Investment Chapter 14 Students Should Be Able to: Calculate Average and Marginal product of capital. Calculate the real and nominal rental cost of capital Calculate the optimal capital stock as a function of the cost of capital. lculate Tobin’s q to estimate the desirability of corporate investment. Evaluate relationship between leverage and investment. Terminology: Investment We use the term investment to refer to real expenditure (public and/or private) on tangible assets. We call the stock of tangible assets capital or physical capital. The unit of measure of aggregate capital is dollars. Gross Investment refers to purchases of new investment. Net Investment is Gross Investment minus depreciation. Components of Investment Investment Fixed Investment Residential Investment Business Investment Structures Machinery & Equipment Changes in Stocks – Inventory Investment Gross Fixed Capital Formation: HK 2002 5% 3% 10% 14% Transfer Costs of Land & Building Real Estate Developers' Margin Machinery & Equipment 14% Public Construction Private Residential Private: Non-residential 54% Investment Facts Investment expenditure is a substantial share of GDP, but not as large as consumption. Fixed and inventory investment are closely correlated with the business cycle. Investment is an especially volatile part of GDP. Investment as a share of GDP: East Asia Private Investment 35.00 30.00 % of GDP 25.00 20.00 15.00 10.00 5.00 0.00 China Hong Kong Indonesia Korea Malaysia Philippines Thailand Easterly, Rodriguez, and Schmidt-Hebbel "Public Sector Deficits and Macroeconomic Performance." (Statistical appendix) 1994 and Bruno and Easterly JME 1998. Investment as a share of GDP: East Asia 1997 Public Investment 20.00 18.00 16.00 % of GDP 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 China Hong Kong Indonesia Korea Malaysia Philippines Thailand Easterly, Rodriguez, and Schmidt-Hebbel "Public Sector Deficits and Macroeconomic Performance." (Statistical appendix) 1994 and Bruno and Easterly JME 1998. Volatility: Investment and GDP Annual Growth Rates Hong Kong 30.00% 25.00% 15.00% 10.00% 5.00% 0.00% 19 65 19 68 19 71 19 74 19 77 19 80 19 83 19 86 19 89 19 92 19 95 19 98 20 01 % Growth Rates 20.00% -5.00% -10.00% -15.00% -20.00% GDP I Marginal Analysis Economists use marginal analysis to determine an optimal level of an activity. Most activities have diminishing marginal returns. Marginal returns are the extra benefit received from doing a bit more of the activity. Do more of the activity until that point when marginal returns from doing a bit more of the activity start to become more than the cost of the activity. Optimal Capital Benefit of owning capital is that it allows us to produce more goods. Marginal product of capital is the extra revenue from the extra goods we could produce if we had just a bit more capital. MPK can be measured in either nominal, current price (PMPK) or real, constant price (MPK) terms. Capital has diminishing returns. MPK is a decreasing function of the capital stock. Productivity of Capital The productivity or average productivity of capital is the revenue generated per dollar of capital. APK is value of output divided by the capital stock. Value of Output APK Value of Capital Value can be measured in constant or current price terms. Marginal productivity of capital is often thought to be roughly proportional to average productivity capital. MPK K Cost of Capital Economists define the (time) cost of capital as the cost of holding a unit of capital for a period of time. A firm invests in capital equipment for a period. The firm borrows money upfront to finance the purchase. The firm produces goods and generates revenues. The firm sells the capital at the end of the period, typically at less than the purchase price due to wear and tear. The firm repays loan. Cost of using capital includes interest payment plus loss on the resale of capital. Optimal Capital Example. K , NEW A firm borrows Pt to buy 1 capital good at interest rate 1+i. The firm produces PMPKt+1 worth of goods and sells the capital good for Pt K ,OLD. Optimal to buy capital good as long as payoff is greater than the cost. Optimal Condition Pt K1,OLD PMPKt 1 it Pt K ,NEW Definition of Capital Cost PMPK t iPt K , NEW [ Pt K1,OLD Pt K , NEW ] Cost of Capital Capital Cost 1. 2. 3. ck iPt K , NEW [ Pt K1,OLD Pt K , NEW ] We can divide the capital cost into three PK K , NEW i g P t parts. Interest cost: Net Pt K1, NEW Pt K1,OLD interest rate. Depreciation: Defined Pt K , NEW as change in value due to aging. K , NEW K , NEW Capital gain: Defined K P P P t 1 t g as change in value Pt K , NEW due to change in price of new goods. Real Capital Cost PMPK i g MPK i g PK t 1 PK t 1 MPK r g Pt K , NEW ptK , NEW pK t 1 Pt K , NEW p Pt k t ptK , NEW rckt Example A taxi agency can produce a certain amount of revenue with larger numbers of taxis (K = # of Taxis). Assume earnings (revenues minus wages minus costs) per year is given by the 3 schedule $200,000 4 K Assume that the purchase price of a new taxi (with license) is $1,000,000. The borrowing interest cost is 4% and a taxi’s value depreciates by 8% per year. We assume that taxi’s prices increase by 2% per year. Optimum Number of Taxis The extra earnings generated by moving from 5 taxis to 6 taxis is less than cost of capital. Maximum profits occurs where marginal cost equals marginal earnings. Taxis 1 2 3 4 5 6 7 8 9 10 Revenues Costs 200000 100000 336358.6 200000 455901.4 300000 565685.4 400000 668740.3 500000 766731.7 600000 860703.4 700000 951365.7 800000 1039230 900000 1124683 1000000 Profits 100000 136358.6 155901.4 165685.4 168740.3 166731.7 160703.4 151365.7 139230.5 124682.7 Marginal Marginal Earnings Cost 200000 100000 136358.6 100000 119542.8 100000 109784 100000 103054.9 100000 97991.42 100000 93971.69 100000 90662.28 100000 87864.79 100000 85452.17 100000 Optimal Capital: Example Solve for Optimal Level of Capital PMPK $150, 000 1 4 (.04 .08 .02) $1, 000, 000 K $150, 000 14 * K K * 1.54 5.0625 $100, 000 MPK rck K K* MPK & Optimal Capital Q: Why does MPK slope down. A: Diminishing returns to capital. Each additional unit of capital generates less additional revenue at a given workforce and technology level. Q: What shifts the MPK curve. A: Changes in productivity of capital. An increase in workforce or technology will make capital more productive and shift MPK curve out. MPK MPK’ rck K K* K** MPK rck’ rck K K** K* Investment Volatility The stock of capital may not be particularly volatile over the business cycle. Capital stock is much larger than the flow of new investment in a given year, perhaps 10-15 times as large. A 1% reduction in optimal capital stock will require a 10% reduction in investment. Tax Rates Corporations frequently must pay taxes on earnings. Define tax rate, . Corporations also receive deductions for costs of capital Define deduction rates = (s1, s2, s3, ….) Maximize after-tax profits implies that after-tax marginal product of capital = after-tax cost of K capital. (1 ) PMPKt (1 s1 )i (1 s2 ) (1 s3 ) g P Pt K , NEW Tax Wedge, tw, is defined as the extra cost of capital beyond the interest rate. PMPKt i g MPKt r g PK pK tw Pt K , NEW tw ptK Which cost of capital? Which interest rates should we use to calculate the cost of capital. This depends on several things including the risk of the investment project & flexibility and duration. If capital project is risky, we might apply a risk premium (i.e. use the interest rate on a risky bond). If capital project is necessarily long term, we might use a long term interest rate. q theory & Corporate Investment A benchmark theory of corporate investment is that investment is a function of a quantity q. The measure of q for a firm is Market Value of Firm q Replacement Cost of Capital The market value of a publicly listed firm without debt is market capitalization (stock price * shares outstanding). The market value of a publicly listed firm with debt is the market capitalization plus value of debt (i.e. the cost of owning the firm lock, stock and barrel). Calculating q: China Steel 2000 Market Capitalization = Stock Price × # of Shares Proxy for Replacement Value of Capital – Book Value of PP&E. Proxy for Firm Value = Market Capitalization + Book Value of Total Debt Caveat: Intangible Assets (i.e. Technology) May Be Large for Some Firms (e.g. Acer Inc. has a 2000 q > 4). Caveat: Book value of PP&E may underestimate replacement costs of capital as it does not adjust for inflation. Firm Balance Sheets. Stock Price # of Shares Market Cap Book Value of PPE Total Debt Firm Value q $19.5 8,748,363,000 $170,593,078,500 $118,415,993,000 $38,228,396,000 $208,821,474,500 1.763456685 q theory If value of firm is greater than the cost of capital (q > 1) than the value of capital inside the firm is greater than the value of capital outside the firm. If q > 1, firm should have positive net investment. If q = 1, firm should have zero net investment. If q < 1, firm should have negative net investment. q as Cost of Capital Theory We might think of q theory as similar to cost of capital theory for firms that get financing through the stock market. Owners of equity have a claim to the profits of the firm. They might require a certain amount of profits relative to what Profits ck Market Capitalization they pay for the stock. A firm generates a certain amount of Profits MPK Price of Capital profits per unit of capital q Market Capitalization Price of Capital Profits Price of Capital Profits Market Capitalization PMPK MPK ck rck Investment & the Stock Market Q theory suggests that a rise in stock market prices could be thought of as a decline in the cost of raising funds through equity. Empirically, q theory seems to do a poor job of explaining connections between the stock market and investment. Why? Many firms change their capital stock infrequently. Short-term fluctuations in stock market may have little effect. Stock market bubbles may keep stock prices from reflecting a realistic assessment of value of corporate capital. Firms may be limited in ability to raise funds in stock market. Investment and Stock Returns 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% 65 9 68 9 71 9 74 9 77 9 80 9 83 9 86 9 89 9 92 9 95 9 98 0 01 19 1 1 1 1 1 1 1 1 1 1 1 2 -20.00% -40.00% -60.00% -80.00% I Stock Return Corporate Finance Two kinds of Finance External Finance – Funds for investment raised through loans or issuing securities. Internal Finance – Funds for investment raised through retaining profits instead of paying dividends. Benchmark M-M Theory says investment decisions and firm value should not depend on sources of financing. Requirements: No distortionary taxation Perfect financial markets with perfect information. Reality Internal Funds are cheaper form of financing than external funds. Much of corporate financing is through internal finance. Investment is more strongly affected by cash flow than q. Cost of capital depends on collateral value that firms can pay if they default on loans or bonds. MPK rck K K* Change in Available Internal Funds MPK rck K K* K** Conclusion Cost of capital includes interest costs plus depreciation costs plus capital losses plus tax wedge. Capital stock that maximizes profits sets the marginal product of capital equal to the cost of capital. Business cycle fluctuations of capital investment are due to fluctuations in productivity and cost of capital. Investment is volatile because capital is large relative to investment in any given period. Small fluctuations in optimal capital have large effects on investment. Conclusion pt. 2 Optimal Capital Theory implies Corporate Investment is a function of q (market value of firm relative to the replacement value of capital). Real Estate prices are determined by rent divided by the determinants of the cost of capital. In reality, internal funds are the dominant source of finance for investment. External Financing interest costs may depend on the state of firms balance sheets. Firms’ balance sheets are an additional channel of business cycle volatility.