Page 615 - Accounting Principles (A Business Perspective)

15. Long-term financing: Bonds

Exhibit 122: Compound interest and future value

Future value (after three periods) of $100
received at the end of the -
First period: 1.12360 x $100=$112.36
Second period: 1.06000 x 100 = 106.00
Third period: 1.00000 x 100 = 100.00
Total future value $318.36

Such a procedure would become quite tedious if the annuity consisted of many receipts. Fortunately, tables are
available to calculate the total future value directly. See the Appendix, Table A.2. For the annuity just described, you

can identify one single factor by looking at the 3 period row and 6 per cent column. The factor is 3.18360 (the sum
of the three factors shown above), and when multiplied by USD 100, yields USD 318.36, which is the same answer.
In Exhibit 123, we graphically present the future value of an annuity.
Present value

Present value is the current worth of a future cash receipt and is the reciprocal of future value. In future value,
we calculate the future value of a sum of money possessed now. In present value, we calculate the current worth of
rights to future cash receipts possessed now. We discount future receipts by bringing them back to their present
values.
Assume that you have the right to receive USD 1,000 in one year. If the appropriate interest rate is 12 per cent
compounded annually, what is the present value of this USD 1,000 future cash receipt? You know that the present
value is less than USD 1,000 because USD 1,000 due in one year is not worth USD 1,000 today. You also know that

the USD 1,000 due in one year is equal to some amount, P, plus interest on P at 12 per cent for one year. Thus, P +
0.12P = USD 1,000, or 1.12P = USD 1,000. Dividing USD 1,000 by 1.12, you get USD 892.86; this amount is the
present value of your future USD 1,000. If the USD 1,000 was due in two years, you would find its present value by
dividing USD 892.86 by 1.12, which equals USD 797.20. Portrayed graphically, present value looks similar to future
value, except for the direction of the arrows (Exhibit 124).
Table A.3 (end-of-text Appendix) contains present value factors for combinations of a number of periods and
interest rates. We use Table A.3 in the same manner as Table A.1. For example, the present value of USD 1,000 due
in four years at 16 per cent compounded annually is USD 552.29, computed as USD 1,000 X 0.55229. The 0.55229
is the present value factor found in the intersection of the 4 period row and the 16 per cent column.

616