Principles of Corporate Finance Brealey and Myers Sixth Edition How to Calculate Present Values Slides by Matthew Will Irwin/McGraw Hill Chapter ©The McGraw-Hill Companies, Inc., 200 3- Topics Covered Valuing Long-Lived Assets PV Calculation Short Cuts Compound Interest Interest Rates and Inflation Example: Present Values and Bonds Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Discount Factor = DF = PV of $1 DF t (1r ) Discount Factors can be used to compute the present value of any cash flow Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values C1 PV DF C1 r1 DF (11r ) t Discount Factors can be used to compute the present value of any cash flow Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Ct PV DF Ct rt Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Example You just bought a new computer for $3,000 The payment terms are years same as cash If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years? Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Example You just bought a new computer for $3,000 The payment terms are years same as cash If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years? PV Irwin/McGraw Hill 3000 (1.08 ) $2,572.02 ©The McGraw-Hill Companies, Inc., 200 3- Present Values PVs can be added together to evaluate multiple cash flows C1 C2 PV (1r )1 (1r ) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 10 Present Values Given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor Assume r1 = 20% and r2 = 7% Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 16 Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever cash flow PV of Cash Flow discount rate C1 PV r Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 17 Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years 1 PV of annuity C t r r 1 r Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 18 Annuity Short Cut Example You agree to lease a car for years at $300 per month You are not required to pay any money up front or at the end of your agreement If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 19 Annuity Short Cut Example - continued You agree to lease a car for years at $300 per month You are not required to pay any money up front or at the end of your agreement If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? Lease Cost 300 48 005 0051 005 Cost $12,774.10 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 20 Compound Interest i ii Periods Interest per per year period iii APR (i x ii) iv Value after one year v Annually compounded interest rate 6% 6% 1.06 1.032 = 1.0609 6.090 1.5 1.0154 = 1.06136 6.136 12 1.00512 = 1.06168 6.168 52 1154 1.00115452 = 1.06180 6.180 365 0164 1.000164365 = 1.06183 6.183 Irwin/McGraw Hill 6.000% ©The McGraw-Hill Companies, Inc., 200 3- 21 FV of $1 Compound Interest 18 16 14 12 10 10% Simple 10% Compound Number of Years Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 22 Inflation Inflation - Rate at which prices as a whole are increasing Nominal Interest Rate - Rate at which money invested grows Real Interest Rate - Rate at which the purchasing power of an investment increases Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 23 Inflation 1+nominal interest rate real interest rate = 1+inflation rate Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 24 Inflation 1+nominal interest rate real interest rate = 1+inflation rate approximation formula Real int rate nominal int rate - inflation rate Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 25 Inflation Example If the interest rate on one year govt bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? Savings Bond Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 26 Inflation Example If the interest rate on one year govt bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? 1+.059 + real interest rate = 1+.033 Savings + real interest rate = real interest rate Irwin/McGraw Hill = 1.025 Bond 025 or 2.5% ©The McGraw-Hill Companies, Inc., 200 3- 27 Inflation Example If the interest rate on one year govt bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? 1+.059 + real interest rate = 1+.033 Savings + real interest rate = real interest rate = 1.025 Bond 025 or 2.5% Approximation =.059-.033 =.026 or 2.6% Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 28 Valuing a Bond Example If today is October 2000, what is the value of the following bond? An IBM Bond pays $115 every Sept for years In Sept 2005 it pays an additional $1000 and retires the bond The bond is rated AAA (WSJ AAA YTM is 7.5%) Cash Flows Sept 01 02 03 04 05 115 115 115 115 1115 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 29 Valuing a Bond Example continued If today is October 2000, what is the value of the following bond? An IBM Bond pays $115 every Sept for years In Sept 2005 it pays an additional $1000 and retires the bond The bond is rated AAA (WSJ AAA YTM is 7.5%) 115 115 115 115 1,115 PV 1.075 1.075 1.075 1.075 1.0755 $1,161.84 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- 30 Bond Prices and Yields 1600 1400 Price 1200 1000 800 600 400 200 0 Year 9% Bond Irwin/McGraw Hill 10 12 14 Yield Year 9% Bond ©The McGraw-Hill Companies, Inc., 200 ... = PV of $1 Discount Factors can be used to compute the present value of any cash flow Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 3- Present Values Discount Factor = DF = PV of $1... Example Assume that the cash flows from the construction and sale of an office building is as follows Given a 7% required rate of return, create a present value worksheet and show the net present... continued Assume that the cash flows from the construction and sale of an office building is as follows Given a 7% required rate of return, create a present value worksheet and show the net present