The present value formula is a useful tool for discovering the value of expected future cash flows for a given level of risk. This measure of risk, called a discount rate, is used to change the present value of an asset to coincide with the riskiness of buying a security. However, sometimes only the present value and cash flows of an asset are known. From this information, the riskiness of the asset, or discount rate, can be calculated.
The present value formula is given as:
PV = FV * [1 / (1 + r)n]
where PV is the present value of the asset, FV is the future value, r is the discount rate, and n is the number of periods.
Suppose that an investor believes that an asset will be worth $10,000 in five years. This $10,000 represents the future value of the investment. Today, the asset is selling for $7,129.86. This amount represents the present value of the asset. If the asset is held for the full five years and the future value cash flow of $10,000 is realized, what is the discount rate of the asset? In other words, how risky is the purchase of the asset?
The present value formula above can be rearranged to solve for the discount rate. Doing so gives the following formula:
r = [FV / PV]1/n – 1
Plugging in the information above, we get:
0.07 = [10,000 / 7,129.86]1/5 – 1
So the discount rate associated with purchasing the asset today is 7%. Recall that this figure represents the riskiness of the asset. Had the present value of the asset been lower, we know that the asset would be riskier. If the present value were higher, the asset would be less risky. The discount rate is a method of comparing different scenarios in purchasing assets and evaluating the riskiness of buying the asset. Had the price of the asset been $5,193.69, the discount rate would be:
0.14 = [10,000 / 5193.69]1/5 – 1
Because the price is lower in this case, the riskiness of the asset is higher than when the price was $7,129.86. Recall that riskier assets cost less to compensate the buyer for taking on higher risk in realizing any future cash flows.