Question

Calculate the fair present value of the following bonds, all of which have a 5 percent coupon rate (paid semiannually), face value of $1000, and a required rate of return of 8 percent.

a. The bond has 10 years remaining to maturity.

b. The bond has 15 years remaining to maturity.

c. The bond has 20 years remaining to maturity.

d. Wha do your answers say about the relationship between time to maturity and present value?

Answer 1

a)

Computation Of Present value of the bond
a	Semi-annual Coupon Amount	$                       25.00
	($1000*5%/2)
b	Present Value Annuity Factor for (20 Years,4%)	13.590326
c	Present Value Of Annual Interest (a*b)	$                    339.76
d	Redemption Value	$                 1,000.00
e	Present Value Factor Of (20 Years,4%)	0.45639
g	Present Value Of Redemption Amount (d*e)	$                    456.39
f	Present value of the bond (c+g)	$                    796.15

b)

Computation Of Present value of the bond
a	Semi-annual Coupon Amount	$                       25.00
	($1000*5%/2)
b	Present Value Annuity Factor for (30 Years,4%)	17.292033
c	Present Value Of Annual Interest (a*b)	$                    432.30
d	Redemption Value	$                 1,000.00
e	Present Value Factor Of (30 Years,4%)	0.30832
g	Present Value Of Redemption Amount (d*e)	$                    308.32
f	Present value of the bond (c+g)	$                    740.62

c)

Computation Of Present value of the bond
a	Semi-annual Coupon Amount	$                       25.00
	($1000*5%/2)
b	Present Value Annuity Factor for (40 Years,4%)	19.792774
c	Present Value Of Annual Interest (a*b)	$                    494.82
d	Redemption Value	$                 1,000.00
e	Present Value Factor Of (40 Years,4%)	0.20829
g	Present Value Of Redemption Amount (d*e)	$                    208.29
f	Present value of the bond (c+g)	$                    703.11

d) As we increase the time of the bond present value of bond is decreases.