Page 592 - Sensors and Control Systems in Manufacturing

Economic and Social Inter ests in the Workplace
be worth $1.05 at the end of one year, $1.1025 at the end of the second 545
year, and $1.1576 at the end of the third year.* Suppose an opportu-
nity to invest some money with the expectation of receiving $1.1576
(including the amount invested and the interest or other income) at
the end of the third year. Investment must not be more than $1.00,
because the present value of $1.1576 to be received three years hence
is $1.00 (based on the best alternative investment at 5 percent).

*First year: $1.00 + 0.05 ($1.00) = 1.05 × $1.00 = $1.05
2
Second year: 1.05 (1.05 × $1.00) = 1.05 × $1.00 = $1.1025
3
2
Third: 1.05 (1.05 × $1.00) = 1.05 × $1.00 = $1.1576
This present value is found by discounting the expected future
value by the opportunity cost rate. This is accomplished by reversing
the process for finding a future value, as follows:

3
$1.1576 ÷ 1.05 = $1.00
or, in general terms,

Present value = value n years hence ÷ (1 + discount rate) n
Table 11.6 shows another way of applying the present-value con-
cept to capital expenditure decisions. Consider an investment of $6.50
in an asset that would yield the amounts shown in Table 11.6 if placed
in a savings account at 5 percent. At the end of five years, the amounts
received from the asset investment would total $7.00 (including the
salvage value of the asset), whereas the savings account would be
3
worth $6.50 × 1.05 , or $7.52. Therefore, the $6.50 should not be
invested in the asset.
The present-value analysis in column (4) of Table 11.6 shows that
the present value of the asset investment is $6.30, which is 20 cents
less than the amount that would be invested. In other words, the
value of the investment opportunity is minus 20 cents. If the amount

(1) (2) (3) (4)
Amount to be
End of year received Discount factor Present value
1 $2.00 1.05 $1.90
2 2.00 (1.05) 2 1.81
3 3.00 (1.05) 3 2.59
Total $7.00 $6.30

TABLE 11.6 Application of Present Values to Capital Investment