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 it first coupon payment? (Round to the nearest cent)

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

Answer 1

We are given,

Face value = $1000

Coupon rate = 7%

Annual coupon = 7% * 1000 = $70

ytm = 6%

Time to maturity = 10 years

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

Using excel,

Future Value	1000
pmt	70
interest	6.0%
No of periods	10
Present Value	1073.60	(=PV(6%,10,-70,-1000,0))

a) Hence Price of bond when it was issued = $1,073.60

b) Price of the bond immediately before it makes it first coupon payment

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

Hence Price of the bond immediately before it makes it first coupon payment = $1,138.02.

c) Price of the bond immediately after it makes its first coupon payment

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

Using Excel,

Future Value	1000
pmt	70
interest	6.0%
No of periods	9
Present Value	1068.02	(=PV(6%,9,-70,-1000,0))

Hence Price of the bond immediately after it makes its first coupon payment = $1,068.02.

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