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Chapter 15 Investment, Time and Capital Markets Topics to be Discussed Stocks Versus Flows Present Discounted Value The Value of a Bond The Net Present Value Criterion for Capital Investment Decisions Adjustments for Risk ©2005 Pearson Education, Inc. Chapter 15 2 Topics to be Discussed Investment Decisions by Consumers Investments in Human Capital Intertemporal Production Decisions – Depletable Resources How Are Interest Rates Determined? ©2005 Pearson Education, Inc. Chapter 15 3 Introduction Markets for factors and output give a reasonably complete picture Capital markets are different Capital is durable It is an input that will contribute to output over a long period of time Must compare the future value to current expenditures ©2005 Pearson Education, Inc. Chapter 15 4 Stocks Versus Flows Stock Capital is a stock measurement The amount of plant and equipment a company owns at a point in time Flow Variable inputs and outputs are flow measurements An ©2005 Pearson Education, Inc. amount needed or used per time period Chapter 15 5 Stocks Versus Flows Profit is also a flow number Must know what the capital stock will allow the firm to earn a flow of profit Was the investment a sound decision? Must be able to value today the expected profit flow over time What is the flow of profit worth today? ©2005 Pearson Education, Inc. Chapter 15 6 Present Discounted Value (PDV) Determining the value today of a future flow of income The value of a future payment must be discounted for the time period and interest rate that could be earned rate – rate at which one can borrow or lend money Interest ©2005 Pearson Education, Inc. Chapter 15 7 Present Discounted Value (PDV) Future Value (FV) One dollar invested today should yield (1 + R) dollars a year from now (1 + R) is the future value of the dollar today What is the value today of getting $1 a year from now? What is the present discounted value of the $1? ©2005 Pearson Education, Inc. Chapter 15 8 Present Discounted Value (PDV) Future Dollar Value of $1 invested today (1 R) n n Number of years in future PDV Present dollar value of $1 received 1 in the future ; (how much would you have to n (1 R) invest today to have a dollar in the future?) ©2005 Pearson Education, Inc. Chapter 15 9 Present Discounted Value (PDV) The interest rate impacts the PDV The lower the interest rate, the less you money you needed invest to reach your future goal We can see how different interest rates will give different future values ©2005 Pearson Education, Inc. Chapter 15 10 PDV of $1 Paid in the Future R 1 YR 5 YR 1% $0.990 $0.951 $0.905 $0.742 2% $0.980 $0.906 $0.820 $0.552 5% $0.952 $0.784 $0.614 $0.231 10% $0.909 $0.621 $0.386 $0.057 ©2005 Pearson Education, Inc. Chapter 15 10 YR 30 YR 11 Valuing Payment Streams Can determine a stream of payments over time Choosing a payment stream depends upon the interest rate Given two streams, we can compute and add the present values of each year’s payment ©2005 Pearson Education, Inc. Chapter 15 12 Two Payment Streams Today Payment Stream A: Payment Stream B: ©2005 Pearson Education, Inc. Chapter 15 $100 $20 1 Year $100 $100 2 Years 0 $100 13 Two Payment Streams 100 PDV of Stream A 100 (1 R) 100 100 PDV of Stream B 20 2 (1 R) (1 R) ©2005 Pearson Education, Inc. Chapter 15 14 PDV of Payment Streams R = .05 R = .10 R = .15 R = .20 PDV of Stream A: $195.24 $190.90 $186.96 $183.33 PDV of Stream B: 205.94 193.54 182.57 172.78 Notice that which stream is worth more depends on the interest rate At lower interest rates, B pays out more As interest rates increase, A ends up paying out more ©2005 Pearson Education, Inc. Chapter 15 15 The Value of Lost Earnings PDV can be used to determine the value of lost income from a disability or death Scenario Harold Jennings died in an auto accident January 1, 1986 at 53 years of age Salary: $85,000 Retirement Age: 60 ©2005 Pearson Education, Inc. Chapter 15 16 The Value of Lost Earnings What is the PDV of Jennings’ lost income to his family? Must adjust salary for predicted increase (g) Assume an 8% average increase in salary for the past 10 years Average rate of growth of airline pilot salary over time Must adjust for the true probability of death (m) from other causes Derived ©2005 Pearson Education, Inc. from mortality tables Chapter 15 17 The Value of Lost Earnings Must adjust for the true probability of death (m) from other causes Derived from mortality tables Assume R = 9% The rate on government bonds ©2005 Pearson Education, Inc. Chapter 15 18 The Value of Lost Earnings W0 (1 g )(1 m1 ) PDV W0 (1 R ) W0 (1 g ) (1 m2 ) ... 2 (1 R ) 2 W0 (1 g ) (1 m7 ) 7 (1 R ) 7 ©2005 Pearson Education, Inc. Chapter 15 19 Calculating Lost Wages ©2005 Pearson Education, Inc. Chapter 15 20 The Value of Lost Earnings Finding PDV The summation of column 4 will give the PDV of lost wages – $650,252 Jennings’ family could recover this amount as partial compensation for his death ©2005 Pearson Education, Inc. Chapter 15 21 The Value of a Bond A bond is a contract in which a borrower agrees to pay the bondholder (the lender) a stream of money Example: A bond issued by a company may make a “coupon” payment of $100 per year for the next 10 years and a final payment of $1000 How much would you pay for this bond? Present value of payment stream ©2005 Pearson Education, Inc. Chapter 15 22 The Value of a Bond Determining the Price of a Bond Coupon Payments = $100/yr. for 10 yrs. Principal Payment = $1,000 in 10 yrs. $100 $100 PDV 2 (1 R) (1 R ) $100 $1000 ... 10 10 (1 R ) (1 R ) ©2005 Pearson Education, Inc. Chapter 15 23 Present Value of the Cash Flow from a Bond PDV of Cash Flow ($ thousands) 2.0 The higher the interest rate, the lower the value of the bond 1.5 1.0 0.5 0 ©2005 Pearson Education, Inc. 0.05 0.10 Interest Rate Chapter 15 0.15 0.20 24 The Value of a Bond Perpetuity is a bond that pays out a fixed amount of money each year forever Present value of a perpetuity is an infinite summation Can express the value of a perpetuity by PDV = $100/R In general, PDV = payment/R ©2005 Pearson Education, Inc. Chapter 15 25 The Effective Yield on a Bond Corporate and government bonds are often traded on the bond market The price of the bond can be determined by looking at the market price The value placed on it by buyers and sellers To compare the bond with other investment options, can determine the interest rate consistent with that value ©2005 Pearson Education, Inc. Chapter 15 26 Effective Yield on a Bond Calculating the Rate of Return from a Bond P is value of perpetuity – market price Can use equations to find value of R given P and the payment Payment Payment P then R R P ©2005 Pearson Education, Inc. Chapter 15 27 Effective Yield on a Bond From previous example R = $100/$1000 = 0.10 = 10% The interest rate calculated here is the effective yield Rate of return one receives by investing in the bond ©2005 Pearson Education, Inc. Chapter 15 28 Effective Yield on a Bond Calculating the Rate of Return from a Bond $100 $100 2 (1 R) (1 R) $100 $1000 ... 10 (1 R) (1 R)10 Calculate R in terms of P Coupon Bond : PDV See graph showing how R depends on P ©2005 Pearson Education, Inc. Chapter 15 29 PDV of Payments (Value of Bond) ($ thousands) Effective Yield on a Bond 2.0 The effective yield is the interest rate that equates the present value of a bond’s payment stream with the bond’s market price. 1.5 Notice the Bond Price is inverse to the effective yield 1.0 0.5 0 ©2005 Pearson Education, Inc. 0.05 0.10 Interest Rate Chapter 15 0.15 0.20 30 Effective Yield on a Bond Yields vary on different bonds Ex: Corporate bonds yield more than government bonds The degree of risk a bond holds is reflected in the yield Riskier bonds have higher yields Government unlikely to default Some corporations are more stable than others ©2005 Pearson Education, Inc. Chapter 15 31 The Yields on Corporate Bonds In order to calculate corporate bond yields, the face value of the bond and the amount of the coupon payment must be known Assume: IBM and Lucent both issue bonds with a face value of $100 and make coupon payments every six months ©2005 Pearson Education, Inc. Chapter 15 32 Yields on Corporate Bonds Closing prices for IBM on March 5, 2003 7 ½ 13 6.2 10 120.25 -.38 Closing prices for Lucent on March 5, 2003 5 ½ 08 7.5 129 73.50 -.38 Wall Street Journal, 3/6 •7.5: coupon payments for one year ($7.5) •13: maturity date of bond (2013) •6.2: annual coupon/closing price ($7.5/120.25) •10: number of bonds traded that day (10) •120.25: closing price ($120.25) •-.38: change in price from previous day (down 0.38) ©2005 Pearson Education, Inc. Chapter 15 33 The Yields on Corporate Bonds The IBM bond yield: Assume annual payments and 10 years to maturity 7.5 7.5 7.5 100 120 .25 ... 2 10 (1 R) (1 R) (1 R) (1 R)10 R* 4.9% ©2005 Pearson Education, Inc. Chapter 15 34 The Yields on Corporate Bonds The Lucent bond matures in 5 years and has a yield of: 5.5 5.5 5.5 100 73.50 ... 2 5 5 ( 1 R) ( 1 R) (1 R) ( 1 R) R* 13.0% ©2005 Pearson Education, Inc. Chapter 15 35 The Yields on Corporate Bonds In 2003, Lucent had significant decline in revenue, laid off many workers and had an uncertain future The more risky financial situation required a higher yield on the bonds to entice investors to buy ©2005 Pearson Education, Inc. Chapter 15 36 The Net Present Value Criterion for Capital Investment Decisions Firms have to decide when and how much capital to invest in Comparing the present value (PV) of the cash flows from the investment to the cost of the investment can give firms information needed to make worthwhile decisions ©2005 Pearson Education, Inc. Chapter 15 37 The Net Present Value Criterion for Capital Investment Decisions NPV Criterion Firms should invest if the present value of the expected future cash flows from an investment exceeds the cost of the investment ©2005 Pearson Education, Inc. Chapter 15 38 The Net Present Value Criterion for Capital Investment Decisions C capital cost n profits for n years (n 10) 1 2 NPV - C ... 10 (1 R) (1 R) (1 R)10 R discount rate or opportunit y cost of capital 2 with a similar risk Invest if NPV 0 ©2005 Pearson Education, Inc. Chapter 15 39 The Net Present Value Criterion for Capital Investment Decisions Determining the Discount Rate The firm must determine the opportunity cost of its money The correct value of the discount rate should equal the rate that the firm could earn on a similar investment One with same risk We assume no risk for now, so opportunity cost is what the firm could earn on a government bond ©2005 Pearson Education, Inc. Chapter 15 40 The Net Present Value Criterion for Capital Investment Decisions The Electric Motor Factory (choosing to build a $10 million factory) 8,000 motors/ month for 20 yrs Cost = $42.50 each Price = $52.50/motor Profit = $10/motor or $80,000/month Factory life is 20 years with a scrap value of $1 million Should the company invest? ©2005 Pearson Education, Inc. Chapter 15 41 The Net Present Value Criterion for Capital Investment Decisions Assume all information is certain (no risk) R = government bond rate .96 .96 2 (1 R ) (1 R ) .96 1 ... (1 R ) 20 (1 R ) 20 R* 7.5% NPV - 10 Discount rates below 7.5, NPV is positive Discount rates above 7.5, NPV is negative ©2005 Pearson Education, Inc. Chapter 15 42 Net Present Value of a Factory 10 •Firm should not invest for discount rates below 7.5 •Firm should not invest for discount rates above 7.5 8 Net Present Value ($ millions) 6 4 2 0 -2 -4 -6 0 ©2005 Pearson Education, Inc. 0.05 0.10 Interest Rate, R R* = 7.5 Chapter 15 0.15 0.20 43 The Net Present Value Criterion for Capital Investment Decisions When determining whether to invest or not, must distinguish between real and nominal rates Real versus Nominal Discount Rates Adjusting for the impact of inflation Assume price, cost, and profits are in real terms Inflation ©2005 Pearson Education, Inc. = 5% Chapter 15 44 Real Versus Nominal Discount Rates Assume price, cost, and profits are in real terms Therefore, P = (1.05)(52.50) = 55.13, Year 2 P = (1.05)(55.13) = 57.88… C = (1.05)(42.50) = 44.63, Year 2, C =…. Profit remains $960,000/year ©2005 Pearson Education, Inc. Chapter 15 45 Real Versus Nominal Discount Rates If the cash flows are in real terms, then the discount rate must be in real terms as well Opportunity cost of the investment, so must include inflation here if doing it elsewhere Real R = nominal R - inflation = 9% - 5% = 4% ©2005 Pearson Education, Inc. Chapter 15 46 Net Present Value of a Factory 10 If R = 4%, the NPV is positive. The company should invest in the new factory. 8 Net Present Value ($ millions) 6 4 2 0 -2 -4 -6 0 ©2005 Pearson Education, Inc. 0.04** 0.10 Interest Rate, R Chapter 15 0.15 0.20 47 The Net Present Value Criterion for Capital Investment Decisions Negative Future Cash Flows Companies expect losses in certain situations Take time to build demand High up front costs that lower over time Investment should be adjusted for construction time and losses ©2005 Pearson Education, Inc. Chapter 15 48 The Net Present Value Criterion for Capital Investment Decisions Electric Motor Factory Construction time is 1 year $5 million expenditure today $5 million expenditure next year Expected loss is $1 million the first year and $0.5 million the second year Profit is $0.96 million/yr. until year 20 Scrap value is $1 million ©2005 Pearson Education, Inc. Chapter 15 49 The Net Present Value Criterion for Capital Investment Decisions .5 1 5 NPV - 5 3 2 (1 R) (1 R) (1 R) .96 .96 ... 5 4 (1 R) (1 R) 1 .96 20 (1 R) 20 (1 R) ©2005 Pearson Education, Inc. Chapter 15 50 Adjustments for Risk Determining the discount rate for an uncertain environment: This can be done by increasing the discount rate by adding a risk-premium to the riskfree rate Amount of money that a risk-averse individual will pay to avoid taking a risk ©2005 Pearson Education, Inc. Chapter 15 51 Diversifiable vs. Nondiversifiable Risk Diversifiable risk can be eliminated by investing in many projects or by holding the stocks of many companies Nondiversifiable risk cannot be eliminated and should be entered into the risk premium ©2005 Pearson Education, Inc. Chapter 15 52 Diversifiable vs. Nondiversifiable Risk Diversifying spreads risk over many options Invest in many types of investments – diversify portfolio Firms invest in many different projects No reward for assets that have only diversifiable risk – tend to earn return close to risk free return on average ©2005 Pearson Education, Inc. Chapter 15 53 Diversifiable vs. Nondiversifiable Risk Some risk cannot be eliminated or avoided Company profits depend on the economy – boom or recession Future economic growth is uncertain so cannot eliminate all risk Investors should be rewarded for bearing this risk Opportunity cost of investing is higher – must include risk premium ©2005 Pearson Education, Inc. Chapter 15 54 Diversifiable vs. Nondiversifiable Risk The Capital Asset Pricing Model (CAPM) Model in which the risk premium for a capital investment depends on the correlation of the investment’s return with the return on the entire stock market If you invest in a mutual fund, there is no diversifiable risk but there is nondiversifiable risk since stocks tend to move with economy Expected return on stock is higher than risk free investment ©2005 Pearson Education, Inc. Chapter 15 55 Capital Asset Pricing Model Suppose you invest in the entire stock market (mutual fund) rm = expected return of the stock market rf = risk free rate rm - rf = risk premium for nondiversifiable risk Additional expected return you get for bearing the nondiversifiable risk of the stock market ©2005 Pearson Education, Inc. Chapter 15 56 Capital Asset Pricing Model Return on some assets is correlated with stock market as a whole CAPM summary of relationship between expected return and risk premium ri r f (rm r f ) ri expected return on an asset asset beta ©2005 Pearson Education, Inc. Chapter 15 57 Adjustments for Risk The asset beta, , measures the sensitivity of an asset’s return to market movements and, therefore, the asset’s nondiversifiable risk 1% rise in market resulting in a 2% rise in asset price means the beta is 2 1% rise in market resulting in a 1% rise in asset price means beta is 1 The larger the beta, the greater the expected return on the asset ©2005 Pearson Education, Inc. Chapter 15 58 Adjustments for Risk Given beta, we can determine the correct discount rate to use in computing an asset’s net present value: Discount Rate r f ( rm r f ) Risk-free rate plus a risk premium to reflect nondiversifiable risk ©2005 Pearson Education, Inc. Chapter 15 59 Determining Beta For a stock, beta determined statistically For a factory, determining beta is more difficult Firms often use the company cost of capital as nominal discount rate Weighted average of the expected return on a company’s stock and the interest rate that it pays for debt Can depend on level of nondiversifiable risk ©2005 Pearson Education, Inc. Chapter 15 60 Investment Decisions by Consumers Consumers face similar investment decisions when they purchase a durable good Compare flow of future benefits with the current purchase cost ©2005 Pearson Education, Inc. Chapter 15 61 Investment Decisions by Consumers Benefits and Costs of Buying a Car If you keep the car for 5 or 6 years, you have benefits that occur in the future Must compare the future flow of net benefits from owning the car (having transportation minus cost of insurance, maintenance and gas) with the purchase price ©2005 Pearson Education, Inc. Chapter 15 62 Benefits and Costs of Buying a Car S = dollar value of transportation services in dollars to a consumer E = total operating cost/yr Insurance, Maintenance, and Gas Price of car is $20,000 Resale value of car is $4,000 in 6 years Decision to buy the car can be framed in net present value terms ©2005 Pearson Education, Inc. Chapter 15 63 Investment Decisions by Consumers Benefits and Cost (S E ) NPV 20,000 ( S E ) (1 R) (S E ) (S E ) 4000 ... 2 6 6 (1 R) (1 R) (1 R) ©2005 Pearson Education, Inc. Chapter 15 64 Investment Decisions by Consumers Whether you should buy the car or not depends on the discount rate If you have to borrow money, then use interest loan rate When comparing to buy or lease, you can use same calculation High interest rate, often better to lease Low interest rate, often better to buy ©2005 Pearson Education, Inc. Chapter 15 65 Choosing an Air Conditioner When buying an air conditioner, must typically face a tradeoff between efficiency and cost Efficiency – how much energy used to cool Do you want to pay more now for lower long run costs or do you want to pay less now for higher long run costs? ©2005 Pearson Education, Inc. Chapter 15 66 Choosing an Air Conditioner Buying a new air conditioner involves making a trade-off Air Conditioner B High price and more efficient Both have the same cooling power Assume an 8 year life ©2005 Pearson Education, Inc. Chapter 15 67 Choosing an Air Conditioner OCi PDV Ci OCi (1 R) OCi OCi ... 2 (1 R) (1 R)8 Ci is the purchase price of i OCi is the average operating cost of i ©2005 Pearson Education, Inc. Chapter 15 68 Choosing an Air Conditioner Should you choose A or B? Depends on the discount rate If you borrow, the discount rate would be high Probably choose a less expensive and inefficient unit If you have plentiful cash, the discount rate would be low Probably ©2005 Pearson Education, Inc. choose the more expensive unit Chapter 15 69 Investments in Human Capital Individuals make choices on whether to invest in human capital Do I finish college? Do I go to graduate school? Human capital is the knowledge, skills, and experience that make an individual more productive and thereby able to earn a higher income over a lifetime ©2005 Pearson Education, Inc. Chapter 15 70 Investments in Human Capital Typically the investment in human capital pays off in the future in terms of higher pay, better promotions, and/or more job opportunities How does one decide to invest in human capital? Can use the net present value rule from before ©2005 Pearson Education, Inc. Chapter 15 71 Investments in Human Capital Suppose you are deciding to go to college for 4 years or skip college and go to work Assume purely financial basis (ignore pleasure or pain from college) Calculate net present value of costs and benefits of going to college ©2005 Pearson Education, Inc. Chapter 15 72 Investments in Human Capital Major costs for college Opportunity cost of lost wages – approximately $20,000 per year Costs for tuition, room and board, and related expenses – assume $20,000 per year Total economic costs of attending college are $40,000 per year for 4 years ©2005 Pearson Education, Inc. Chapter 15 73 Investments in Human Capital Benefits of college Higher salary throughout working life On average, college grad earns $20,000 higher than high school grad Assume that persists for 20 years Can now calculate net present value of investing in a college education ©2005 Pearson Education, Inc. Chapter 15 74 Investments in Human Capital 40 40 40 NPV 40 ... 2 (1 R) (1 R) (1 R)3 20 20 ... 4 (1 R) (1 R) 23 ©2005 Pearson Education, Inc. Chapter 15 75 Investments in Human Capital What discount rate should be used? We are ignoring inflation, so you should use a real discount rate About 5% would reflect opportunity cost of money for many households Return of investing in other assets This gives an NPV of about $66,000; therefore, investing in college is a good idea ©2005 Pearson Education, Inc. Chapter 15 76 Investments in Human Capital Although NPV is positive, it is not very large Almost free entry system to attend college Free entry markets tend to lead to zero economic profits ©2005 Pearson Education, Inc. Chapter 15 77 Should You Go to Business School? Getting an MBA often means a large increase in salary Can see the typical change in salary from getting an MBA from top business schools For US as a whole, average salary preMBA is about $45,000 and obtaining the MBA increases salary by about $30,000 ©2005 Pearson Education, Inc. Chapter 15 78 Should You Go to Business School? ©2005 Pearson Education, Inc. Chapter 15 79 Should You Go to Business School? ©2005 Pearson Education, Inc. Chapter 15 80 Should You Go to Business School? Assuming the $30,000 per year gain persists for 20 years Typical MBA takes 2 years and has expenses of about $45,000 Opportunity cost of forgone pre-MBA salary is also $45,000 per year Total economic cost of getting MBA is $90,000 ©2005 Pearson Education, Inc. Chapter 15 81 Should You Go to Business School? Net present value of the investment is 90 30 30 NPV 90 ... 2 (1 R) (1 R) (1 R) 21 With real discount rate of 5%, NPV is about $158,000 ©2005 Pearson Education, Inc. Chapter 15 82 Should You Go to Business School? Why is payoff from MBA in Table 15.6 so much greater than from 4-year undergrad degree? Entry into many MBA programs, especially those listed in table, is highly selective and difficult Many more people apply than are accepted, so return remains high ©2005 Pearson Education, Inc. Chapter 15 83 Should You Go to Business School? Financial decision is easy Although costly, return is very high But some find it more fun than others Many do not have undergraduate grades and test scores to go to business school You may find a career you like better, such as teaching or law ©2005 Pearson Education, Inc. Chapter 15 84 Intertemporal Production Decisions – Depletable Resources Firms’ production decisions often have intertemporal aspects – production today affects sales or costs in the future Firms may gain experience, which lowers future costs Use of depletable resources – extracting the resource today means less is available in the future Must take these into account in decisions ©2005 Pearson Education, Inc. Chapter 15 85 Intertemporal Production Decisions – Depletable Resources Scenario You are given an oil well containing 1000 barrels of oil MC and AC = $10/barrel Should you produce the oil or save it? If you only look at extraction costs versus price, you ignore an important piece – opportunity cost Decision depends on price today, but also on how fast you expect the price to rise in future ©2005 Pearson Education, Inc. Chapter 15 86 Intertemporal Production Decisions – Depletable Resources If you expect price of oil to rise slowly, might be better off extracting today If you expect price of oil to rise rapidly, better off waiting and extracting later How fast must price rise to keep in ground? Value must rise at least as fast as the rate of interest Can show this mathematically ©2005 Pearson Education, Inc. Chapter 15 87 Intertemporal Production Decisions – Depletable Resources Scenario Pt = price of oil this year Pt+1 = price of oil next year C = extraction costs R = interest rate If ( Pt 1 c) (1 R)( Pt c) : Keep the oil in the ground If ( Pt 1 c) (1 R)( Pt c) : Sell all the oil now If ( Pt 1 c) (1 R)( Pt c) : Indifferen t ©2005 Pearson Education, Inc. Chapter 15 88 Intertemporal Production Decisions – Depletable Resources Do not produce if you expect its price less its extraction cost to rise faster than the rate of interest Extract and sell all of it if you expect price less cost to rise at less than the rate of interest But how fast will the price of oil rise? ©2005 Pearson Education, Inc. Chapter 15 89 The Behavior of Market Price If OPEC cartel didn’t exist, could estimate oil prices by production decisions of producers To maximize return, producers will follow production rule stated previously Price minus marginal cost must rise at exactly the rate of interest Why? ©2005 Pearson Education, Inc. Chapter 15 90 The Behavior of Market Price If price – MC rose faster than R, no one would produce oil This would drive up market price of oil If price – MC rose slower than R, everyone would try to sell all their oil This would drive down the market price of oil Can show how market price must rise given these situations ©2005 Pearson Education, Inc. Chapter 15 91 Price of an Exhaustible Resource Price Price PT Demand P0 P-c P0 c c Marginal Extraction Cost T ©2005 Pearson Education, Inc. Time Chapter 15 Quantity 92 Price of an Exhaustible Resource Notice P > MC Is it a contradiction to the competitive rule that P = MC? Total marginal cost must include extraction costs AND opportunity cost User cost of production Opportunity cost of producing and selling a unit today, making it unavailable for production and sale in the future ©2005 Pearson Education, Inc. Chapter 15 93 Price of an Exhaustible Resource P = MC MC = extraction cost + user cost User cost = P - marginal extraction cost User cost rises over time As resource remaining in ground becomes scarcer, opportunity cost of depleting another unit becomes higher ©2005 Pearson Education, Inc. Chapter 15 94 Resource Production by a Monopolist How would a monopolist choose their rate of production? Value of unit is marginal revenue minus marginal cost They will produce so that marginal revenue less marginal cost rises at exactly the rate of interest, or (MRt+1 – c) = (1 + R)(MRt – c) ©2005 Pearson Education, Inc. Chapter 15 95 Resource Production by a Monopolist For a monopolist with a downward sloping demand, price is greater than MR (MR – MC) < (P – MC) The monopolist is more conservationist than in a competitive industry They start out charging a higher price and deplete the resources more slowly ©2005 Pearson Education, Inc. Chapter 15 96 How Depletable Are Depletable Resources? For some resources such as oil, natural gas and helium, in ground reserves are only equal to about 50 – 100 years of current consumption User cost is a significant part of market price For resources like coal and iron, reserves are close to thousands of years of current consumption User cost is very small ©2005 Pearson Education, Inc. Chapter 15 97 How Depletable Are Depletable Resources? Can estimate user cost from geological information about existing and potential reserves Also need to know demand curve and likely factors shifting it over time In competitive market, determine user cost from economic rent earned by owners of resource-bearing lands ©2005 Pearson Education, Inc. Chapter 15 98 User Cost as Fraction of Competitive Price Resource User Cost/Competitive Price Crude Oil 0.4 – 0.5 Natural Gas 0.4 – 0.5 Uranium 0.1 – 0.2 Copper 0.2 – 0.3 Bauxite 0.05 – 0.2 Nickel 0.1 – 0.3 Iron Ore 0.1 – 0.2 Gold 0.05 – 0.1 ©2005 Pearson Education, Inc. Chapter 15 99 How Depletable Are Depletable Resources? Notice that only crude oil and natural gas have a user cost as a substantial component of price Of the sharp price fluctuations, user cost has almost nothing to do with them Oil prices change from OPEC and conflict in Persian Gulf Resource depletion has not had much effect on the prices of those resources ©2005 Pearson Education, Inc. Chapter 15 100 How Are Interest Rates Determined? The interest rate is the price that borrowers pay lenders to use their funds Determined by supply and demand for loanable funds Supply of loanable funds comes from household savings Demand for loanable funds comes from Household consuming more than income Firms wanting to make capital investments ©2005 Pearson Education, Inc. Chapter 15 101 How Are Interest Rates Determined? For households, the higher the interest rate, the greater the cost of consuming Less willing to borrow Demand is declining function of interest rate Firms invest in project when NPV > 0 Higher interest rate means lower NPV Demand is downward sloping Total demand for loanable funds is sum of household demand and firm demand ©2005 Pearson Education, Inc. Chapter 15 102 How Are Interest Rates Determined? R Interest Rate DH and DF, the quantity demanded for loanable funds by households (H) and firms (F), respectively, varies inversely with the interest rate. DF DH ©2005 Pearson Education, Inc. Chapter 15 Quantity of Loanable Funds 103 Supply and Demand for Loanable Funds R Interest Rate S Equilibrium interest rate is R*. R* DF DH ©2005 Pearson Education, Inc. Q* Chapter 15 Quantity of Loanable Funds 104 How Are Interest Rates Determined? The supply and demand for loanable funds determines the equilibrium interest rate If recession hits, the NPV of projects will fall, firms will invest less, and demand for loanable funds will fall DF and DT will fall, causing interest rate to fall If government has to borrow money, demand will increase and R also increases Fed shifts supply of loanable funds, as well ©2005 Pearson Education, Inc. Chapter 15 105 Changes in the Equilibrium R Interest Rate S During a recession, interest rates fall due to a decrease in the demand for loanable funds. R* R1 DT D’T Q1 ©2005 Pearson Education, Inc. Q* Chapter 15 Quantity of Loanable Funds 106 Changes in the Equilibrium R Interest Rate S When the federal government runs large budget deficits, the demand for loanable funds increases. R2 R* D’T DT ©2005 Pearson Education, Inc. Q* Q2 Chapter 15 Quantity of Loanable Funds 107 Changes in the Equilibrium R Interest Rate S S’ When the Federal Reserve increases the money supply, the supply of loanable funds increases. R* R1 DT ©2005 Pearson Education, Inc. Q* Q Chapter 15 1 Quantity of Loanable Funds 108 A Variety of Interest Rates 1. Treasury Bill Rate Short-term (1 yr or less) bond issued by US government Pure discount bond – no coupon payments Short-term, risk-free rate 2. Treasury Bond Rate Longer-term bond, typically 10-30 yrs Rates depend on maturity of bond ©2005 Pearson Education, Inc. Chapter 15 109 A Variety of Interest Rates 3. Discount Rate The rate the Federal Reserve charges commercial banks for short period loans, called discounts 4. Federal Funds Rate Interest rate banks charge one another for overnight loans of federal funds Banks with excess reserves may loan them to banks with reserve deficiencies ©2005 Pearson Education, Inc. Chapter 15 110 A Variety of Interest Rates 5. Commercial Paper Rate Short-term (6 months or less) discount bonds used by high-quality corporate borrowers Slightly riskier than treasury bills, so rate is less than 1% higher than Treasury bill rate ©2005 Pearson Education, Inc. Chapter 15 111 A Variety of Interest Rates 6. Prime Rate Sometimes called the reference rate Rate large banks post as a reference point for short-term loans to biggest corporate borrowers Does not fluctuate from day to day ©2005 Pearson Education, Inc. Chapter 15 112 A Variety of Interest Rates 7. Corporate Bond Rate Long-term (typically 20 yrs) corporate bonds with different risks High grade, medium grade, etc. Average yields indicate how much corporations are paying for long term debt Vary considerably ©2005 Pearson Education, Inc. Chapter 15 113