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## Investment

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**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**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**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**Easterly, Rodriguez, and Schmidt-Hebbel "Public Sector Deficits and Macroeconomic Performance." (Statistical appendix) 1994 and Bruno and Easterly JME 1998.**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 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.**A firm borrows to buy 1 capital good at interest**rate 1+i. The firm produces PMPKt+1 worth of goods and sells the capital good for . Optimal to buy capital good as long as pay-off is greater than the cost. Optimal Condition Definition of Capital Cost Optimal Capital Example.**Capital Cost**• We can divide the capital cost into three parts. • Interest cost: Net interest rate. • Depreciation: Defined as change in value due to aging. • Capital gain: Defined as change in value due to change in price of new goods.**Real Capital Cost**• We can convert the optimal capital equation into real terms by dividing both sides by the price level. • Define the real price of capital good as price of capital good relative to the firm’s output price.**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 schedule • 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.**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. Optimum Number of Taxis**Optimal Capital: Example**• Solve for Optimal Level of Capital**MPK**rck K K***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 & Optimal Capital**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 capital. • Tax Wedge, tw, is defined as the extra cost of capital beyond the interest rate.**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 • 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).**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. Calculating q: China Steel 2000**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 they pay for the stock. • A firm generates a certain amount of profits per unit of capital**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 & the Stock Market**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.