The basic present value concept is that cash paid (or
received) in the future has less value now than the same amount of cash
paid (or received) today. To illustrate, if we must pay $1 one year from
now, its present value is less than $1. To see this, assume that we
borrow $0.9259 today that must be paid back in one year with 8%
interest. Our interest expense for this loan is computed as $0.9259 ×
8%, or $0.0741. When the $0.0741 interest is added to the $0.9259
borrowed, we get the $1 payment necessary to repay our loan with
interest. This is formally computed in Exhibit 14A.1.
The $0.9259 borrowed is the present value of the $1 future payment.
More generally, an amount borrowed equals the present value of the
future payment. (This same interpretation applies to an investment. If
$0.9259 is invested at 8%, it yields $0.0741 in revenue after one year.
This amounts to $1, made up of principal and interest.)
| EXHIBIT 14A.1 | Components of a One-Year Loan |
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Point: Benjamin Franklin is said to have described compounding as “the money, money makes, makes more money.”
To
extend this example, assume that we owe $1 two years from now instead
of one year, and the 8% interest is compounded annually.
Compounded
means that interest during the second period is based on the total of
the amount borrowed plus the interest accrued from the first period. The
second period’s interest is then computed as 8% multiplied by the sum
of the amount borrowed plus interest earned in the first period. Exhibit 14A.2
shows how we compute the present value of $1 to be paid in two years.
This amount is $0.8573. The first year’s interest of $0.0686 is added to
the principal so that the second year’s interest is based on $0.9259.
Total interest for this two-year period is $0.1427, computed as $0.0686
plus $0.0741.
| EXHIBIT 14A.2 | Components of a Two-Year Loan |
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