Several Periods in the Future
Now we know how to calculate the present value of a single sum that is
receivable one year in the future. The next step is to ask what would
happen if the sum were receivable at a later date. For example, what is
the present value of $100 to be received two years hence when the
interest rate is 5 percent? The answer is
can check this by seeing what would happen if $90.70 were lent out for
two years. In the first year, the loan would earn interest of
, and hence after one year, the outstanding loan
would be worth $95.24. If we assume that interest is compounded
annually, then in the second year the interest earned would equal
. Hence, after two years the firm would be repaid
$100.
In general, the present value of MRP dollars received t years in the future
when the interest rate is i per year is
This formula simply discounts the MRP by the interest rate, repeatedly,
once for each of the t periods that must pass until the MRP becomes
available. If we look at the formula, we see that the higher is i or t, the
higher is the whole term. This term, however, appears in the
denominator, so PV is negatively related to both i and t.
$ 100 /((1.05)(1.05))=$90.70(0.05)($90.70)=$4.54
(0.05)($95.24)=$4.76
PV = MRP
( 1 +i)t( 1 +i)t