Donald Snellman Professor of Entrepreneurship and Finance

NPV: DOING IT BETTER

Herbert Kierulff

Donald Snellman Professor of Entrepreneurship and Finance

School of Business and Economics

Seattle Pacific University

3307 Third Avenue West

Seattle, WA 98119

Phone: (206) 281-3523

Fax: (206) 281-2733

NPV: DOING IT BETTER

Abstract: Net Present Value has become the single most important tool in investment analysis and capital budgeting. It is a valuable method that is significantly limited by seven basic suppositions that almost always attend its use. These suppositions are either unknown, ignored, or treated in a cursory way by those who practice and write about the method. We ignore these assumptions at our peril because doing so easily leads to erroneous financial conclusions. This article examines the five and shows how academics, practitioners, and students can deal with them without undue effort. Doing so leads to a better NPV.

Key Words: Net Present Value, Present Value, Discounted Cash Flow, Capital Budgeting, Discount Rate, Risk Adjusted Discount Rate, Capital Asset Pricing Model.

INTRODUCTION

Ryan and Ryan’s (2002) survey indicates that 85% of Fortune 1000 companies use Net Present Value (NPV) 75-100% of the time in making investment decisions. Earlier studies (Burns & Walker, 1987; Gitman & Forrester, 1977) show a similar preference among executives, and a propensity to use NPV over others such as payback and return on funds employed. The model prevails in the textbooks, articles, computer spreadsheets, and calculators.

The literature tends to make seven basic and important suppositions when discussing NPV that are rarely examined in sufficient detail. The central message of this article is that these suppositions can easily lead to very large errors—errors that may lead to bad decisions. Academics, executives, and finance professionals can deal with the negative consequences of all of these assumptions with relative ease if they recognize that they exist and apply the simple measures discussed here to deal with them.

The article begins with an introduction to the assumptions and then demonstrates their implications using an example. Finally, it introduces briefly other factors beyond the scope of this paper that may bring needed adjustments to NPV.

WHAT ARE THE ASSUMPTIONS; WHAT ARE THEIR IMPLICATIONS

The discounted cash flow models presented in textbooks and other educational materials in the finance literature typically take for granted seven suppositions. These seven are either potentially misleading or completely wrong:

1.  All cash flows, including the initial investment, come at the end of the year in which they occur.

2.  The initial investment happens all at once.

3.  The initial investment is not risky.

4.  The firm uses its cost of capital or the project hurdle rate to discount fixed costs and investments made after the initial one.

5.  The firm uses its cost of capital or the project hurdle rate to discount the project terminal value.

6.  The cost of capital or project hurdle rate is appropriate to measure the required rate of return on the free cash flows resulting from the investment.

7.  The positive cash flows resulting from the investment are reinvested at the cost of capital or project hurdle rate.

The following example, similar to ones found in articles and textbooks, is used to demonstrate the logical and practical inconsistencies in the assumptions:

The initial investment for the new Apex Project is $5 million at the end of year 0, of which $4 million is tax-deductable research and development (R&D). The rest is equipment. The expected sales are $22 million over six years, at which time the product will become obsolete and the project liquidated. The $4 million R&D includes start-up costs and constitutes the entire year 0 operating costs. The company expects the TV of the patents, working capital, and equipment to be $1 million after taxes at the end of year 5. The riskless rate of interest is 5.5% and the beta-adjusted risk factor is 10%, giving a hurdle rate of 15.5%. The tax rate is 34%, and depreciation on the capital expenditures (CAPX) is 5 years, straight line. Table 1 shows the calculation of NPV.

[Table 1 (below) about here.]

This project is clearly desirable, with a NPV of $1,286,000.

The Half-Year Convention

Table 1 contains the assumption that all cash flows, including the first, occur exactly at the end of the year. For most companies, it is more reasonable to assume that cash flows occur evenly throughout the year. The year-end assumption has resulted in an overstatement of the value of the project in this case. The half-year convention discounts cash flows assuming that they occur at mid-year rather than year-end.

Applying the half-year convention involves moving cash flows back by a six months, such that year 0 is discounted by (1 + i)0.5,, year one by (1 + i)1.5, year two by (1 +i )2.5, and so on (Pratt, 253). Year 0 becomes year 0.5, with the initial investment beginning at the start of year 0 and the funds being spread evenly throughout the first year. The TV occurs at the end of the final year rather than at the middle. Table 2 demonstrates the half-year convention, using the operating cash flows and the TV from Table 1. The NPV drops from $1,286,000 to $1,170,000.

[Table 2 about here]

The reduction in NPV comes about because the initial investment is large and is discounted by only a half-year, while the inflows are relatively small at first and then increase. As the inflows increase in size over time, the discount rate increases geometrically, reducing the inflows geometrically. When the reverse is true—small up-front investment and large, earlier cash inflows—NPV may increase (Bruckner, 1991).

All up-front investment occurs at one time

Tables 1 and 2 are seriously flawed in that they fix all R&D and CAPX in period 0. If the company is purchasing a relatively small piece of easily installed equipment that goes to work immediately, it is reasonable to assume that the entire outlay will take place at the end of time 0. However, for major projects in such industries as aerospace, pharmaceuticals, mining, and large-scale construction, this assumption is far off the mark. In these and other industries, CAPX and R&D begin many years before product launch and continue after positive cash flow generation.

There is disagreement regarding the value of NPV analysis during the early stages of project research. The issue is whether an early-stage forecast can be based upon information that is sufficiently reliable (Varila & Sievanen, 2005; Uppal & Van Gool, 1991). However, at some point during the R&D cycle—well before product roll out—discounted cash flow analysis becomes highly relevant. For company acquisitions and most (if not all) R&D and plant and equipment purchase decisions, NPV analysis is relevant from the start.

Table 3 demonstrates the dramatic shift in NPV when the company spreads the same amount of initial R&D and CAPX over a period of four years instead of the end of time 0. NPV drops from $1,170,000 to $437,000.

[Table 3 about here.]

Risky costs and capital investments

Tables 2 and 3 deal with the investment in capital and R&D costs in the traditional way—by discounting them over time for inflation, the real rate of interest, maturity or investment rate risk, and market risk. However, simple logic would indicate that risk-averse managers should increase costs to account for risk over time, not decrease them. This means lowering the discount rate—perhaps using a rate less than one.

Literature discussions that took place in the 1970s and early 1980s deal with this issue (Lewellen, 1977; Lewellen, 1979; Celec & Pettway, 1979; Berry and Dyson, 1980; Booth, 1982). It seems clear from that discussion that variable costs and working capital changes should be discounted at the same rate as revenues, and that the above simple logic misses the point. Booth’s (1982, p. 299) summary explains why: “In evaluating cash outflows, remember that a negative correlation between the value of a project’s cash flows and the market rate of return translates into a positive correlation between the project’s rate of return and the market rate of return.”

In other words, the variable components of a typical set of cash outflows are correlated to sales in a direct way. If sales over five periods were 4, 8, 12, 8, and 4 respectively, the associated variable costs plus changes in working capital should follow a similar pattern; say -3, -6, -9, -6, and -3. The two are perfectly negatively correlated. If the discount rate for sales were 15.5%, the discount rate for the variable costs and working capital changes would also have to be 15.5% to maintain the correlation at minus 100%. Any other discount rate would disrupt the relationship and would invalidate the logic behind the definition of variable costs and changes in working capital as those elements that vary directly with sales.

Note that it is the free cash flow, not the sales or variable costs and working capital changes, which is being measured. If investment and fixed costs are not involved, the correlation between sales and the resulting cash flow (1, 2, 3, 2, and 1) is 100%.

However, up-front costs such as R&D and expenditures on plant and equipment where there are no sales are another matter. The same is true of depreciation and other fixed costs. Experienced investors are familiar with the impact on free cash flow of cost overruns, delays, and mid-course changes in R&D and capital expenditures—especially in those industries involved with technology (Davis, 2002; Uppal, 2001).

It is not unusual for managers to increase original R&D cost estimates by 5% to 200% to establish certainty equivalent proxies for risk prior to market introduction. One executive who managed the new technical projects division at a Global-100 manufacturer occasionally used pi (3.14159) as a cost multiplier for up-front costs in highly risky projects (Personal conversation, 2008). Estimates such as these, when transformed into risk adjusted discount rates (RADRs), can yield discount rates of considerably less than one.

Everett and Schwab (1979) demonstrate that the discount rate could actually be less than one if the risks are great enough. Booth (1982, p. 299) concludes: “Given risk-free revenues and cost uncertainty, the cost stream for a normal firm with a positive risk premium attached to its cash flows must be discounted with a RADR below the risk-free rate.” Risk-free revenues are consistent with the revenues of zero that attend up-front investment and maintenance of that investment (if any) after start-up.

The exceptions would include cases of contractual arrangements such as fixed-price contracts and other riskless costs (Hartl, 1990). In these cases, the discount rate would be the risk-free rate.

When the initial and subsequent investments are spread out over a period of time the issue of systematic risk may become relevant. The business cycle may well affect investment costs. Spreading expenditures over a longer period will affect the present value through the discount rate.

What to do with fixed investments? As proxy variables for risk, the S & P 500 and other similar measures already reflect fixed investments and other fixed costs intrinsic to the companies that constitute them. Therefore, since risk is measured by cash flow variation, company or project fixed costs and investments are already reflected to some extent in the beta. Nevertheless, companies with high fixed costs will tend to have higher than average betas because fixed costs intensify variation.

Table 4 demonstrates the difference in cash flow variation between a high fixed cost/high investment and a low fixed cost/low investment company. The average return in each of the three examples is $334. The variation, as measured by standard deviation, is over three times greater in the high fixed cost/high investment firm—$659 vs. $210—and will influence the firm’s beta. Other things equal, that firm will have a significantly higher beta and therefore a higher cost of capital. The firm that varies its investments with sales (Table 4 C) modifies its standard deviation to $434.

[Table 4 about here]

It follows from the table above that the firm should treat its fixed costs differently from its variable costs notwithstanding the fact that fixed costs are captured in the proxy variable such as the S&P 500 when beta is calculated. Although the science is imperfect, start-up costs and investments in property, plant, and equipment prior to start-up should be discounted separately in cases where significant investment is contemplated. In the absence of forecast bias, it may be reasonable to discount these outlays at no more than the risk-free rate. That rate should be adjusted downward if systematic risk such as timing with the business cycle is involved.

When the company spreads the same amount of R&D and CAPX over a period of four years instead of one, discounts R&D, CAPX, and depreciation by 5.5% (assuming no systematic risk), uses the half-year convention, and assumes that the discount rate after market introduction is reasonably accurate at 15.5%, NPV drops to a negative $278,000.

Terminal Values

Terminal value systematic risks and biases may be significantly different from operating cash flow risks and may be more or less difficult to forecast. Even forecasts of the same terminal value using different methods can produce significantly different results. The market value of future cash flows will produce one estimate, while models that forecast free cash flow into perpetuity will produce another.

A 4% factor for terminal value added to the normal discount rate will reduce NPV by an additional $71,000. When the terminal value is large, as in corporate acquisitions, the amount can become highly significant. Table 5 demonstrates the effect of all of the adjustments. As a result of the above analysis, NPV moved from a positive $1,286,000 in Table 1 to a negative $349,000. This $1.6 million shift represents nearly 33% of the initial $5 million investment.