# Net Present Value

There are times when an investor will pay an amount that is greater than the present value of the future cash ﬂows and there are times when an investor will pay an amount that is less than the present value. The net present value or NPV of an investment is equal to the value initially paid for the investment (stated as a negative cash flow number because the money is paid out or invested at the outset) plus the present value of the investment‘s future cash ﬂows.

NPV = CF(0) + PV (future cash ﬂows) where CF(0) is generally a negative number

If the net present value is equal to zero, then the investor is “earning his cost of capital.” In other words, the investor will earn a return on his initial cash flow (i.e., his investment) that is equal to the discount rate he applied in calculating the present value of the investment. Said another way, the investor’s discount rate is equal to the interest rate that his money is earning.

Let’s consider a simple bond. Assume that DebtCo is issuing or selling \$100 million of bonds with a ﬁve year maturity and paying interest of 8 percent. Interest will be paid annually. This means that DebtCo will sell bonds (which are essentially interest-paying IOUs) and each year for ﬁve years DebtCo will pay investors 8 percent on their investment (or \$8 million per year during the life of the bond). At the end of the ﬁfth year, DebtCo will pay its last interest payment and return the principal to the investors. How much would this investment be worth to an investor considering buying \$10,000 of these bonds at par (at the face value of the bonds)? The investor’s discount rate is 8 percent. Notice that the discount rate is equal to the coupon or interest paid on the bond. In this situation, the present value (or investment value) of the cash ﬂows is equal to the original investment amount. Why is that? Because, if you can earn your “cost of capital,” then the present value of an investment is equal to the amount paid for the investment. This is an example of a situation in which the NPV is zero. The amount paid was \$10,000 and the present value of the cash ﬂows earned was \$10,000 because the interest earned was 8 percent and the investor’s discount rate was 8 percent. The investor’s discount rate is 8 percent because there are similarly risky investments available in the market that are currently paying 8 percent – not because the bond is paying a coupon of 8 percent interest.

What would happen if, instead of 8 percent, the cost of capital, or discount rate, were 5 percent but the investor still paid \$10,000 for the investment? Let’s see how the net present value of the investment would change. A positive NPV, as in this example, means that you bought an investment or asset at a price that was less than the present value of its future cash flows. That is good since it means that you earned a return on your capital which is greater than the cost of your capital (the opportunity cost or your discount rate for the asset). An NPV-negative transaction, on the other hand, is not good since it means that you do not even earn enough to cover your cost of capital.