1 / 52

Chapter 4

Chapter 4. Foundations of Valuation: Time Value. Shapiro and Balbirer: Modern Corporate Finance: A Multidisciplinary Approach to Value Creation Graphics by Peeradej Supmonchai. Learning Objectives.

skah
Download Presentation

Chapter 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 4 Foundations of Valuation: Time Value Shapiro and Balbirer: Modern Corporate Finance: A Multidisciplinary Approach to Value Creation Graphics by Peeradej Supmonchai

  2. Learning Objectives • Explain why money has time value and the importance of the interest rate in the valuation process. • Use the concepts of compound interest to determine the future value of both individual amounts as well as streams of payments. • Use discounting to determine the present value of both individual amounts as well as streams of payments.

  3. Learning Objectives (Cont.) • Explain how the concept of present value can be used to value assets ranging from plant and equipment to marketable securities. • Understand the difference between the stated and annual percentage rate (APR), and how this difference influences the present and future values of a stream of payments. • Understand the concept of an investment’s net present value (NPV) and how it relates to the building of shareholder value.

  4. Time Value of Money The time value of money is based on the simple idea that a dollar today is worth more than a dollar tomorrow. How much more depends on time preferences of individuals for consumption of goods and services, the rates of return that can be earned on available investments, and the expected rate of inflation.

  5. Future Value Formula FV = PV [(1+ k)n] Where: k = the periodic interest rate n = the number of periods

  6. Future Value of $1,000 Investment ACCOUNT BALANCES FOR $1,000 INVESTMENT FIVE YEARS AT 6 PERCENT INTEREST BEGINNING INTEREST EARNED ENDING YEAR BALANCE DURING YEAR BALANCE 1 $1,000.00 $60.00 $1,060.00 2 1,060.00 63.60 1,123.60 3 1,123.60 67.42 1,191.02 4 1,191.02 71.46 1,262.48 5 1,262.48 75.75 1,338.23

  7. Future Value Interest Factor Future Value Interest Factor = [(1+ k)n] Where: k = the periodic interest rate n = the number of period

  8. Determinates of Future Value • Amount Invested • Interest Rate • Number of Compounding Periods

  9. Future Value of $1 r=10% Future Value r=5% r=3% r=1% Period

  10. Frequency of Compounding The future value in n years, when interest is paid m times a year is: F n,m = PV [ (1+k/m)nxm] Where: k = the annual interest rate

  11. Frequency of Compounding - An Example Suppose you invested $1,000 for five years at a six percent interest rate. If interest were compounded semi-annually, the future value would be: Fn,m = $1,000[1+(0.06/2)]5x2 = $1,000[1.3439] = $1,343.90

  12. Annual Percentage Rate (APR) APR = FVIF k/m,m - 1 = [1+(k/m)m - 1]

  13. Annual Percentage Rate - An Example Suppose a U.S. corporate bond paying interest semiannually has a quoted rate of 9 percent. Its APR is: APR = [ (1.045)2] -1 = 9.2 percent

  14. Financial Calculator Keystrokes N or n = the number of periods interest is compounded I or I/Y = the periodic interest rate FV = the future value of a current or present amount PV = the current or present value of a future amount PMT = the periodic payment or receipt. Used when dealing with a stream payments which are the same in each period. CPT = the “compute” button. Some calculators require that you hit this key prior to running a calculation.

  15. Inputs 5 6 1,000 N I PV PMT FV Answer: 1,338.23 Financial Calculator Solutions -An Example Future value of $1,000 earning 6 percent for 5 years

  16. Present Value Formula FV PV = ¾¾¾ (1+ k)n Where: k = the discount rate n = the number of years

  17. Present Value - An Example Suppose you have the opportunity to buy a piece of land for $10,000 today, and sell it in eight years for $20,000. Is this a “good deal” if you can put your money in a risk-equivalent that is expected to earn 10 percent a year compounded annually?

  18. Present Value - An Example The present value of the $20,000 you expect to receive at the end of eight years is: PV = $20,000 [ 1/(1.10)8] = $9330.15 This is a “bad deal” since the present value of return in eight years is less than the cost of the land.

  19. Inputs 8 10 20,000 N I FV PMT PV Answer: 9,330.15 Calculator Solution

  20. Present Value Interest Factor (PVIF) 1 PVIF = ¾¾¾ (1+ k)n Where: k = the discount rate n = the number of years

  21. Valuing a Zero-Coupon Bond Suppose that a zero-coupon bond matures in 20 years at a face value of $10,000. If an investor’s opportunity cost of money is 8 percent, the value of the bond would be: PV = FV(PVIF8,20) = $10,000(0.2145) = $2,145.00

  22. Inputs 20 8 10,000 N I FV PMT PV Answer: 2,145.48 Valuing a Zero-Coupon Bond - Calculator Solution

  23. Present Value of $1 Present Value Period

  24. The Discounting Period When interest is compounded more than once a year, the present value is: 1 PV = FV ¾¾¾¾¾¾ (1+ k/m)nxm Where: k = the discount rate n = the number of years m = the number of times that interest is paid a year

  25. The Discount Period - An Example If you can earn 8 percent, compounded semiannually, the value of a zero-coupon bond maturing in 20 years at a face amount of $10,000 would be PV = FV(PVIF4,40) = $10,000(0.2083) = $2,083.00

  26. Present Value of a Constant Perpetuity CF PV = ¾¾¾ k Where: CF = Cash Flow per Period k = Opportunity Cost of Money

  27. Present Value of a Constant Perpetuity - An Example Suppose a console pays £50 a year, and the investor’s opportunity cost of money is 10 percent. The price of the console is: £50 Price = ¾¾ 0.10 = £ 500

  28. Present Value of a Growing Perpetuity CF PV = ¾¾¾ (k - g) Where: CF = Cash Flow per Period k = Opportunity Cost of Money g = Growth Rate per Period

  29. Present Value of a Growing Perpetuity - An Example A firm’s cash flows are estimated to be $200,000 next year and are expected to grow at a five percent annual rate of return indefinitely. If the appropriate discount rate is 10 percent, the value of the firm is: $200,000 Value = ¾¾¾¾¾ (0.10 - 0.05) = $4,000,000

  30. Annuities An annuity is a series of equal cash flows per period for a specified number of periods. There are two basic kinds of annuities: • Annuity Due • Deferred Annuity

  31. Present Value of Annuity (PVA) Present Value Present Value Present Value PVAn = of Payment + of Payment + ·· + of Payment in Period 1 in Period 2 in Period n = PMT(PVIFk,1) + PMT(PVIFk,2) + ··+ PMT(PVIFk,n)

  32. Present Value Interest Factorof an Annuity (PVIFA) (1+ k)n- 1 PVIFA n,m = ¾¾¾¾¾ k(1+ k)n Where: k = the discount rate n = the number of years

  33. Present Value of an Annuity - An Example Suppose you are negotiating with a supplier to buy a piece of equipment that will reduce production costs. The after-tax savings are expected to be $50,000 a year for the next six years. How much is the equipment worth if your company’s opportunity cost of capital is 10 percent?

  34. Present Value of an Annuity - Solution PV = PMT (PVIFA 6,10) = $50,000 (4.35526) = $217,763

  35. Installment Payments on a Loan Suppose a small business borrows $200,000 from a bank at an interest rate of 12 percent compounded annually. The loan, including interest, is to be repaid in equal installments starting next year. The annual payments would be: $200,000 $200,000 PMT = ¾¾¾¾¾ = ¾¾¾¾¾ PVIFA 12,3 2.4018 = $83,269.80

  36. LOAN AMORTIZATION SCHEDULE $200,000 LOAN @ 12 PERCENT INTEREST Interest Principal Year-End Year Payment Portion Repayment Balance 1 $83, 269.80 $24,000.00 $59,269.80 $140,730.20 2 83,269.80 16,887.62 66,383.20 74,348.00 3 83,269.80 8,921.76 74,348.04 ( 0.04 )

  37. Future Value of an Annuity (FVA) Future Value Future Value Future Value Future Value FVAn = of Payment + of Payment + · + of Payment of Payment in Period 1 in Period 2 in Period n - 1 in Period n FVAn = PMT(1+k)n–1 + PMT(1+k)n–2 + ·· + PMT(1+k)1 + PMT

  38. Future Value of an Annuity - An Example Suppose you were to receive $1,000 a year for three years, and then deposit each receipt in an account paying 8 percent interest, compounded annually. How much would you have at the end of three years?

  39. Future Value of an Annuity - Solution CALCULATING THE FUTURE VALUE OF A 3-YEAR ANNUITY PeriodCash FlowFuture Value 1 $1,000 x (1.08)2 = $1,166.40 2 1,000 x (1.08)1 = 1,080.00 3 1,000 x (1.08) = 1,000.00 $3,246.40

  40. Future Value Interest Factor for an Annuity (FVIFA) (1+k)n- 1 FVIFAk,n = ¾¾¾¾¾ k Where: k = the discount rate n = the number of years

  41. The Annuity Period FVAnm = PMT [FVIFAk/m, nm] PVAnm = PMT [PVIFAk/m, nm]

  42. Valuing Social Security Suppose you’re 25 years old and have just graduated with an engineering degree. You begin work for a company under a lifetime contract where your salary would remain unchanged at $30,000 a year until retirement in 40 years. Suppose that Social Security has been privatized, so that your 6.2 percent payment, plus the employers’ matching contribution can be put into a personal retirement account. With a salary of $30,000 a year, this means that $310 a month for 480 months will be put in an account earning 6 percent. You can also continue with the existing Social Security program, in which case $310/month would be sent to the government and credited to your account.

  43. Value of the Private Retirement Account FVA = PMT[FVIFA0.50,480 ] = $310 [1,991.49] = $617,362.13

  44. VALUE OF $1,232 A MONTH SOCIAL SECURITY PAYMENT Life Expectancy Present Value of Beyond Age 65 Social Security Benefits Years (Months) Discounted @0.5 Percent 5 (60) $ 63,725.89 10 (120) 110,970.50 15 (180) 145,996.33 20 (240) 171,963.51 25 (300) 191,214.85 30 (360) 205,487.27 40 (480) 223,913.02

  45. Present Value of Uneven Cash Flow Stream - Equipment Problem Revisited After-Tax Year Cash Flow X PVIF@10% = Present Value 1 $50,000 0.9091 $45,455.00 2 48,000 0.8264 39,667.20 3 45,000 0.7513 33,808.50 4 40,000 0.6830 27,320.00 5 35,000 0.6209 21,731.50 6 40,000* 0.5645 22,580.00 Total Present Value = $190,562.20 * Includes an estimated $10,000 salvage value

  46. Present Value of Uneven Cash Flow Streams - Valuing John Smoltz’s Contract Year Payment X PVIF@8% = Present Value 1997 $7,000,000 0.9259 $6,481,481 1998 7,750,000 0.8573 6,644,376 1999 7,750,000 0.7938 6,152,200 2000 8,500,000 0.7350 6,247,754 Total Contract Value = $25,525,811

  47. Net Present Value (NPV) • The difference between the present value of an investment’s cash flows and its cost. • Measures how much better off we’ d be by taking on the investment. If the discount rate used in calculating present values represents the stockholders opportunity cost of money, taking on positive NPV projects will create shareholder value.

  48. Determinants of the Opportunity Cost of Money • Risk • Inflation • Taxes • Maturity

  49. Risk • Default Risk • Price, or Variability Risk • Type of Claim

  50. Expected Inflation - The Fisher Effect r = a + i + ai Where: r = the nominal interest rate a = the real or inflation-adjusted interest rate i = the expected rate of inflation

More Related