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Chapter 15

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. Topics to be Discussed. Investment Decisions by Consumers

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Chapter 15

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  1. Chapter 15 Investment, Time and Capital Markets

  2. 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 Chapter 15

  3. Topics to be Discussed • Investment Decisions by Consumers • Investments in Human Capital • Intertemporal Production Decisions – Depletable Resources • How are Interest Rates Determined? Chapter 15

  4. Introduction • Markets for factors and output give a reasonably complete picture • Capital market 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 Chapter 15

  5. 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 amount needed or used per time period Chapter 15

  6. Stocks Versus Flows • Profit is also a flow number • Must know what the capital stock will allow the firm to earn as 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? Chapter 15

  7. 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. • Interest rate – rate at which one can borrow or lend money Chapter 15

  8. 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? Chapter 15

  9. Present Discounted Value (PDV) Chapter 15

  10. Present Discounted Value (PDV) • The interest rate impacts the PDV • The lower the interest rate, the less you have to invest to reach your goal in the future • We can see how different interest rates will give different future values Chapter 15

  11. PDV of $1 Paid in the Future Chapter 15

  12. 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 Chapter 15

  13. Two Payment Streams Payment Stream A: $100 $100 0 Payment Stream B: $20 $100 $100 Today 1 Year 2 Years Chapter 15

  14. Two Payment Streams Chapter 15

  15. PDV of Payment Streams PDV of Stream A: $195.24 $190.90 $186.96 $183.33 PDV of Stream B: 205.94 193.54 182.57 172.77 R = .05 R = .10 R = .15 R = .20 • Notice which stream is worth more depends on interest rate • More is paid out in A even though it is paid out sooner Chapter 15

  16. 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 Chapter 15

  17. 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 from mortality tables Chapter 15

  18. 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 Chapter 15

  19. The Value of Lost Earnings Chapter 15

  20. Calculating Lost Wages Chapter 15

  21. 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. Chapter 15

  22. 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 Chapter 15

  23. 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. Chapter 15

  24. 2.0 1.5 PDV of Cash Flow ($ thousands) 1.0 0.5 0 0.05 0.10 0.15 0.20 Interest Rate Present Value of the Cash Flow from a Bond The higher the interest rate, the lower the value of the bond Chapter 15

  25. 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 Chapter 15

  26. 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 Chapter 15

  27. 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 Chapter 15

  28. 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 received by investing in the bond Chapter 15

  29. Effective Yield on a Bond • Calculating the Rate of Return From a Bond • Can graph showing how R depends on P Chapter 15

  30. 2.0 1.5 PDV of Payments (Value of Bond) ($ thousands) 1.0 0.5 0 0.05 0.10 0.15 0.20 Interest Rate Effective Yield on a Bond The effective yield is the interest rate that equates the present value of a bond’s payment stream with the bond’s market price. Notice the Bond Price is inverse to the effective yield Chapter 15

  31. 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 more stable than others Chapter 15

  32. 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. Chapter 15

  33. Yields on Corporate Bonds 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 bonds traded that day (10) • 120.25: closing price ($120.25) • -.38: change in price from previous day (down 0.38) Chapter 15

  34. The Yields on Corporate Bonds • The IBM bond yield: • Assume annual payments and 10 years to maturity Chapter 15

  35. The Yields on Corporate Bonds • The Lucent bond matures is 5 years and has a yield of: Chapter 15

  36. 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 Chapter 15

  37. The Net Present Value Criterionfor 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 firm information needed to make worthwhile decisions. Chapter 15

  38. The Net Present Value Criterionfor 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. Chapter 15

  39. The Net Present Value Criterionfor Capital Investment Decisions Chapter 15

  40. The Net Present Value Criterionfor 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 Chapter 15

  41. The Net Present Value Criterionfor 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? Chapter 15

  42. The Net Present Value Criterionfor Capital Investment Decisions • Assume all information is certain (no risk) • R = government bond rate • Discount rates below 7.5, NPV is positive • Discount rates above 7.5, NPV is negative Chapter 15

  43. R* = 7.5 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 6 4 Net Present Value ($ millions) 2 0 -2 -4 -6 0 0.05 0.10 0.15 0.20 Interest Rate, R Chapter 15

  44. The Net Present Value Criterionfor Capital Investment Decisions • When determining whether should 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 = 5% Chapter 15

  45. 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 Chapter 15

  46. 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% Chapter 15

  47. 10 8 6 4 Net Present Value ($ millions) 2 0 -2 -4 -6 0 0.10 0.15 0.20 0.04** Interest Rate, R Net Present Value of a Factory If R = 4%, the NPV is positive. The company should invest in the new factory. Chapter 15

  48. The Net Present Value Criterionfor 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. Chapter 15

  49. The Net Present Value Criterionfor Capital Investment Decisions • Electric Motor Factory • Construction time is 1 year • $5 million expenditure today • $5 million expenditure next year • Expected to lose $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 Chapter 15

  50. The Net Present Value Criterionfor Capital Investment Decisions Chapter 15

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