# 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.

# 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.