FINANCIAL CALCULATIONS

FINANCIAL CALCULATIONS[1]

This paper explains two major concepts in valuing investments, Present Value and Net Present Value. These two concepts are based on two fundamental financial principles: 1) a dollar today is worth more than a dollar tomorrow and 2) a safe dollar is worth more than a risky dollar. The following examples will tie these concepts and principles together.

Introduction to Present Value

You have been saving for years in the hopes of investing in small-market radio stations. You recently inherited some money, and putting your savings and inheritance together, you have total cash assets of $350,000. You have been working closely with a radio station broker whom you trust and he tells you about a station for sale for $350,000. The broker assures you that radio stations at this price level are in demand and he is highly confident that that station will sell for $400,000 in a year. Therefore, you would be investing $350,000 now with the expectation of realizing $400,000 in a year.

Before you make this investment, you need to ask yourself, “What is the value today of $400,000 to be received a year from now, and is that present value greater than $350,000? If the present value (PV) of the expected $400,000 payoff is greater than the $350,000 investment, you should go ahead with the deal.

Calculating Present Value

The present value of $400,000 one year from now must be less than $400,000 because of the financial principle, a dollar today is worth more than a dollar tomorrow, mentioned above. The present value of a delayed payoff can be calculated by multiplying the payoff by a discount factor. The discount factor is the value today of $1 received in the future. If C¹ denotes the expected payoff 1 year in the future, the formula looks like this:

Present value (PV) = discount factor X C¹

The discount factor is expressed as the reciprocal of 1 plus a rate of return.

Discount factor = ____1___

1 + r

The rate of return r is the reward that investors demand for accepting delayed payment.

Now, we can value the radio station investment, assuming that the broker is right and the $400,000 payoff is a sure thing. The radio station is not the only way to realize $400,000 in a year. You could invest in US Government securities maturing in a year. Suppose the securities offer 4.25 percent interest (as of January, 2003 for 30-year for US Treasury bonds). How much would you have to invest in them to realize $400,000 in a year? Using the above formulas, you would invest $400,000/1.0425, which is $383,693.

To double check, if you invest $383,693 at 4.25 percent, at the end of the year you get back your initial investment plus interest of .0425 X 383,693 = $16,307. The total, therefore, is $383,693 + $16,307, or $400,000.

To calculate present value, you discount expected payoffs by the rate of return offered by equivalent investment alternatives. The rate of return is often referred to as the discount rate, hurdle rate, or opportunity cost of capital or, simply, the cost of capital. It is called opportunity cost because it is the return foregone by investing in a project rather than investing in safe securities. In the example of the radio station investment, the opportunity cost, or cost of capital (the two terms are interchangeable), was 4.25 percent. Present value was calculated by dividing $400,000 by 1.0425.

PV = discount factor X C¹ = __1___ X C¹ = 400,000 = $383,693

1 + r 1.0425

Calculating Net Present Value

The radio station is worth, in terms of present value, $383,693, but this does not mean that you are $383,693 better off. You committed $350,000, so, therefore, your net present value (NPV) is $33,693. Net present value is calculated by subtracting the initial investment from the present value of the investment a year from now:

NPV = PV – initial investment = 383,693 - 350,000 = $33,693

In other words, you radio station is worth more than it costs—it makes a net contribution to value, to your assets, although it entails some risk—more risk than safe US government securities provide. If Cº designates cash flow, or cash, or assets today (after the investment). Thus, Cº is a negative number that represents cash outflow, or, in this case, - $350,000.

The formula for calculating net present value (NPV) is:

NPV = Cº + __ C¹___

1 + r

Remember that Cº is a negative number, -$350,000 in this case. Thus, -$350,000 plus $383,693 equals a net present value of $33,693.

Rate of Return

What was your rate of return on your radio station investment? Rate of return is a pretty straightforward calculation:

Rate of return = _profit__ = 400,000 – 350,000 = .14 (14%)

investment 350,000

Using PV and NPV to Make Investment Decisions

You should make investments that have a positive net present value.

You should make investments that offer rates of return in excess of their opportunity costs of capital, always keeping in mind the risk involved and the second financial principle stated above: a safe dollar is worth more than a risky dollar. Therefore, the rate of return from an investment should be significantly higher than the opportunity cost of capital.

Thus, your 14% rate of return on your radio station investment is double the discount rate, or cost of capital, and is a reasonable investment.

Warning

Keep in mind that the calculation of present value and net present value in the above examples involve an investment of one year. A one-year investment is a short-term investment. Present value and net present value calculations do not take into consideration the long-term value of an investment. For example, what an investment in, say, a radio station, might be worth in five or ten years. Short-term perspectives are dangerous because they overlook the possibilities (and probabilities) of improvements in market share, in programming, in improved sales effort, and in increased profits that a new, competent owner might well bring to the station.

One of the ills of the current American economy, acerbated by Wall Street, is the obsession with short-term, usually quarterly, profits. If American investors took a more long-term view such as many Japanese investors do, they might reward a company for its long-term vision and growth potential. For instance, in 1990, the Honda Motor Car Company unveiled its 100-year plan. Its CEO at the time said that his company was “planting tress under which none of us will enjoy the shade.” That is long-term planning. Do you have any doubts that Honda will be successful in 2090?