Emphasis on After Tax Cash Flows
In computing NPV, notice that the focus is on cash flows, not "income" Items like depreciation do not impact the cash flows, and are not included in the present value calculations. That is why the illustration for Markum Real Estate did not include deductions for deprecation. However, when applying net present value considerations in practice, one must be well versed in tax effects. Some noncash expenses like deprecation can reduce taxable income, which in turn reduces the amount of cash that must be paid for taxes. Therefore, cash inflows and outflows associated with a particular investment should be carefully analyzed on an after-tax basis. This often entails the preparation of pro forma cash flow statements and consultation with professionals well versed in the details of specific tax rules!
As a simple illustration, let's assume that Mirage Company purchases a tract of land with a prolific spring-fed creek. The land cost is $100,000, and $50,000 is spent to construct a water bottling facility. Net water sales amount to $40,000 per year (for simplicity, assume this amount is collected at the end of each year, and is net of all cash expenses). The bottling plant has a five-year life, and is depreciated by the straight-line method. Land is not depreciated. At the end of five years, it is anticipated that the land will be sold for $100,000. Mirage has an 8% cost of capital, and is subject to a 35% tax rate on profits. The following spreadsheet shows the calculation of annual income and cash flows in blue. The annual cash flow from water sales (not the net income!) is incorporated into the schedule of all cash flows. The annual net cash flows are then multiplied by the appropriate present value factors corresponding to an 8% discount rate. The project has a positive net present value of $35,843. Interestingly, had the annual net income of $19,500 been erroneously substituted for the $29,500 annual cash flow, this analysis would have produced a negative net present value! One cannot underestimate the importance of considering tax effects on the viability of investment alternatives.
Accounting Rate of Return
The accounting rate of return is an alternative evaluative tool that focuses on accounting income rather than cash flows. This method divides the average annual increase in income by the amount of initial investment. For Mirage's project above, the accounting rate of return is 13% ($19,500/$150,000). The accounting rate of return is simple and easy. The decision rule is to accept investments which exceed a particular accounting rate of return. But, the method ignores the time value of money, the duration of cash flows, and terminal returns of invested dollars (e.g., notice that Mirage plans to get the $100,000 back at the end of the project). As a result, by itself, the accounting rate of return can easily misidentify the best investment alternatives. It should be used with extreme care.
Internal Rate of Return
The internal rate of return (also called the time-adjusted rate of return) is a close cousin to NPV. But, rather than working with a predetermined cost of capital, this method calculates the actual discount rate that equates the present value of a project's cash inflows with the present value of the cash outflows. In other words, it is the interest rate that would cause the net present value to be zero. IRR is a ranking tool. The IRR would be calculated for each investment opportunity. The decision rule is to accept the projects with the highest internal rates of return, so long as those rates are at least equal to the firm's cost of capital. This contrasts with NPV, which has a general decision rule of accepting projects with a "positive NPV," subject to availability of capital. Fundamentally, the mathematical basis of IRR is not much different than NPV.
The manual calculation of IRR using present value tables is a true pain. One would repeatedly try rates until they zeroed in on the rate that caused the present value of cash inflows to equal the present value of cash outflows. If the available tables are not sufficiently detailed, some interpolation would be needed. However, spreadsheet routines are much easier. Let's reconsider the illustration for Greenspan. Below is a spreadsheet, using an interest rate of 8.8361%. Notice that this rate caused the net present value to be zero, and is the IRR. This rate was selected by a higher-lower guessing process (trying each interest rate guess in cell C7). This does not take nearly as many guesses as you might think; with a little logic, you can quickly zero in on the exact correct rate.