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

To check this formula, consider the present discounted value of $100. According
to the formula, it is $100/(1 + r). In other words, take the present discounted value,
$100/ (1 + r), and put it in a bank. At the end of the year you will have
$100
1 + r
× (1 + r) = $100,
confirming our conclusion that $100/(1 + r) today is worth the same as $100 one year
from now.
We can now evaluate the two options for purchasing the stereo. To compare
$400 today with $425 in one year, we need to calculate the present discounted value
of $425. If the interest rate is 5 percent, the present discount value of $425 is $404.76.
Since this is greater than $400, you are better off paying for the stereo today.
Present discounted values depend on the rate of interest. If the interest rate
increases, the present discounted value of future amounts will decrease. If the interest
rate rises to 10 percent, the present discounted value of $425 falls to $386.96.
Now it is cheaper to postpone payment for the stereo. You can take your $400, put
it in the bank, and earn 10 percent interest. In one year, you will have $440. After
paying $425 for the stereo, you are left with $15 more than if you had paid for it
immediately.
The concept of present discounted value is important because so many decisions
in economics are oriented to the future. Whether a person is buying a car or
a house or saving for retirement, or a company is building a factory or making an
investment, the decision maker must be able to value money that will be received one,
two, five, or ten years in the future.
Wrap-Up
PRESENT DISCOUNTED VALUE
Present discounted value of $1.00 next year = $1.00/(1 + interest rate).
Inflation and the Real Rate of Interest The interest rate, we have seen, is
a price. It tells us how many dollars we can get in the next period if we give up one
dollar today. But dollars are of value only because of the goods that can be bought
with them. If prices rise, then a dollar will buy less. Suppose a couple has been saving
so that in a year they will have $40,000, which they plan to use to buy a BMW. If
prices double between now and next year, their $40,000 will get them only a Honda
Civic. Thus, to know how much we can actually purchase in the future if we save
today, we need to take into account more than just the interest rate: we also need
to consider how the general level of prices will change. The rate at which the general
level of prices increases each year is the rate of inflation. If the inflation rate is 5 percent,
then prices on average will be 5 percent higher in one year; if inflation is 10
percent, prices will go up 10 percent. Some prices will rise faster than the overall
inflation rate; others will rise more slowly or even decline. For example, over the
194 ∂ CHAPTER 9 CAPITAL MARKETS