Table15-1 The Present Value of a Single Sum One Year in the
Future
Anyone who lends out $95.24 for one year at 5 percent interest will
receive $95.24 back plus $4.76 in interest, or $100 in total. When we
calculate this present value, the interest rate is used to discount (reduce to
its present value) the $100 to be received in one year’s time.
The actual present value that we have calculated depended on our
assumption that the interest rate was 5 percent. What if the interest rate is
7 percent? At that interest rate, the present value of the $100 receivable in
one year’s time would be.
These examples are easy to generalize. In both cases, we have found the
present value by dividing the sum that is receivable in the future by 1 plus
the rate of interest. In general, if the interest rate is i per year, then the
present value of the MRP (in dollars) received one year hence is
Table 15-1 computes the present value of an MRP of $500, received one
year from now, under alternative assumptions of the interest rate. There
is a negative relationship between present value and the interest rate.
For any given sum at a given point in the future, the present value of the
sum is negatively related to the interest rate. The firm earns an MRP of
$500 in one year’s time. Using the formula developed in the text, it is
clear that present value is lower when the interest rate is higher.
$ 100 /1.07=$93.46PV = (M 1 +RPi)