# Evaluation of Long-Term Projects

Now that you have learned some basic principles about how dollars are impacted by compound interest and present value calculations, let's see how you can use these tools to make better business decisions. There are a number of alternative methods for evaluating capital budgeting decisions. These include net present value, accounting rate of return, internal rate of return, and payback.

## Net Present Value

The net present value (NPV) method offsets the present value of an investment's cash inflows against the present value of the cash outflows. Present value amounts are computed using a firm's assumed cost of capital. The cost of capital is the theoretical cost of capital incurred by a firm. This cost may be determined by reference to interest rates on debt, or a blending of debt/equity costs. In the alternative, management may simply adopt a minimum required threshold rate of return that must be exceeded before an investment will be undertaken. If a prospective investment has a positive net present value (i.e., the present value of cash inflows exceeds the present value of cash outflows), then it clears the minimum cost of capital and is deemed to be a suitable undertaking. On the other hand, if an investment has a negative net present value (i.e., the present value of cash inflows is less than the present value of cash outflows), the investment opportunity should be rejected.

To illustrate NPV, let's return to our illustration for Markum Real Estate. Assume that the firm's cost of capital is 5%. You already know the present value of the cash inflows is $807,828. Let's additionally assume that the up-front purchase price for the building is $575,000. $60,000 per year will be spent on the remodel effort at the end of Year 1 and Year 2. Maintenance, insurance, and taxes on the building will amount to $10,000 per year, payable at the end of each of the five years. The present value of the cash outflows is $729,859:

This project has a positive net present value of $77,969 ($807,828-$729,859). This suggests the project's returns exceed the 5% cost of capital threshold. Had the up-front investment been $675,000 (instead of $575,000), the project would have a negative net present value of $22,031 ($807,828-$829,859).

## Impact of Changes in Interest Rates

Carefully consider the mathematics (or table values), and you will observe that higher interest rates produce lower present value factors, and vice versa. You also know that the logic of making certain investments changes with interest rates. Perhaps you have considered buying a house or car on credit; in considering your decision, the interest rates on the deal likely made a big difference in how you viewed the proposed transaction. Even a casual observer of macro-economic trends knows that government policies about interest rates influence investment activity and consumer behavior. In simple terms, lower rates can stimulate borrowing and investment, and vice versa.

To illustrate the impact of shifting interest rates, consider that Greenspan is considering a $500,000 investment that returns $128,000 at the end of each year for five years. The following spreadsheet shows how the net present value shifts from a positive net present value of $39,183 (when interest rates are 6%), to positive $11,067 (when interest rates are 8%), to negative $14,779 (when interest rates rise to 10%). This means that the investment would make sense if the cost of capital was 6%, but not 10%.

In the above spreadsheet, formulas were used to determine present value factors. For example, the "balloon" shows the specific formula for cell H17 - (1/(1+i)n) - where "i" is drawn from cell C17 which is set at 8%. Similar formulas are used for other present value factor cells. This simple approach allows rapid recalculation of net present value by simply changing the value in the interest rate cell.