NPV Calculation Example

Rates of Return and Net Present Value

NPV Calculation Example

Most investors want to know about an investment's rate of return. An investment's return for a period equals its income during the period, which is its cash flows plus its increase (or decrease) in value, divided by its starting value:

Return=Rate of return = Cash flow + (Ending value - Beginning value)/Beginning value

For example, suppose you bought a share of stock for $20, it paid you a $0.50 dividend during the next year and was worth $24.50 at the end of one year. Your rate of return for the year would be

Return = 0.50 + 24.50 - 20.00)/20.00 = 5.00/20.00 = 25%

Your total income consists of $0.50 of dividends and $4.50 in increased value, for a total of $5.00. With $5.00 of income and an original investment of $20.00, your return was 25%

Realized, Expected and Required Returns

The example we just gave is of a realized (or actual) return. There are, however, other concepts of return. We describe and discuss here three different returns. Distinguishing among these three concepts is critical.

Realized Return

The Realized return is the rate of return actually earned on an investment during a given time period. The realized return depends on what the future cash flows turn out to be after the investment is made. In the return example above, with the same $0.50 dividend, but an unchanged stock price, the realized return would have been 2.5% ($0.50 divided by $20). or if the stock price declined to $16.00, the realized return would have been minus 17.5% (=[0.50 + (16.00 - 20.00)]/20.00).

It's critical to understand that a realized return is an outcome, the result of having mad the decision to invest. You cannot go back and change the realized return. You can only make new decisions in reaction to it.

Expected Return

The expected return is the rate of return you expect to earn if you make the investment. If you expected to make 15% in our example investment, including an expected $0.50 dividend, you would be expecting the value of the stock next year to be $22.50 (15% = [0.50 + (22.50 - 20.00)]/20.00).

Required Return

The required return is the rate of return that exactly reflects the riskiness of the expected future cash flows. This is the return the market would require of an investment of identical risk. The market evaluates all of the available information about an investment and prices it in comparison with all other investments. This pricing process establishes an investment's required return the fair return for an investment.

Net Present Value

Using the required return to calculate the present value of an asset's expected future cash flows PV=FV/(1+r)n is one way to value the asset. Another way is to find out what it would cost to buy such an asset. The difference between what an asset is worth (the present value of its expected future cash flows) and its cost is the asset's net present value (NPV).

NPV = Net present value = Present value of expected future cash flows - Cost

A positive NPV increases wealth because the asset is worth more than it costs. A negative NPV decreases wealth, because the asset costs more than it is worth.

The net present value concept is important because it provides a framework for decision making. NPV appears in connection with virtually every topic in this book and most financial decisions can be viewed in terms of net present value. NPV measures the value created or lost by a financial decision. However, NPV is measured from a benchmark of the "normal" market return. Therefore, a zero NPV decision earns the required return and is "fair". A decision that earns less than the required return is undesirable and has a negative NPV. Positive NPV decisions earn more than the appropriate return. Companies that pursue the goal of maximizing shareholder wealth seek to make positive NPV decisions.

Another way to state the Principle of Capital Market Efficiency is to say that financial securities are priced fairly. A fair price is a price that does not favor either the buyer's or seller's side of the transaction. A fair price makes the NPV from investing equal zero. Sometimes, people ask, "If the NPV is zero, why would anyone purchase a financial security? "The answer is to earn a profit. Remember, a zero NPV implies that the investor will earn the required return for the investment risk, not a zero return.

The Principle of Risk Return Trade Off implies that investors who take more risk will earn a larger profit on average. The decision to invest in (purchase) a financial security with NPV = 0 often involves risk. But in exchange for that risk, you get a chance at a higher return. 

Confusion between the expected and required returns arises because, if capital markets were perfect, an investment's expected return would always equal its required return and the investment's NPV would be zero. In fact, financial analysis often starts off assuming a perfect capital market environment, where everyone can expect to earn the required return for the risk they bear. While this is a good starting place for analysis and the capital markets are efficient, we must add that they are not, if fact perfect.

Confusion between the expected and realized returns is created by risk. Because of risk, the outcome rarely equals the expected amount. In fact, one way to think about risk is to consider how different the outcome can be from the expected amount. The risk is high when the difference can be great. The risk is low when there cannot be much difference.

Let's review and summarize the relationships among these concepts by using an investment you might make. First, on the basis of other possible market investments of the same risk, you determine a minimum return you would have to earn to be willing to invest. This is the required return. Next, you estimate the return if you were to make the investment. This is the expected return. Then you decide whether to make the investment. If the expected return is more than the required return, the investment is worth more than its cost, and the NPV is positive. A positive NPV creates value, whereas a negative NPV loses value. Let's say the NPV is positive and you make the investment.

Finally, later on, the investment pays off. The payoff is the realized return. If the realized return is bad (low, negative, or perhaps even zero you get nothing back), you are not happy, but that is the fundamental nature of risk! After the return is realized, you can not turn back the clock and decide not to make the investment after all. Therefore, the realized return is disconnected by risk from the required and expected returns, despite its vital importance and our desire for its to be large.