Input Demand: The Capital Market and the Investment Decision (Part D)
by
Charles Lamson
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Calculating Present Value We have seen in the last several posts that a firm's major goal in making investment decisions is to evaluate revenue streams that will not materialize until the future. One way for the firm to decide whether or not to undertake an investment project is to compare the expected rate of return from the investment with the current interest rate available in the financial market. We discussed this procedure in the last several posts. The purpose of this post is to present an alternative method of evaluating future revenue streams through present-value analysis. Present Value Consider the expected flow of profits from the investment shown in Table 1. If such a project cost $1,200 to put in place, would the firm undertake it? At first glance, you might answer yes. After all, the total flow of profit is $1,600, but this flow of profit is fully realized only after five years have passed. The same $1,200 could be put into a money market account, where it would earn interest and perhaps produce a higher yield than if it were invested in the project. You can easily see that the desirability of the investment project will depend on the interest rate that is available in the market.  One way of thinking about interest is to say that it allows us to buy and sell claims to future dollars. Future dollars have prices in the present. That is, a contract for $1 to be delivered in one year, two years, or 10 years can be purchased today. This can be done by simply depositing a certain amount in an interest-bearing certificate or account. Using the present prices of future dollars gives us a way to compare present costs with values that will be realized in the future. This method allows us to evaluate investment projects that will yield benefits into the future. It is not difficult to figure the "price" of $1 to be delivered in one year. You must now pay an amount (X) such that when you get X back in one year with interest you will have $1. If r is the interest rate available in the market, r times X, or rX, is the amount of interest that X will earn for you in one year. Thus, at the end of the year you will have X + rX, or X(1 + r), and you want this to be equal to $1. Solving for X algebraically: $1 = X(1 + r), so X = $1 / 1 + r  Now let us go more than one year into the future and consider more than a single dollar. For example, what is the present value of a claim on $100 in 2 years? Using the same logic, let X be the present value, or current market price, of $100 payable in 2 years. Thus, X plus the interest it would earn compounded for 2 years is equal to $100. After 1 year, you would have X + rX, or X(1 + r). After two years, you would have this amount plus another year's interest on the whole amount: X(1 + r) + r [X(1 + r)] or   all for the low price of $1,126.06. To put this another way, it could lend out or deposit $1,126.06 in an account paying a 10 percent interest rate, withdraw $100 next year, withdraw $100 in the following year, take another $400 at the end of three years, and so forth. When it takes its last $500 at the end of the fifth year, the account will be empty---the balance in the account will be exactly zero. Thus the firm has exactly duplicated the income stream that the investment project would have yielded for a total present price of $1,126.06. Why then would it pay out $1,200 to undertake this investment? The answer, of course, is that it would not.  We can restate the point this way: If the present value of the income stream associated with an investment is less than the full cost of the investment project, the investment should not be undertaken. It is important to remember here that we are discussing the demand for new capital. Business firms must evaluate potential investments to decide whether they are worth undertaking. This involves predicting the flow of potential future profits arising from each project and comparing those future profits with the return available in the financial market at the current interest rate. The present value method allows firms to calculate how much it would cost today to purchase a contract for the exact same flow of earnings in the financial market.  Lower Interest Rates, Higher Present Values Now suppose that the interest rate falls from 10 percent to 5 percent. With a lower interest rate, the firm will have to pay more now to purchase the same number of future dollars. Take, for example, the present value of $100 in 2 years. You saw that if the firm put aside $82.65 at 10 percent interest, it will have $100 in 2 years---at a 10 percent interest rate, the present discounted value, or current market price, of $100 in two years is $82.65. However $82.65 put aside at a 5 percent interest rate would generate only $4.13 in interest in the first year and $4.34 in the second year, for a total balance of $91.11 after 2 years. To get $100 in 2 years, the firm needs to put aside more than $82.65 now. Solving for X as we did before:  When the interest rate falls from 10 percent to 5 percent, the present value of $100 in 2 years rises by $8.05 ($90.70 - $82.65). Table 3 recalculates the present value of the full stream at the lower interest rate; it shows that a decrease in the interest rate from 10 percent to 5 percent causes the total present value to rise to $1,334.59. Because the investment project costs less than this (only $1,200), it should be undertaken. It is now a better deal than can be obtained in the financial market. Under these conditions, a profit-maximizing firm will make the investment. As discussed in the last several posts, a lower interest rate leads to more investment.  The basic rule is if the present value of an expected stream of earnings from an investment exceeds the cost of the investment necessary to undertake it, then the investment should be undertaken. However, if the present value of an expected stream of earnings falls short of the cost of the investment, then the financial market can generate the same stream of income for a smaller investment, and the investment should not be undertaken.  *CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 229-231* end |
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