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 |
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