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# Michael Boehlje and Cole Ehmke Department of Agricultural Economics - page 3 / 12

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Where N denotes net present value; n denotes the time period, with K indicating the last period an inflow is expected; d e n o t e s a s u m m a t i o n o f a l l n p e r i o d s ; I n d e n o t e s t h e n e t c a s inflow in period n; d the rate of discount; and O the cash outlay required to purchase the capital asset. h

There are six steps to complete this net present value analysis procedure:

Step 1. Choose an appropriate discount rate to reflect the time value of money.

Step 2. Calculate the present value of the cash outlay required to purchase the asset.

Step 3. Calculate the benefits or annual net cash flow for each year from the investment over its useful life.

Step 4. Calculate the present value of the annual net cash flows.

Step 5. Compute the net present value. Step 6. Accept or reject the investment.

These computation steps are explained in the next section. The section after that uses the example of a mechanic considering the purchase of a tow truck to illustrate the procedure.

Step 1. Choose an appropriate discount rate to reflect the time value of money.

You use the discount rate to adjust future flows of income back to their present value. The discount rate you choose essentially indicates the minimum acceptable rate of return for an investment; it represents the “cutoff criterion” in judging whether or not an investment returns at least the cost of the debt and equity funds that must be committed or acquired by the business to obtain the asset.

How should you determine the combination of debt and equity funds used to finance an investment? In the long run, the funds you use to acquire any capital item will come from both debt (borrowed funds) and equity (your financial contribution to the business) sources. Therefore, you should base the cost of capital on the combination of debt and equity capital used in the “long run” to finance the operation, not the specific combination of debt and equity that you may use to finance a particular purchase. Even though you may use a high proportion of debt to finance current investments, using

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this debt now will reduce your business’s ability to use credit in the financing of future investments.

The objective is to evaluate investment alternatives based on the long-run optimal capital structure of the business—the capital structure or combination of debt and equity that you expect to maintain over a number of years. To determine the long-run cost of capital (based on this optimal capital structure) for the business, you must weight the cost of debt funds and the cost of equity funds by the long-run proportions of debt and equity that will be used to finance the business. This results in a weighted cost of capital that can be summarized as:

d = K e W e ( 1 t ) + K d W d ( 1 t )

Where d is the discount rate, Ke is the cost of equity funds (rate of return on equity capital), We is the proportion of equity funds used in your business, Kd is the cost of debt funds (interest), t is the marginal tax rate, and Wd is the proportion of debt funds in your business.

The purpose of the weighted cost of capital formula is to obtain a discount rate that accurately reflects the long-run direct cost of debt funds and the opportunity cost of equity funds, along with the long-run proportions of debt and equity that will be used in the firm. Note that the cost of equity funds is best estimated as the opportunity cost (income foregone) of committing equity to this particular investment compared to other investments.

The best way to specifically measure this cost is to look at the rate of return being generated by the equity capital currently being used in your business. You calculate this rate of return as the sum of the cash return plus the gain in asset values divided by net worth or equity (market value basis) as measured on your business’s balance sheet. You calculate the annual cash return as annual net income from the income statement. You determine annual capital gain by comparing the market value of assets of the business this year to the value last year; you can obtain these data from your balance sheet.

Because the cash flows that you will discount in Step 3 will be computed on an after-tax basis to reflect all costs and cash flows, you should compute the discount rate on an after-tax

basis as well. So you multiply the cost of equity (Ke) times one minus the marginal tax rate (1 – t) to adjust it to an after-tax rate. Also note that because interest (the cost of debt funds) is

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