1. Chapter 11: Capital Inputs & Capital Investment Decisions

2. Key Topics 1. Capital (general & specific types) 2. Capital markets (i.e. S&D of funds for capital purchases) 3. Investment decisions a. “percentage” costs and returns b. “dollar” costs and returns (i.e. present value)

3. Capital Definition =Items (man-made inputs) used to produce other goods and services over time Examples (categories): 1. Tangible capital (nonresidential structures, durable equipment, residential structures, inventories)

4. Capital Definition 2. Social capital = “infrastructure” (public works like roads, bridges, mass transit systems, sewer & water systems; public services like police, fire protection, schools, city halls, courthouses). 3. Intangible (non physical) capital (good will, patents, worker knowledge/skills)

5. Capital Stock and Flows Capital stock = current market value ($) given or measured at point in time Capital flow = either an increase in the stock of capital (i.e. investment) or decrease in the stock of capital (i.e. depreciation)

6. Capital Markets  The supply of and demand for funds to buy capital goods  Household savings = supply of funds (for income in form of interest and/or profits/dividends)  Business investments in capital = demand for (uses of) funds

7. Interest (rate) Payment for use of money paid by borrower to lender Price of money; cost of a loan Types of rates – Fixed rate is known initially and does not vary over life of the loan – Variable or adjustable or floating rate may vary over life of the loan

8. Financial “Instruments” (markets) =specific mechanisms whereby consumer savings are made available to business firms for capital spending  bonds, business loans, venture capital funds, retained earnings, company stock purchases

9. Bonds  A financial contract between a borrower (e.g. bond seller who is a business firm or governmental agency) whereby the borrower agrees to pay back to the lender (consumer or bond buyer) the initial price of the bond plus any additional payments (i.e. interest).  A loan from a consumer to a borrower.

10. Profit-maximizing quantity of capital (company capital investment decisions)  MRP K = P K  Rate of return (%) = cost of capital (%)  Incremental $ return = incremental $ cost (present value of incremental returns = present value of incremental costs)

11. Graph of profit-maximizing K (based on interest rates) r PkPk MRP K K K*

12. Time Value of Money (Basic Concept) A dollar is worth more (or less) the sooner (later) it is received or paid due to the ability of money to earn interest.  Present value + interest earned = future value or  Future value - interest lost = present value

13. Time Value of Money to a Borrower PV=present value =the number of $ you will be able to borrow presently in order to pay back a given number of $ in the future FV=future value =the number of $ you will have to pay back in the future as a result of having borrowed a given number of $ presently

14. Time Value of Money to a Saver PV=present value =the number of $ you will have to save presently in order to collect a given number of $ in the future FV=future value =the number of $ you will be able to collect in the future as a result of having saved a given number of $ presently

15. Time Value of Money Relationships FV 1 =PV + PV (r ) =PV (l + r) FV 2 =FV 1 + FV 1 (r ) =FV 1 (l + r) =PV(l + r)(l + r) =PV (l + r) 2. FV n =PV (l + r) n

16. Time Value Problems FV n =PV (l + r) n GivenSolve for PV, r, nFV n = PV (l + r) n = ‘compounding’ FV n, r, nPV = FV n [1/(l + r) n ] = ‘discounting’ NOTE: In text, PV = R/(l + r) t. Thus, R = FV n, t=n.

17. How to compare two different $ amounts, two different time periods? $X$Y 0 t1t1 t2t2 t3t3

18. Comparing Two Different $ Amounts, Two Different Time Periods—A Summary of Different Ways Using Time Value of Money Concepts Methods: 1. Discount each ‘back’ to t = 0 2. Discount $Y from t = 2 to t = 1 3. Compound each ‘forward’ to t = 3 4. Compound $X from t = 1 to t = 2 0 $X$Y t1t1 t2t2 t3t3

19. What is the present value? 012 3 4 7 77 r = 7%

20. Present Value 0 1 2 34 7 77 r = 7% PV=7(1/1.07) 1 + 7(1/1.07) 2 + 7(1/1.07) 3 =7(.9345) + 7(.8734) + 7(.8163) =6.5415 + 6.1138 + 5.7141 =18.37

21. Graph of profit-maximizing k (based on $ present value) PV($) PV of incremental initial cost K* K PV of incremental future profits