2) XYZ Company issued $30,000,000 of 10-year, 6% bonds, with interest payable semiannually, at a market (effective) interest rate of 8%. Calculate the present value of the bonds using the tables in Appendix A of your textbook. (5
Solution:
Calculation of the Present Value of the Bond
Calculation of Present Value of the Interest Payments
Amount of Interest Payment Semi annually = 1/2 x 6/100 x 30,000,000 = $900,000
Following are the steps to be followed on Microsoft Excel to calculate the Present Value of the Interest Payments :
Step 1: Click on "FORMULAS" tab at the top of Microsoft
Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "PV"
Step 4: Insert Rate = 0.08/2 Nper = 10*2 PMT = -900,000
PV = $12,231,293.71
Following are the steps to be followed on Microsoft Excel to calculate the Present Value of the Face value of the Bond to be received at the end of 10th Year
Step 1: Click on "FORMULAS" tab at the top of Microsoft
Excel
Step 2: Select the option "Financial"
Step 3: Under "Financial" select the option "PV"
Step 4: Insert Rate = 0.08/2 Nper = 10*2 FV = -30,000,000
PV = $13,691,608.39
Present Value of the Face value of the Bond to be received at the end of 10th Year is $13,691,608.39
Therefore, the Present value of the Bond
= Present Value of the Interest Payments + Present Value of the Face value of the Bond
= $12,231,293.71 + $13,691,608.39 = $25,922,902.10
Alternatively, the Present value of Bond can be calculated as follows:
|
Period |
Cash Inflows $ |
Df@ 4% |
Present Value of Cash Inflows $ |
|
1 |
9,00,000.00 |
0.961538 |
8,65,384.62 |
|
2 |
9,00,000.00 |
0.924556 |
8,32,100.59 |
|
3 |
9,00,000.00 |
0.888996 |
8,00,096.72 |
|
4 |
9,00,000.00 |
0.854804 |
7,69,323.77 |
|
5 |
9,00,000.00 |
0.821927 |
7,39,734.40 |
|
6 |
9,00,000.00 |
0.790315 |
7,11,283.07 |
|
7 |
9,00,000.00 |
0.759918 |
6,83,926.03 |
|
8 |
9,00,000.00 |
0.730690 |
6,57,621.18 |
|
9 |
9,00,000.00 |
0.702587 |
6,32,328.06 |
|
10 |
9,00,000.00 |
0.675564 |
6,08,007.75 |
|
11 |
9,00,000.00 |
0.649581 |
5,84,622.84 |
|
12 |
9,00,000.00 |
0.624597 |
5,62,137.34 |
|
13 |
9,00,000.00 |
0.600574 |
5,40,516.68 |
|
14 |
9,00,000.00 |
0.577475 |
5,19,727.57 |
|
15 |
9,00,000.00 |
0.555265 |
4,99,738.05 |
|
16 |
9,00,000.00 |
0.533908 |
4,80,517.36 |
|
17 |
9,00,000.00 |
0.513373 |
4,62,035.92 |
|
18 |
9,00,000.00 |
0.493628 |
4,44,265.31 |
|
19 |
9,00,000.00 |
0.474642 |
4,27,178.18 |
|
20 |
3,09,00,000.00 |
0.456387 |
1,41,02,356.64 |
|
Total Present Value of Cash Inflows $ |
2,59,22,902.10 |
Note: The Cash Inflows for 20th Period also includes Face value of the Bond $30,000,000.
2) XYZ Company issued $30,000,000 of 10-year, 6% bonds, with interest payable semiannually, at a market...