How To Calculate Present Values Principles of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Lu Yurong Chapter 3 McGraw Hill/Irwin

3- 2 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Topics Covered  Valuing Long-Lived Assets  PV Calculation Short Cuts  Compound Interest  Nominal and Real Rates of Interest (inflation)  Example: Present Values and Bonds

3- 3 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values Discount Factor = DF = PV of $1  Discount Factors can be used to compute the present value of any cash flow.

3- 4 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values  Discount Factors can be used to compute the present value of any cash flow.

3- 5 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values  Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time

3- 6 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values Example You just bought a new computer for $3,000. The payment terms are 2 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?

3- 7 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values Example You just bought a new computer for $3,000. The payment terms are 2 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?

3- 8 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values  PVs can be added together to evaluate multiple cash flows.

3- 9 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved 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 r 1 = 20% and r 2 = 7%.

3- 10 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved 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 r 1 = 20% and r 2 = 7%.

3- 11 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values 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 value.

3- 12 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Present Values Example - 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 value.

3- 13 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Short Cuts  Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tolls allow us to cut through the calculations quickly.

3- 14 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever.

3- 15 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever.

3- 16 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years.

3- 17 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years.

3- 18 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Annuity Short Cut Example You agree to lease a car for 4 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?

3- 19 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Annuity Short Cut Example - continued You agree to lease a car for 4 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?

3- 20 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Compound Interest i ii iii iv v Periods Interest Value Annually per per APR after compounded year period (i x ii) one year interest rate 1 6% 6% % = = = = =

3- 21 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Compound Interest

3- 22 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Compound Interest

3- 23 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Compound Interest Example Suppose you are offered an automobile loan at an APR of 6% per year. What does that mean, and what is the true rate of interest, given monthly payments?

3- 24 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Compound Interest Example - continued Suppose you are offered an automobile loan at an APR of 6% per year. What does that mean, and what is the true rate of interest, given monthly payments? Assume $10,000 loan amount.

3- 25 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved 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.

3- 26 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Inflation approximation formula

3- 27 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved 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

3- 28 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Valuing a Bond Example If today is October 2002, what is the value of the following bond?  An IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an additional $1000 and retires the bond.  The bond is rated AAA (WSJ AAA YTM is 7.5%) Cash Flows Sept

3- 29 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Valuing a Bond Example continued If today is October 2002, what is the value of the following bond?  An IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an additional $1000 and retires the bond.  The bond is rated AAA (WSJ AAA YTM is 7.5%)

3- 30 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Bond Prices and Yields Yield Price

3- 31 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Summary  Present value formula  Perpetuity  Annuity  Compound and simple interest rate  Nominal and real rate of interest  Bond valuing

3- 32 McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved Preparation for Next Class  Please read:  BM Chapter4, P61-91  Questions:  How to value common stocks?  How to estimate the capitalization rate?  What is the earnings per share and E-P ratio?