Question

Suppose that Ally Financial Inc. issued a bond with 10 years until​ maturity, a face value of $1,000​ and a coupon rate of 7% ​(annual payments). The yield to maturity on this bond when it was issued was 6 %.

a. What was the price of this bond when it was​ issued? (round to the nearest cent).   

b. Assuming the yield to maturity remains​ constant, what is the price of the bond immediately before it makes its first coupon​ payment?

c. Assuming the yield to maturity remains​ constant, what is the price of the bond immediately after it makes its first coupon​ payment?

Answer 1

Answer a.

Face Value = $1,000

Annual Coupon Rate = 7%
Annual Coupon = 7% * $1,000
Annual Coupon = $70

Time to Maturity = 10 years
Annual YTM = 6%

Price of Bond = $70/1.06 + $70/1.06^2 + $70/1.06^3 + ... + $70/1.06^10 + $1,000/1.06^10
Price of Bond = $70 * (1 - (1/1.06)^10) / 0.06 + $1,000 / 1.06^10
Price of Bond = $1,073.60

Answer b.

Face Value = $1,000

Annual Coupon Rate = 7%
Annual Coupon = 7% * $1,000
Annual Coupon = $70

Time to Maturity = 10 years
Annual YTM = 6%

Price of Bond = $70 + $70/1.06 + $70/1.06^2 + $70/1.06^3 + ... + $70/1.06^9 + $1,000/1.06^9
Price of Bond = $70 * 1.06 * (1 - (1/1.06)^10) / 0.06 + $1,000 / 1.06^9
Price of Bond = $1,138.02

Answer b.

Face Value = $1,000

Annual Coupon Rate = 7%
Annual Coupon = 7% * $1,000
Annual Coupon = $70

Time to Maturity = 10 years
Annual YTM = 6%

Price of Bond = $70/1.06 + $70/1.06^2 + $70/1.06^3 + ... + $70/1.06^9 + $1,000/1.06^9
Price of Bond = $70 * (1 - (1/1.06)^9) / 0.06 + $1,000 / 1.06^9
Price of Bond = $1,068.02