Question

Sam wants to purchase a bond that has a par (face) value of $1000, an annual coupon rate of 7%, and a maturity of 10 years. Sam's annual required rate of return is 11%. What should Sam be willing to pay for this bond?

760.99

1000

2100.00

764.43

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

Principal = Face Value of the Bond = $1,000

Rate of interest = 7%

Annual interest payment

= Principal x Rate x Time

= $1,000 x 7% x 1 year

= $70

Required rate of return = 11%

Present Value Factor

= 1 / ( 1 + Required rate of return ) ^ Number of years

So, PV Factor for year 2 will be

= 1 / ( 1.11 ^ 2)

= 1 / 1.2321

= 0.811622

The following table shows the calculations :

Calculations	A	B	C = A x B
Years	Cash Flows	PV Factor	Present Value
1	70	0.900901	63.06
2	70	0.811622	56.81
3	70	0.731191	51.18
4	70	0.658731	46.11
5	70	0.593451	41.54
6	70	0.534641	37.42
7	70	0.481658	33.72
8	70	0.433926	30.37
9	70	0.390925	27.36
10	70	0.352184	24.65
10	1000	0.352184	352.18
		Price	764.43

So, as per above calculations, the price of the bond or the amount that the investor should be willing to pay is $764.43 and option D is the correct option