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Students often note that while the real interest rate is around 5%, companies usually require a projected 20% or 25% rate of return in order to undertake additional capital spending. How can these two figures be reconciled?

Three separate items must be considered. First, while capital spending decisions are actually based on the expected real rate of return – the nominal rate minus the expected rate of inflation – budgetary decisions are usually quoted in nominal terms. Second, the total rate of return must include setting aside capital for replacement purposes – the depreciation proportion. Third, the rate of return is calculated only after the payment of corporate income taxes. In some extreme situations, the benefit of the investment tax credit and accelerated depreciation allowances more than offset the burden of corporate taxes, but that rarely happens.

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MANAGER’S BRIEFCASE (continued )

During the 1990s, the Aaa corporate bond rate averaged about 8%, while the inflation rate was about 3%, so the real rate of interest was about 5%. However, depreciation allowances were about 7% of total capital stock on a straight-line basis, boosting the return on capital in nominal terms to about 15%. The marginal statutory corporate income tax rate was 35% at the Federal level, but that is partially offset by accelerated depreciation allowances, so the actual figure is closer to 25%. Hence the required rate of return would be equal to 15%/0.75, or 20%, right at the lower end of the usual range. If the nominal interest rate were 10% instead of 8% because of higher inflation, the hurdle rate calculated in this manner would be 22.7%, and if the nominal rate rose to 12%, the hurdle rate would increase to 25.3%. Hence there is no inconsistency between these measures of the rate of return and the cost of capital.

5.4 The cost of capital

While investment is negatively related to the expected real rate of interest, the rate of depreciation and the price of the capital good are also important factors in determining whether the investment will be made. In addition, tax laws regarding depreciation, the rate of investment tax credit, and the marginal corporate income tax rate also affect capital spending. It is useful to find some way to combine all these factors when specifying the investment function.

According to standard microeconomic theory, equilibrium in factor markets occurs when the marginal product of labor equals the real wage rate, and the marginal product of capital equals the real cost of capital. But what is the cost of capital?

It certainly is not the price of the capital good itself, since that lasts for several years. In the example given above, a firm purchased a machine for $10 million and the machine lasted for ten years. The sensible approach is to consider the annual cost of the machine over its economic lifetime.

For any given period of time (usually one year), the cost of capital – sometimes known as the rental cost of capital – equals the price of that capital good times the sum of the interest rate and the depreciation rate, adjusted for tax laws that affect the tax rate on business income. The real cost of capital is the rental cost divided by the average price of the product, which in the aggregate is the implicit GDP deflator.

As already noted, the relevant interest rate is the expected real rate of inter-est, which is the nominal rate minus the expected rate of inflation. Empirically, as discussed in greater detail in chapter 8, the long-run expected rate of inflation can be closely approximated by the average rate of inflation over the past five years. Hence in the figures and calculations that follow, the real rate of interest equals the nominal Aaa corporate bond yield minus the average rate of inflation over the past five years. Figure 5.1 shows the ratio of fixed business invest-ment to GDP compared to a five-year weighted average of the cost of capital variable.³

’60 ’65 ’70 ’75 ’80 ’85 ’90 ’95 ’00 Fixed investment to GDP

Simulated value based on rental cost of capital 0.08

0.09 0.10 0.11 0.12 0.13 0.14

Figure 5.1 The ratio of fixed investment to GDP as compared to simulated values derived from a five-year distributed lag of the rental cost of capital

The various tax factors that influence fixed investment include the corporate income tax rate, the rate of investment tax credit, and the regulations affecting depreciation allowances, especially those that permit firms to write off plant and equipment more rapidly than the actual economic rate of depreciation. These are discussed in more detail in section 5.8.

The concept of the cost of capital can be formalized as follows. Let p_kequal the cost of the capital equipment, and p_gdpthe price of the product. Both terms need to be included; otherwise the cost of capital would differ depending on whether pk was measured in dollars, euros, yen, or some other currency. Besides, the cost of capital should reflect both the price of the capital good and the price at which the products can be sold.

Also, let r be the long-term real rate of interest, δ be the rate of depreciation, τ be the tax rate on income used to purchase capital goods, κ the rate of investment tax credit, andζ the present value of the depreciation deduction. Then the cost of capital, rcc, can be written as:

rcc= (pk/pgdp)(r + δ)(1 − τζ − κ)/(1 − τ).

If the price of the capital good rises relative to the price of the good produced, the rcc will rise, so fewer investment projects will be undertaken. If the rate of interest rises, investment will decline, and if the rate of taxation on corporate income rises, investment will also decline.

The cost of capital term developed above only includes debt capital; for many firms, the cost of equity capital is also important. However, that term is treated

separately for several reasons. First, the tax treatment is different because interest costs are deductible, whereas dividends are not. Second, while the debt cost of capital is roughly similar for most firms, the cost of equity capital can vary widely, as some firms have P/E ratios of under ten while other firms have ratios over 100 – or, in the late 1990s, infinite ratios, since they had no earnings at all. Third, stock prices contain an important element of expectations. For all these reasons, the cost of equity capital is considered separately and is not directly included in the cost of capital term.

5.5 The availability of credit

Because most capital spending is undertaken by large firms, one might think that the availability of credit, as opposed to the cost of capital, would not have as large an effect on investment as is the case for consumption. However, it does have a major influence on the timing of investment patterns, particularly for relatively short-lived assets such as motor vehicles and high-tech equipment, which now account for almost half of all producer durable equipment.

Yet if firms determine capital spending investments based on the expected future rate of return, why should the availability of credit be an important determinant of capital spending?

1. One major issue is that the corporation really does not know what lies ahead. If the firm spends money it already has, it will not face a crisis in repaying loans if business turns sour, while if it borrows the money, it may be difficult to repay loans on a timely basis if cash flow dries up. Under these circumstances, some firms might run the risk of violating loan covenants if they had borrowed heavily to finance capital spending.

2. The availability of credit also serves as an expectations variable. If credit is being tightened, the economy is probably heading into a slump, which would hurt sales for most firms even if they were not subject to credit restraints. In that sense, the yield spread between long- and short-term rates is one of the key variables in the index of leading indicators.

3. Borrowing money may push some firms into a higher risk category. Thus, even if market interest rates do not change, the interest rate paid by the firm might rise if it substantially increased the proportion of its borrowings to total capital.

Such a shift could affect the rate the firm would have to pay on all its loans, not just the latest round of borrowed funds, so the marginal cost of borrowing more money could be very high.

4. Many smaller firms finance their capital spending through the equity market.

When the stock market is booming, IPOs and secondary offerings are readily available; when the market is plunging, investment bankers will not bring these issues to market at all. In such cases, availability rather than cost is the principal criterion.

–3 –2 –1 0 1 2 3 4 5

’60 ’65 ’70 ’75 ’80 ’85 ’90 ’95 ’00 Four-quarter change in investment ratio (%) Yield spread lagged one and two years

–0.20 –0.15 –0.10 –0.05 0.00 0.05 0.10 0.15 0.20

Figure 5.2 The four-quarter percentage changes in the ratio of capital spending to GDP in current dollars are correlated with the moving average of the yield spread between the Aaa corporate bond rate and Fed funds rate, lagged an average of one and two years

The same general arguments explain why cash flow is often an important deter-minant of capital spending even if firms have access to bank credit and capital markets. In a world of perfect information, these constraints would not be nearly as important. However, lenders have learned from bitter experience that a certified financial statement from a major accounting firm often conceals more information than it reveals. Decisions cannot be made about the appropriate risk factor based on published accounting data alone. As a result, many firms run the risk of being turned down for loans, even if their financial statements are actually in good shape, if their liquid assets appear to be a small percentage of their liabilities. Such firms would be more likely to invest available cash flow, as opposed to running the risk of having to pay a higher rate of interest or being rejected entirely by lending insti-tutions or financial markets. The correlation between changes in the ratio of capital spending to GDP, and the lagged values of the yield spread, are shown in figure 5.2.

MANAGER’S BRIEFCASE: RAISING MONEY FROM BANKS OR