[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Table 9.3
CALCULATING PRESENT DISCOUNTED VALUE OF A THREE-YEAR PROJECT
Discount factor
Present discounted
Year Return (r = 0.10) value (r = 0.10)
1 $10,000
1
1.10
$ 9,091
2 $15,000
1 1
=
(1.10) 2 1.21
$12,397
3 $50,000
1 1
=
(1.10) 3 1.331
$37,566
Total $75,000 — $59,054
If the rate of interest is 10 percent and is compounded annually, $100 today is
worth $110 a year from now and $121 (not $120) in two years’ time. Thus, the present
discounted value today of $121 two years from now is $100. Table 9.2 shows how to
calculate the present discounted value of $100 received next year, two years from now,
and three years from now.
We can now see how to calculate the value of an investment project that will yield
a return over several years. We look at what the returns will be each year, adjust
them to their present discounted values, and then add these values up. Table 9.3
shows how this is done for a project that yields $10,000 next year and $15,000 the
year after, and that will be sold in the third year for $50,000. The second column of
the table shows the return in each year. The third column shows the discount factor—
what we multiply the return by to obtain the present discounted value of that year’s
return. The calculations assume an interest rate of 10 percent. The fourth column
multiplies the return by the discount factor to obtain the present discounted value of
that year’s return. In the bottom row of the table, the present discounted values of each
year’s return have been added up to obtain the total present discounted value of the
project. Notice that it is much smaller than the number we obtain simply by adding
up the returns, which is the “undiscounted” yield of the project.
212 ∂ CHAPTER 9 CAPITAL MARKETS