Custom Search

Net Present Value

Earlier you learned how to discount future cash payments to find their present value. We now apply these ideas to evaluate a simple investment proposal. Suppose that you are in the real estate business. You are considering construction of an office block. The land would cost $50,000 and construction would cost a further $300,000. You foresee a shortage of office space and predict that a year from now you will be able to sell the building for $400,000. Thus you would be investing $350,000 now in the expectation of realizing $400,000 at the end of the year. You should go ahead if the present value of the $400,000 payoff is greater than the investment of $350,000. Assume for the moment that the $400,000 payoff is a sure thing. The office building is not the only way to obtain $400,000 a year from now. You could invest in a 1-year U.S. Treasury bill. Suppose the T-bill offers interest of 7 percent. How much would you have to invest in it in order to receive $400,000 at the end of the year? That s easy: you would have to invest

Therefore, at an interest rate of 7 percent, the present value of the $400,000 payoff from the office building is $373,832. Let s assume that as soon as you have purchased the land and laid out the money for construction, you decide to cash in on your project. How much could you sell it for? Since the property will be worth $400,000 in a year, investors would be willing to pay at most $373,832 for it now. That s all it would cost them to get the same $400,000 payoff by investing in a government security. Of course you could always sell your property for less, but why sell for less than the market will bear?

The $373,832 present value is the only price that satisfies both buyer and seller. In general, the present value is the only feasible price, and the present value of the property is also its market price or market value.

To calculate present value, we discounted the expected future payoff by the rate of return offered by comparable investment alternatives. The discount rate 7 percent in our example is often known as the opportunity cost of capital. It is called the opportunity cost because it is the return that is being given up by investing in the project. The building is worth $373,832, but this does not mean that you are $373,832 better off. You committed $350,000, and therefore your net present value (NPV) is $23,832. Net present value is found by subtracting the required initial investment from the present value of the project cash flows:

NPV = PV required investment

= $373,832 $350,000 = $23,832 In other words, your office development is worth more than it costs it makes a net contribution to value.

The net present value rule states that managers increase shareholders wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value.

A COMMENT ON RISK AND PRESENT VALUE

In our discussion of the office development we assumed we knew the value of the completed project. Of course, you will never be certain about the future values of office buildings. The $400,000 represents the best forecast, but it is not a sure thing. Therefore, our initial conclusion about how much investors would pay for the building is wrong. Since they could achieve $400,000 risklessly by investing in $373,832 worth of U.S. Treasury bills, they would not buy your building for that amount. You would have to cut your asking price to attract investors interest. Here we can invoke a basic financial principle:

A risky dollar is worth less than a safe one.

Most investors avoid risk when they can do so without sacrificing return. However, the concepts of present value and the opportunity cost of capital still apply to risky investments. It is still proper to discount the payoff by the rate of return offered by a comparable investment. But we have to think of expected payoffs and the expected rates of re turn on other investments. Not all investments are equally risky. The office development is riskier than a Treasury bill, but is probably less risky than investing in a start-up biotech company. Suppose you believe the office development is as risky as an investment in the stock market and that you forecast a 12 percent rate of return for stock market investments. Then 12 percent would be the appropriate opportunity cost of capital. That is what you are giving up by not investing in comparable securities. You can now recompute NPV:

PV = $400,000 АГАз 1 = $400,000 АГАз .893 = $357,143 1.12 NPV = PV $350,000 = $7,143

If other investors agree with your forecast of a $400,000 payoff and with your assessment of a 12 percent opportunity cost of capital, then the property ought to be worth $357,143 once construction is under way. If you tried to sell for more than that, there would be no takers, because the property would then offer a lower expected rate of return than the 12 percent available in the stock market. The office building still makes a net contribution to value, but it is much smaller than our earlier calculations indicated.

OPPORTUNITY COST OF CAPITAL Expected rate of return given up by investing in a project.

NET PRESENT VALUE (NPV) Present value of cash flows minus initial investment.