Question

1. Three years ago you purchased a 15-year $1,000 bond with a coupon rate of 6 percent. You now wish to sell the bond and read that yields are 10 percent. What price should you receive for the bond?

   	a	$727.45
   	b	$1,037.20
   	c	$912.55
   	d	$1,135.35

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

As nothing is mentioned, we are assuming annual interest payments at the end of the year

3 years have passed for a 15 year maturity bond. So, remaining life of the bond

= 15 – 3

= 12 years

Coupon rate = 6.0% or 0.06

Periodic interest

= Face Value x Coupon Rate

= $1,000 x 0.06

= $60 per annum

Time period = 12 years

Interest rate for discounting =10% or 0.10

Present value factor

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

So, discounting factor for period 2

= 1 / ( 1.10 ^ 2 )

= 1 / 1.21

= 0.826446

The following table shows the calculations

Calculations	A	B	C = A x B
Years	Cash Flow	PV Factor	Present Value
1	60	0.909091	54.55
2	60	0.826446	49.59
3	60	0.751315	45.08
4	60	0.683013	40.98
5	60	0.620921	37.26
6	60	0.564474	33.87
7	60	0.513158	30.79
8	60	0.466507	27.99
9	60	0.424098	25.45
10	60	0.385543	23.13
11	60	0.350494	21.03
12	60	0.318631	19.12
12	1000	0.318631	318.63
		Price	727.45

So, as per above calculations, the price of the bond is $727.45 and option a is the correct option