to show answer, please show the work through using the correct formulas for each part. Thank you.

Answer 1

Answer Part 1:

Par value = $1,000

Coupon rate = 8%

Yield = 8%

Since yield is equal to coupon rate, price of the bond will be same as par value.

Price of the bond = $1,000

Answer Part 2:

Annual coupon = 1000 * 8% = $80

Yield = 6%

Price = Value of bond = Present value of annuity of $80 for 9 years + Present value of Redemption amount

PV factor for annuity of $1 at 6% discount rate for 9 years = (1 - 1 / (1 + k) ⁿ) / k = (1 - 1 / (1 + 6%) ⁹) / 6%

PV factor of $1 at 6% discount rate for 9 years = 1 / ( 1 + k) ⁿ = 1 / (1 + 6%) ⁹

Price = Value of bond = 80 * (1 - 1 / (1 + 6%) ⁹) / 6% + 1000 * 1 / (1 + 6%) ⁹

= $1,136.03

Price of the bond = $1,136.03

Answer Part 3:

Yield = 10%

Callable in 4 years at = 110% * 1000 = $1,100

Price = Value of bond = 80 * (1 - 1 / (1 + 10%) ⁴) / 10% + 1100 * 1 / (1 + 10%) ⁴

= $1,004.90

Price of the bond = $1,004.90