Question

A $5 million bond was issued at face value on June 1, 2017. The bond has a twenty five year term and a fixed interest rate of 4% paid annually. At the time of issuance, the current market rate of interest is also 4%.

Using the present value tables, demonstrate why the bond was issued at face value ($5 million) by calculating the present value of both the principal and interest using Table P and Table I.
Present Value of 1 Table (PV of 1 Table) Present Value Factors for 1.000 at Compound Interest Rounded to three decimal places. Example: When interest is 89 per period and it is compounded each period, receiving 1.000 at the end of the 10th period has a present value of 0.463. 152434445465 84 105 12% 11 0.990 0.980 0.971 0.962 0.952 0.9431 0.9261 0.909 0.893 2 0.980 0.961 0.943 0.925 0.907 0.890 0.857 0.826 0.797 3 0.971 0.942 0.915 0.889 0.864 0.840 0.794 0.751 0.712 4 0.961 0.9241 0.880.8551 0.8231 0.7921 0.7351 0.60306361 5 0.951 0.906 0.863 0.822 0.784 0.747 0.681 0.621 0.567 6 0.942 0.888 0.837 0.790 0.746 0.7051 0.630 0.564 0.507 71 0.933 0.871 0.813 0.760 0.711 0.665 0.583 0.513 0.452 $ 0.923 0.853 0.780 0.731 0.6771 0.622105401 0.4671 0.404 91 0.914 0.837 0.766 0.7031 0.645 0.592 0.500 0424 0.361 101 0.905 0.820 0.7441 0.6761 0.6141 0.558 0463 0.3861 0.322 11 0.896 0.804 0.722 0.650 0.585 0.527 0.429 0.350 0.287 12 0.887 0.788 0.701 0.625 0.557 0.497 0.397 0.319 0.257 13 0.879 0.773 0.681 0.601 0.530 0.469 0.368 0.290 0.229 1758 0.661 0.577 0.05 0.442 0.340 0.263 0.205 15 0.861 0.743 0.642 0.555 0.481 0.417 0.313 0.239 0.183 16 0.853 0.728 0.623 0.534 0.45 0.394 0.292 0.218 0.163 17 0.844 0.714 0.605 0.513 0.436 0.371 0.270 0.198 0.146 18 0.836 0.700 0.587 0.494 0.416 0.350 0.250 0.180 0.130 19 0.828 0.686 0.570 0.475 0.396 0.331 0.232 0.164 0.116 201 0.820 0.673 0.354 0.456 0.377 03121 0.2151 0.149 0.104 21 0.811 0.660 0.538 0.439 0.359 0.294 0.1991 0.135 0.093 22 0.803 0.647 0.522 0.422 0.342 0.278 0.184 0.123 0.083 23 0.795 0.634 0.507 0.406 0.326 0.262 0.170 0.1121 0.074 241 0.788 0.622 0.492 0.390 0.310 0.247 0.158 0.1021 0.066 25 0.780 0.610 0.478 0.375 0.295 0.233 0.146 0.092] 0.059 26 0.772 0.598 0.464 0.361 0.281 0.220 0.135 0.084 0.053 27 0.764 0.586 0.450 0.347 0.268 0.207 0.125 0.076 0.047 28 0.757 0.574 0.437 0.333 0.25% 0.196 0.116 0.069 0.042| 29 0.749 0.563 0.424 0.321 0.243 0.185 0.107| 0.063 0.037 30 0.742 0.552 0.412 0.308 0.231 0.174 0,099 0.057 0.033

Answer 1

Interest	200000	=5000000*4%
	Amount	PV factor 4%	Present value
Interest	200000	15.622	3124400
Principal	5000000	0.375	1875000
Total present value			4999400

It can be seen that the present value of bonds calculated is $4999400 based on PV factors given

The slight difference is due to rounding off of PV factors to 3 decimal places.

So when contract interest rate equals current market rate, bonds will issue at face value.