Chapter 14

1. Chapter 14 Capital Markets © 2004 Thomson Learning/South-Western

2. Time Periods and the Flow of Economic Transactions • Ways transactions can occur across periods. • Durable goods that last more than one period. • An individual can borrow or lend. • Individual Savings--The Supply of Loans. • Savings frees up resources that can be used to produce investment goods. • Savings provide funds for firms to finance investment goods.

3. Two-Period Model of Saving • Suppose there are only two time periods. • C0 is consumption this year. • C1 is consumption in the following year. • Only consumption yields utility which can be purchased with current income, Y. • Income saved earns interest (at a real interest rate of r) before it is used to buy C1. • The consumers goal is to maximize utility.

4. A Graphical Analysis • The indifference curves in Figure 14.1 show the utility obtainable from various combinations of C0 and C1. • When C0 = Y, no income is saved for the second period. • When C0 = 0, C1 = (1 + r)Y. • The person can consume all income in the second period plus what is earned in interest.

5. FIGURE 14.1: The Savings Decision C 1 (1+r) Y U3 U2 U1 Y C 0

6. A Graphical Analysis • Between these two endpoints, the budget constraint is the black straight line. • Utility is maximized at C*0, C*1 where the MRS equals (1 + r). • Utility is maximized where the rate the individual is willing to trade C0 for C1 equals the rate he or she is able to trade these in the market through savings.

7. FIGURE 14.1: The Savings Decision C 1 (1+r) Y C* 1 U 3 U 2 U 1 C* Y C 0 0

8. Substitution and Income Effects of a Change in r • A change in r changes the “price” of future versus current consumption. • The substitution effects of an increase in r are shown in Figure 14.2. • The move along U2 to S. • The higher opportunity cost of C0 rises and the person substitutes C1 for C0. • The person saves more do to the increase in r.

9. FIGURE 14.2: Effect of an Increase in r on Savings Is Ambiguous C 1 (1+r’) Y (1+r) Y S C* 1 U 2 C* Y C 0 0

10. Substitution and Income Effects of a Change in r • The income effect is S to C0**, C1**. • If consumption in both periods is a normal good, both should increase. • The net effect of increased r on C0 (and on savings) is ambiguous. • Savings increase if the substitution effect dominates (as shown in Figure 14.2), but decrease if the income effect dominates. • Savings probably increase with higher r.

11. FIGURE 14.2: Effect of an Increase in r on Savings Is Ambiguous C 1 (1+r’) Y (1+r) Y C** 1 S C* U 3 1 U 2 C** C* Y C 0 0 0

12. Firms’ Demand for Capital and Loans • The profit maximizing firm will rent additional capital equipment up to the point at which the marginal revenue product of the equipment is equal to the rental rate on the equipment. • Assume all firms rent all of the capital they use from other firms.

13. Rental Rates and Interest Rates • The per-period rate that firms have to pay to rent the equipment will be determined by the average costs that the rental firms incur. • Two important costs of the equipment are: • Depreciation costs reflect the wear and tear. • Borrowing costs are the explicit or implicit opportunity (interest) costs for the funds tied up in the equipment.

14. Rental Rates and Interest Rates • If depreciation (d) and borrowing (r = interest) costs are proportional to the market price of the equipment being rented (P) we have the following expression for the per-period rental rate, v.

15. Rental Rates and Interest Rates • This equation shows why there is an inverse relationship between the demand for equipment and the interest rate. • When the interest rate is high, rental rates will be high and firms will try to substitute toward cheaper inputs while low interest rates induce firms to rent more equipment. • This will change the demand for loans, with low rates encouraging greater borrowing.

16. Ownership of Capital Equipment • Firms that own equipment are really in two businesses. • They produce goods. • They lease capital equipment to themselves. • The implicit rates they pay for leasing capital equipment are the same as for a firm that rents such equipment.

17. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • Total U.S. personal savings amounted to less than one percent of disposable income in 1998. • This is a steep decline from earlier savings levels in the U.S. • This is much lower than typical 10 percent rates found in other countries.

18. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • Concerns are whether individuals will have adequate savings for their own retirement or to provide sufficient capital accumulation for future generations. • Recent attempts to stimulate savings. • All allow tax deductions for contributions, and do not tax assets in the plan until paid at retirement.

19. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • Individual Retirement Accounts (IRAs). • Set up by individuals acting on their own. • Only low-income individuals receive tax deductions, but everyone can avoid taxation of returns from assets in the plan. • 401(k) Plans • Set up by employers who sometimes match employees contributions.

20. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • Both contributions and assets returns are tax-exempt until retirement. • Keogh Plans • Similar to the other plans except that they are intended for self-employed individuals. • These generally have higher contribution limits.

21. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • The effect of these plans on savings is ambiguous. • The after-tax interest rate for savers is higher, but the substitution and income effects work in opposite directions. • Also, since only the contributions to specific plans are apply, they provide incentives for individuals to shift to these plans without changing their total amount of savings.

22. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • Most studies use date on individual savings behavior. • Studies suggest that people have very different attitudes toward savings. • Some are serious savers who will accumulate assets in many forms. • Others never save. • Plan participants are the serious saver types.

23. APPLICATION 14.1: Do We Need Tax Breaks for Savers? • But it is not possible to determine if these plans themselves have increased savings. • A more correct interpretation is that plan participation acts only to identify savers who are predisposed to save more. • The true impact of these savings plans remains unknown.

24. Determination of the Real Interest Rate • Figure 14.3 shows the supply of loans assumed to be an upward sloping function of the interest rate, r. • The demand for loans is negatively related to the interest rate. • Higher rates increase the equipment rental rate. • Q*, r* is the equilibrium, with the rate that links economic time periods together.

25. FIGURE 14.3: The Real Interest Rate Is Determined in the Market for Loans Real interest rate S r* D Q* Quantity of loans per period

26. Changes in the Real Interest Rate • Factors that increases firms’ demand for capital equipment will increase the demand for loans. These include: • Technical progress that makes equipment more productive. • Declines in the equipment market prices. • Optimistic views of the demand for products. • The increased demand causes an increase in the real interest rate.

27. Changes in the Real Interest Rate • Factors that affect savings by individuals will shift the supply curve of loans. These include • Government-provided pension plans that reduce individuals’ current savings which increases the real interest rate. • Reductions in taxes on savings increase the supply of loans and decrease the real interest rate.

28. APPLICATION 14.3: Inflation-Indexed Bonds • Most government bonds do not explicitly take account of economy-wide inflation. • Recently, however, several nations have issued “inflation-indexed” bonds that adjust payments for changes in inflation. • In theory, these bonds pay a real interest rate. • Israel, Australia, Turkey, and Brazil are significant issuers of such bonds.

29. APPLICATION 14.3: Real and Nominal Interest Rates • Assume the nominal interest rate of i for a one-period loan of $1 with a e percent expected increase in the price level by next year. • The real value of your repayment will be:

30. APPLICATION 14.3: Real and Nominal Interest Rates • As previously shown, this real payment is also given by (1 + r), where r is the real interest rate. • So,

31. APPLICATION 14.3: Real and Nominal Interest Rates • Nominal and real interest rates differ by the expected rate of inflation, e. • This equation also provides a way to estimate expected inflation. • For example, on August 11, 1999 a 30-year U.S. Treasury bond yield was 6.13 percent with a 4.00 percent rate on an indexed bond • The expected inflation rate was over 2 percent.

32. APPLICATION 14.3: The Design of Inflation-Indexed Bonds • The previous calculation assumed that inflation-indexed bonds paid the real interest rate. • In the U.S., changes in the Consumer Price Index (CPI) is used to adjust such bonds. • But, the IRS has decided that both the higher interest payments caused by inflation and the annual increase in redemption value are taxable.

33. APPLICATION 14.3: The Design of Inflation-Indexed Bonds • Thus, the actual, after-tax real interest rate promised by inflation-indexed bonds may be much lower than reported. • In addition, these bonds are subject to differing risk factors. • For nominal bonds, the risk is in higher inflation rates. • For these bonds, the risk is in possible changes in government policy toward them.

34. Present Discounted Value • Transactions that take place at different times cannot be compared directly because of the interest that is received or paid. • A promise to pay a dollar today is not the same as a promise to pay a dollar in one year. • A dollar today is more valuable because it can be invested at interest for the year.

35. Single-Period Discounting • In a two period model, a dollar invested today will grow by a factor of (1 + r) next year. • The present value of a dollar that will not be received until next year is 1/(1 + r) dollars. • The present value of $1 a year from now, with r = 0.05 is $0.95 [$0.95 = $1/(1.05)].

36. Present Value • The present value is discounting the value of future transactions back to the present day to take account of the effect of potential interest payments. • Table 14.1 demonstrates the discount factor for various interest rates. • The first row demonstrates that the higher the interest rate, the smaller the discount factor.

37. Table 14.1: Present Discounted Value of $1 for Various Time Periods and Interest Rates

38. Multiperiod Discounting • The present value of $1 that is not to be paid until n years in the future is given by: • Table 14.1 shows various interest rates and different values of n. • For example, with r = 0.10 and n = 10, the present value of $1 is $0.39.

39. Present Value and Economic Motives • The goal of the firm making decisions over time is changed to “maximize the present value of all future profits.” • This yields nearly the same results as we have shown for one period profit maximization. • This is sometimes stated as the firm makes decisions to “maximize the present value of the firm.”

40. Present Value and Economic Motives • For individuals, present value enters the utility maximization decision through the budget constraint. • In some cases, individuals may “discount” the future in that they would prefer to consume in the present relative to the future.

41. APPLICATION 14.4: Discounting Cash Flows and Derivative Securities • Mortgages typically are long-lived and there is an active secondary market that permits the initial lender to sell the mortgage. • Often many mortgages are sold in a bundle to gain economies of scale in buying and selling. • Collateralized mortgage operations (CMOs) carry this one step further by selling only a portion of the cash flow such as the interest payments from a given pool of mortgages.

42. APPLICATION 14.4: Discounting Cash Flows and Derivative Securities • Each expected cash flow from the CMO must be appropriately discounted to the present. • Variability in payment complicates this calculation: • For example, an unexpected increase in repayments increases the value of a “repayment CMO” because the funds are available sooner.

43. APPLICATION 14.4: Discounting Cash Flows and Derivative Securities • A security, such as a CMO, is called a “derivative” because its value is derived from some underlying, more basic security such as a mortgage. • Other examples include futures contracts on commodities, metals, and foreign currencies and options on common stocks or indexes of common stocks.

44. APPLICATION 14.4: Discounting Cash Flows and Derivative Securities • Some firms aggregate their derivative portfolios into a single stream of discounted cash flows. • They use historical data to study how changes in the general economic environment might be expected to affect those cash flows.

45. APPLICATION 14.4: Discounting Cash Flows and Derivative Securities • The Long-Term Capital Management hedge fund, run by two recent Nobel prize winners in economics, was such a fund. • In the summer of 1998, cash flows did not follow previous historical relationships and this fund ran into serious problems. • The fund was bailed out by the U.S. Federal Reserve.

46. Pricing of Exhaustible Resources • Scarcity costs are the opportunity costs of future production foregone because current production depletes exhaustible resources. • These are in addition to the usual production costs. • In Figure 14.4, the usual production marginal costs are reflected in the supply curve, S.

47. FIGURE 14.4: Scarcity Costs Associated with Exhaustible Resources Price S P* D 0 Quantity per week Q*

48. Pricing of Exhaustible Resources • Scarcity costs shift the marginal cost curve up to S’. • Because of scarcity costs, current output falls from Q* to Q’, and the market price increases from P* to P’. • The charges effectively encourage “conservation” of the exhaustible resource.

49. FIGURE 14.4: Scarcity Costs Associated with Exhaustible Resources S’ Price P’ S P* D 0 Quantity per week Q’ Q*

50. The Size of Scarcity Costs • The actual value depends upon the future resource price. • For example, suppose the firm believes that copper will sell for $1 per pound in 10 years. • Selling one pound today will mean $1 foregone in the future since copper supply is fixed. • If r = 5 percent, the present value equals $0.61. • If production marginal costs = $0.35 per pound, scarcity costs = $0.26 per pound ($0.61-$0.35).