Question

Converse Company has a bond currently outstanding. The bond has a face value of $1,000 and matures in 10 years. The bond makes no coupon payments for the first three years, then pays $40 every six months over the subsequent four years, and finally pays $60 every six months over the last three years. If the required return on these bonds is 6.2 percent compounded semiannually, what is the current price of the bond? (Hint: it may be useful to draw a timeline of the cash flows)

Answer 1

Price of Bond = Present value of coupon payment + Present value of face value
The coupon payment paid would be semi annual and therefore the semi annual yield is 3.1% (6.2%/2)
Time	Cash flow	Discount factor @ 3.1% (1/(1+r^n)		Present Value (Cash flow*Discount factor)
1	0	0.96993	1/(1.031^1)	0.00
2	0	0.94077	1/(1.031^2)	0.00
3	0	0.91248	1/(1.031^3)	0.00
4	0	0.88504	1/(1.031^4)	0.00
5	0	0.85843	1/(1.031^5)	0.00
6	0	0.83262	1/(1.031^6)	0.00
7	$40	0.80759	1/(1.031^7)	32.30
8	$40	0.78330	1/(1.031^8)	31.33
9	$40	0.75975	1/(1.031^9)	30.39
10	$40	0.73691	1/(1.031^10)	29.48
11	$40	0.71475	1/(1.031^11)	28.59
12	$40	0.69326	1/(1.031^12)	27.73
13	$40	0.67241	1/(1.031^13)	26.90
14	$40	0.65220	1/(1.031^14)	26.09
15	$60	0.63259	1/(1.031^15)	37.96
16	$60	0.61357	1/(1.031^16)	36.81
17	$60	0.59512	1/(1.031^17)	35.71
18	$60	0.57722	1/(1.031^18)	34.63
19	$60	0.55987	1/(1.031^19)	33.59
20	$1,060	0.54303	1/(1.031^20)	575.62
		Price of bond		987.12
The current price of bond is $987.12