Question

Bond Valuation Time to Maturity (Years) Coupon Rate Required Return Frequency Bond Valuations This bond has 20 years to maturity Coupon rate Current required return 9.00 % Semi Annual interest payments 8.00% Face Value Value cach year $1,000.00 Par value 20 Find the value of this bond for each of the 18 years to maturity listed 16 14 Why does the value of the bond continue to increase over time? 12 10 Is this bond currently selling for a premium or a discount? 4

Answer 1

Bond Valuation
Time to maturity (Years)	20Years
Coupon Rate	8%
Required Return	9%
Frequency	Semiannual
Face Value	$1,000
Value each Year
20	$907.99
18	$911.67
16	$916.06
14	$921.29
12	$927.52
10	$934.96
8	$943.83
6	$954.41
4	$967.02
2	$982.06
0	$1,000.00

Explanation:

Price of bond = C x PVIFA (r, n) + F x PVIFA (r, n)

                        =C x [{1-(1+r) ^–n}/r] +M x (1+r) ^-n

M = Face Value = $ 1,000

C = Coupon amount = Face value x Coupon rate/Coupon frequency in a year

                                    = $ 1,000 x 0.08/2 = $ 1,000 x 0.04 = $ 40

n = No of periods

r = Rate of interest = 9 % p.a. or 0.09/2 = 0.045 semiannually

Year to maturity	n	Coupon amount (C)	PVIFA (r ,n)	C x PVIFA(r, n)	Face Value (F)	PVIF (r, n)	F/ PVIF(r, n)	Value of bond
20	40	$40	18.4015844202798	$736.06	$1,000	5.81636453759743	$171.93	$907.99
18	36	$40	17.6660405771548	$706.64	$1,000	4.87737846147563	$205.03	$911.67
16	32	$40	16.7888908626532	$671.56	$1,000	4.08998103586761	$244.50	$916.06
14	28	$40	15.7428735125770	$629.71	$1,000	3.42969999270791	$291.57	$921.29
12	24	$40	14.4954783660347	$579.82	$1,000	2.87601383400679	$347.70	$927.52
10	20	$40	13.0079364514537	$520.32	$1,000	2.41171402483740	$414.64	$934.96
8	16	$40	11.2340150491065	$449.36	$1,000	2.02237015303025	$494.47	$943.83
6	12	$40	9.1185807807607	$364.74	$1,000	1.69588143276786	$589.66	$954.41
4	8	$40	6.5958860673587	$263.84	$1,000	1.42210061283661	$703.19	$967.02
2	4	$40	3.5875256979286	$143.50	$1,000	1.192518600625	$838.56	$982.06
0	0	$40	0.0000000000000	$0.00	$1,000	1.00000000000	$1,000.00	$1,000.00

The value of bond continues to increase over time as the bond is proceeding towards maturity date and effect of time value is diminishing.

This is a discount bond as coupon rate is less than prevailing interest rate.