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 6 % ​(annual payments). The yield to maturity on this bond when it was issued was 5 %.

a. What was the price of this bond when it was​ issued? 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

Price of bond is calculated as present value of coupon payment and par value of bond at maturity using yield to maturity as the discount rate.
Formula to calculate price of bond
Price of bond	Present value of coupon payment+Present value of par value.
a.
Calculation of price of bond when it was issued.
Year	Cash flow	Discount factor @ 5%		Present value
1	$60	0.95238	1/(1.05^1)	$57.14
2	$60	0.90703	1/(1.05^2)	$54.42
3	$60	0.86384	1/(1.05^3)	$51.83
4	$60	0.82270	1/(1.05^4)	$49.36
5	$60	0.78353	1/(1.05^5)	$47.01
6	$60	0.74622	1/(1.05^6)	$44.77
7	$60	0.71068	1/(1.05^7)	$42.64
8	$60	0.67684	1/(1.05^8)	$40.61
9	$60	0.64461	1/(1.05^9)	$38.68
10	$1,060	0.61391	1/(1.05^10)	$650.75
		Price of bond		$1,077.22
Coupon payment = 1000*6% = $60.
Thus, price of bond when it was issued is $1,077.22
b.
Calculation of price of bond immediately before first coupon payment
Year	Cash flow	Discount factor @ 5%		Present value
0	$60	1.00000	1/(1.05^0)	$60.00
1	$60	0.95238	1/(1.05^1)	$57.14
2	$60	0.90703	1/(1.05^2)	$54.42
3	$60	0.86384	1/(1.05^3)	$51.83
4	$60	0.82270	1/(1.05^4)	$49.36
5	$60	0.78353	1/(1.05^5)	$47.01
6	$60	0.74622	1/(1.05^6)	$44.77
7	$60	0.71068	1/(1.05^7)	$42.64
8	$60	0.67684	1/(1.05^8)	$40.61
9	$1,060	0.64461	1/(1.05^9)	$683.29
		Price of bond		$1,131.08
Thus, price of bond immediately before first coupon payment is $1,131.08.
c.
Calculation of price of bond immediately after first coupon payment
Year	Cash flow	Discount factor @ 5%		Present value
1	$60	0.95238	1/(1.05^1)	$57.14
2	$60	0.90703	1/(1.05^2)	$54.42
3	$60	0.86384	1/(1.05^3)	$51.83
4	$60	0.82270	1/(1.05^4)	$49.36
5	$60	0.78353	1/(1.05^5)	$47.01
6	$60	0.74622	1/(1.05^6)	$44.77
7	$60	0.71068	1/(1.05^7)	$42.64
8	$60	0.67684	1/(1.05^8)	$40.61
9	$1,060	0.64461	1/(1.05^9)	$683.29
		Price of bond		$1,071.08
Thus, price of bond immediately after first coupon payment is $1,071.08.