Question

A bond with face Value =$1,000 with semi-annual payments, a coupon rate of 7%, and has 8 years to maturity. The market requires a yield of 8% on bonds of this risk. What is this bond’s price?

Answer 1

Price of a bond is the present value of all future cash flows receivable from the bond discounted at required rate of return

Future cash flows are periodic interest payments and maturity value of the bond

When interest is paid semi-annually, interest rate for discounting the bond is divided by 2 and time period of maturity is multiplied by 2

Coupon rate = 7% or 0.07

Periodic interest

= Face Value x Coupon Rate x 6 months / 12 months

= $1,000 x 0.07 x 6 / 12

= $35 every 6 months

Time period = 8 x 2 = 16 periods each of 6 months

Interest rate for discounting = 8 / 2 = 4% or 0.04

Present value factor

= 1 / ( 1 + Rate of discounting ) ^ Number of periods

So, discounting factor for period 2

= 1 / ( 1.04 ^ 2 )

= 1 / 1.0816

= 0.924556

The following table shows the calculations

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present Value
1	35	0.961538	33.65
2	35	0.924556	32.36
3	35	0.888996	31.11
4	35	0.854804	29.92
5	35	0.821927	28.77
6	35	0.790315	27.66
7	35	0.759918	26.60
8	35	0.73069	25.57
9	35	0.702587	24.59
10	35	0.675564	23.64
11	35	0.649581	22.74
12	35	0.624597	21.86
13	35	0.600574	21.02
14	35	0.577475	20.21
15	35	0.555265	19.43
16	35	0.533908	18.69
16	1000	0.533908	533.91
		Price	941.74

So, as per above calculations, the price of the bond is $ 941.74