The typical capital investment is composed of a string of cash flows, both in and out, that will continue until the investment is eventually liquidated at some point in the future. These cash flows are comprised of many things: the initial payment for equipment, continuing maintenance costs, salvage value of the equipment when it is eventually sold, tax payments, receipts from product sold, and so on. The trouble is, since the cash flows are coming in and going out over a period of many years, how do we make them comparable for an analysis that is done in the present? As noted in the article on hurdle rates, we can use a discount rate to reduce the value of a future cash flow into what it would be worth right now. By applying the discount rate to each anticipated cash flow, we can reduce and then add them together, which yields a single combined figure that represents the current value of the entire capital investment. This is known as its net present value.
For an example of how net present value works, we have listed in the following table the cash flows, both in and out, for a capital investment that is expected to last for five years. The year is listed in the first column, the amount of the cash flow in the second column, and the discount rate in the third column. The final column multiplies the cash flow from the second column by the discount rate in the third column to yield the present value of each cash flow. The grand total cash flow is listed in the lower right corner of the table.
Year |
Cash Flow |
Discount Factor* |
Present Value |
0 |
-$100,000 |
1.000 |
-$100,000 |
1 |
+25,000 |
.9259 |
+23,148 |
2 |
+25,000 |
.8573 |
+21,433 |
3 |
+25,000 |
.7938 |
+19,845 |
4 |
+30,000 |
.7350 |
+22,050 |
5 |
+30,000 |
.6806 |
+20,418 |
|
|
Net Present Value |
+$6,894 |
Note: Discount factor is 8%.
Notice that the discount factor becomes progressively smaller in later years, since cash flows further in the future are worth less than those that will be received sooner. The discount factor is published in present value tables, which are listed in many accounting and finance textbooks. They are also a standard feature in mid-range hand-held calculators. Another variation is to use the following formula to manually compute a present value:
Present value of (Future cash flow)
a future cash flow = ---------------------------------------------------------------------------
(1 + Discount rate) (squared by the number of periods of discounting)
Using the above formula, if we expect to receive $75,000 in one year, and the discount rate is 15%, then the calculation is:
$75,000
Present value = ------------
(1 + .15)1
Present value = $65,217.39
The example shown was of the simplest possible kind. In reality, there are several additional factors to take into consideration. First, there may be multiple cash inflows and outflows in each period, rather than the single lump sum that was shown in the example. To know precisely what is the cause of each cash flow, it is best to add a line to the net present value calculation that clearly identifies the nature of each item, and discount it separately from the other line items. Here are the most common cash flow line items to include in a net present value analysis:
- Cash inflows from sales. If a capital investment results in added sales, then all gross margins attributable to that investment must be included in the analysis.
- Cash inflows and outflows for equipment purchases and sales. There should be a cash outflow when a product is purchased, as well as a cash inflow when the equipment is no longer needed and is sold off.
- Cash inflows and outflows for working capital. When a capital investment occurs, it normally involves the use of some additional inventory. If there are added sales, then there will probably be additional accounts receivable. In either case, these are additional investments that must be included in the analysis as cash outflows. Also, if the investment is ever terminated, then the inventory will presumably be sold off and the accounts receivable collected, so there should be line items in the analysis, located at the end of the project time line, showing the cash inflows from the liquidation of working capital.
- Cash outflows for maintenance. If there is production equipment involved, then there will be periodic maintenance needed to ensure that it runs properly. If there is a maintenance contract with a supplier that provides the servicing, then this too should be included in the analysis.
- Cash outflows for taxes. If there is a profit from new sales that are attributable to the capital investment, then the incremental income tax that can be traced to those incremental sales must be included in the analysis. Also, if there is a significant quantity of production equipment involved, the annual personal property taxes that can be traced to that equipment should also be included.
- Cash inflows for the tax effect of depreciation. Depreciation is an allowable tax deduction. Accordingly, the depreciation created by the purchase of capital equipment should be offset against the cash outflow caused by income taxes. Though depreciation is really just an accrual, it does have a net cash flow impact caused by a reduction in taxes, and so should be included in the net present value calculation.
The net present value approach is the best way to see if a proposed capital investment has a sufficient rate of return to justify the use of any required funds. Also, because it reveals the amount of cash created in excess of the corporate hurdle rate, it allows management to rank projects by the amount of cash they can potentially spin off, which is a good way to determine which projects to fund if there is not enough cash available to pay for an entire set of proposed investments.