Question

Compute the price of a 5.7 percent coupon bond with fifteen years left to maturity and a market interest rate of 8.0 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Bond price

$

Is this a discount or premium bond?

Discount bond Premium bond

Answer 1

Assuming face value of the bond to be $1,000

When payments are made semiannually, interest rate is divided by 2 and time period is multiplied by 2

Time period n = 15 x 2 = 30 semi annual periods

Interest rate r = 8 / 2 = 4% or 0.04

Semi annual payments

= Principal x Rate x Time / 12 months

= $1,000 x 5.7% x 6 / 12

= $ 28.5

Maturity payment = Face value = $1,000

Present value factor

= 1 / (1 + r) ^ n

So, PV Factor for n = 2 will be

1 / (1.04 ^ 2)

= 1 / 1.0816

= 0.924556

The following table shows the calculations

Calculations	A	B	C = A x B
Time	Cash flow	PV Factor	Present value
1	28.5	0.961538	27.40384615
2	28.5	0.924556	26.34985207
3	28.5	0.888996	25.33639622
4	28.5	0.854804	24.36191944
5	28.5	0.821927	23.42492254
6	28.5	0.790315	22.52396398
7	28.5	0.759918	21.65765768
8	28.5	0.73069	20.82467084
9	28.5	0.702587	20.02372196
10	28.5	0.675564	19.25357881
11	28.5	0.649581	18.51305655
12	28.5	0.624597	17.80101591
13	28.5	0.600574	17.11636145
14	28.5	0.577475	16.45803986
15	28.5	0.555265	15.82503833
16	28.5	0.533908	15.21638301
17	28.5	0.513373	14.63113751
18	28.5	0.493628	14.06840145
19	28.5	0.474642	13.52730909
20	28.5	0.456387	13.00702797
21	28.5	0.438834	12.50675766
22	28.5	0.421955	12.02572852
23	28.5	0.405726	11.5632005
24	28.5	0.390121	11.11846202
25	28.5	0.375117	10.69082886
26	28.5	0.360689	10.27964314
27	28.5	0.346817	9.884272249
28	28.5	0.333477	9.504107931
29	28.5	0.320651	9.138565319
30	28.5	0.308319	8.787082037
30	1000	0.308319	308.318668
		Price	801.14

So, the price of the bond is $801.14

The bond is trading at below its face value. So, it is a discount bond