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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

- Fixed 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.

Volatility: Investment and GDPAnnual Growth Rates

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.

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 rate 1+i.

- 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 rate 1+i.

- 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 rate 1+i.

- 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 TaxisOptimal Capital: Example taxis is less than cost of capital.

- Solve for Optimal Level of Capital

Q: Why does MPK slope down. taxis is less than cost of capital.

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 CapitalInvestment Volatility taxis is less than cost of capital.

- 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 taxis is less than cost of capital.

- 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? taxis is less than 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 taxis is less than cost of capital.

- 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 taxis is less than cost of capital.

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 2000q theory taxis is less than cost of capital.

- 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 taxis is less than cost of capital.

- 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 MarketInvestment and Stock Returns be thought of as a decline in the cost of raising funds through equity.

Corporate Finance be thought of as a decline in the cost of raising funds through equity.

- 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 be thought of as a decline in the cost of raising funds through equity.

- 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.

Change in Available Internal Funds be thought of as a decline in the cost of raising funds through equity.

MPK

rck

K

K*

K**

Conclusion be thought of as a decline in the cost of raising funds through equity.

- 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 be thought of as a decline in the cost of raising funds through equity.

- 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.

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