Present Value
by MaestriSuppose you have some extra cash, and you have a chance to buy a low-risk security that will pay $127.63 at the end of five years. Your local bank is currently offering 5 percent interest on five-year certificates of deposit (CDs), and you regard the security as being exactly as safe as a CD. The 5 percent rate is defined as your opportunity cost rate, or the rate of return you could earn on an alternative investment of similar risk. How much should you be willing to pay for the security?
From the future value example presented in the previous section, we saw that an initial amount of $100 invested at 5 percent per year would be worth $127.63 at the end of five years. As we will see in a moment, you should be indifferent between $100 today and $127.63 at the end of five years. The $100 is defined as the present value, or PV, of $127.63 due in five years when the opportunity cost rate is 5 percent. If the price of the security were less than $100, you should buy it, because its price would then be less than the $100 you would have to spend on a similar-riskalternative to end up with $127.63 after five years. Conversely, if the security cost more than $100, you should not buy it, because you would have to invest only $100 in a similar-risk alternative to end up with $127.63 after five years. If the price were exactly $100, then you should be indifferent—you could either buy the security or turn it down. Therefore, $100 is defined as the security’s fair, or equilibrium,
value.
In general, the present value of a cash ?ow due n years in the future is the amount which,
if it were on hand today, would grow to equal the future amount. Since $100 would grow to
$127.63 in ?ve years at a 5 percent interest rate, $100 is the present value of $127.63
due in ?ve years when the opportunity cost rate is 5 percent.
Taken From : Five-Minute MBA – Corporate Finance
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