Question

Fresh Water, Inc. sold an issue of 25-year $1,000 par value bonds to the public. The bonds have a 8.41 percent coupon rate and pay interest annually. The current market rate of interest on the Fresh Water, Inc. bonds is 8.25 percent. What is the current market price of the bonds? Round the answer to two decimal places.

Answer 1

The market price of the bond is calculate by using the below steps: -

1. Determine interest payments.

In our case interest payment would be $841 (1000x8.41%)

2. Present Value annuity factor:

The present value annuity factor of 8.25% is to be considered since that is the market rate (Calculation of Annuity factor for 8.25% is explained below after the answer is completed). Annuity factor is 10.45

3.Present value of interest payments:

PV of $841 = 841 x 10.45 = $8,788.45

4. Present value of the Bonds face value:

We can assume that the bonds face value would be repaid after 25 years, Present value factor of 8.25 for 25th year is 0.1378. Present value of the bond is thus $1,000 x 0.1378 = $137.8

5. Market value of the bond:

PV of Face value + PV of Interest payments = 137.8 + 8,788.45 = $8,926.25

Calculation of PV:-

Calculate in excel for first year = 1/1.0825 [i.e 1/(1+interest rate)] for second year = first year PVF/1.0825 and so on for 25 years. Annuity factor is the total of PV factors till 25th year. below is the table:-

Year	PV Factor @ 8.25%
1	0.9238
2	0.8534
3	0.7883
4	0.7283
5	0.6728
6	0.6215
7	0.5741
8	0.5304
9	0.4899
10	0.4526
11	0.4181
12	0.3862
13	0.3568
14	0.3296
15	0.3045
16	0.2813
17	0.2599
18	0.2400
19	0.2218
20	0.2049
21	0.1892
22	0.1748
23	0.1615
24	0.1492
25	0.1378
Annuity Factor	10.4507