Question

please answer both and show work!

Calculate the current price of a $5,000 par value bond that has a coupon rate of 20 percent, pays coupon interest quarterly (i.e. 4 times per year), has 22 years remaining to maturity, and has a current yield to maturity (discount rate) of 8 percent. (Round your answer to 2 decimal places and record without dollar sign or commas).

Answer 1

1.

Number of periods to maturity = n = 22*4 = 88 quarters

Yield to Maturity = r = 8%/4 = 2% quarterly

Face Value FV = $5000

Quarterly Coupon Payment P = 20%*5000/4 = $250

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 250(1 - 1.02^-88)/0.02 + 5000/1.02⁸⁸ = $11187.06

2.

Number of periods to maturity = n = 25*2 = 50 semiannual periods

Yield to Maturity = r = 13%/2 = 6.5% semiannual

Face Value FV = $1000

Semiannual Coupon Payment P = 16%*1000/2 = $80

Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ

= P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 80(1 - 1.065^-50)/0.065 + 1000/1.065⁵⁰ = $1220.87