Financial Accounting: An Integrated Statements Approach, 2nd Edition

Chapter 10 Liabilities 449

In this case, $100,000 to be received 10 years in the future is worth $55,840 today. This

process of converting a future amount into a present value is called discounting.

Discounting converts future dollars into current dollars as shown in Exhibit 6.

In other words, if $55,840 is invested today at 6% annual interest, it will be worth

$100,000 in 10 years.

Present Value of a Series of Payments to Be Received in the Future. Up to this

point, we have discussed the present value of $1 to be received in the future. Assume,

however, that several amounts are to be received in the future. For example, assume

that you inherit $60,000, to be received in 10 annual payments of $6,000, with the first

payment being received one year from today. How much would your inheritance be

worth in today’s dollars assuming 6% annual interest?

One way to determine the present value of this stream of cash receipts is to add

the present values of the individual future amounts. Using the present value of $1 table

in Exhibit 5, your inheritance has a present value of $44,160.54, as shown in Exhibit 7.

Today  1  9

Present

Value

Future

Amount

$55,840

Present value of $100,000 for 10 years at 6%

$100,000

Exhibit 6 10 years forward

Converting a Future
Amount to Its Present
Value

Periods 5% 51 – 2 %6%6^1 – 2 % 7% 10% 11% 12% 13% 14%

1 0.95238 0.94787 0.94340 0.93897 0.93458 0.90909 0.90090 0.89286 0.88496 0.87719

2 0.90703 0.89845 0.89000 0.88166 0.87344 0.82645 0.81162 0.79719 0.78315 0.76947

3 0.86384 0.85161 0.83962 0.82785 0.81630 0.75132 0.73119 0.71178 0.69305 0.67497

4 0.82270 0.80722 0.79209 0.77732 0.76290 0.68301 0.65873 0.63552 0.61332 0.59208

5 0.78353 0.76513 0.74726 0.72988 0.71299 0.62092 0.59345 0.56743 0.54276 0.51937

6 0.74622 0.72525 0.70496 0.68533 0.66634 0.56447 0.53464 0.50663 0.48032 0.45559

7 0.71068 0.68744 0.66506 0.64351 0.62275 0.51316 0.48166 0.45235 0.42506 0.39964

8 0.67684 0.65160 0.62741 0.60423 0.58201 0.46651 0.43393 0.40388 0.37616 0.35056

9 0.64461 0.61763 0.59190 0.56735 0.54393 0.42410 0.39092 0.36061 0.33288 0.30751

10 0.61391 0.58543 0.55840 0.53273 0.50835 0.38554 0.35218 0.32197 0.29459 0.26974

Exhibit 5

Present Value of $1 Factors

Present ValueFuture AmountPresent Value of $16%,n 10

$55,840 $100,000 0.55840

multiplying the $100,000 by the present value of $1 factor for 10 periods at 6% annual

interest, as shown below.