1 VALUE AND CAPITAL BUDGETING # NET PRESENT VALUE –We need to know the relationship between a dollar today and a (possibly uncertainty) dollar in the future before deciding on the project. This relationship is called the time value-of-money concept. 1.The One Periode Case Example: Don Simkowitz is trying to sell a piece of raw land in Alaska. Yesterday, he was offered $ for the property. He was about ready to accept the offer when another individual offered him $11,424. However, the second offer was to be paid a year from now. Which offer should Mr. Simkowitz choose? (interest rate of 12 percent in the bank) $10,000 + (0.12 x $10,000) = $11,200 (This analysis uses the concept of future value or compound value)

2 The formula for PV can be written as PV = C1/(1+r) The formula for NPV can be written as NPV = -Cost + PV 2.The Multiperiod Case Future Value of an Investment: FV = C O x (1+r) T Present Value of an Investment: PV = C T / (1+r) T an alternative method employs the concept of Present Value. PV = $11,424/1.12 = $10,200

3 Example 1: Suh-Pyng Ku put $500 in a savings account at the First National Bank of Kent. The account earns 7 percent, compounded annually. How much will Ms. Ku have at the end of three years? FV = $500 x (1.07) 3 = $ The table A.3 presents Future values of $1 at the end of t periods. Example 2: Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his investments, and so the appropriate discount rate is 8 percent. What is the present value of his future cash flow? PV = $10,000 / = $7,938 The table A.1 presents Present values of $1 to be received after t periods.

4 Example 3: Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The computer will generate cash flows (from costs savings). Of $25,000 one year from now, $20,000 two years from now, and $15,000 three years from now. The computer will be worthless after three years, and no additional cash flows will occur. Finance.com has determined that the appropriate discount rate is 7 percent for this investment. Should Finance.com make this investment in a new high-speed computer? What is the present value of the investment? Simplifications for four classes of cash flow stream: 1.A perpetuity as a constant stream of cash flows without end. PV = C/(1+r) + C/(1+r) 2 + C/(1+r) PV =C/r 2.Growing Perpetuity Formula for PV of Growing Perpetuity PV = C / (r - g)

5 COMPOUNDING PERIODS Imagine that a bank pays a 10 percent interest rate “compounded semiannually. Co(1 + r/m) m Example : What is the end-of-year wealth if Jane receives a stated annual interest rate of 24 percent compounded monthly on a $1 investment? $1( /12) 12 = $ The annual rate of return (effective annual interest rate or the effective annual yield) is percent. Effective Annual Interest Rate : (1 + r/m) m - 1

6 continue Compounding over many years: FV = Co(1 + r/m) mt Example: Harry De Angelo is investing $5,000 at a stated annual interest rate of 12 percent per year, compounded quarterly, for five years. What is his wealth at the end of five years? $5,000( /4) 4x5 = $9, Continuous compounding (Advanced) : C o xe rT Example: Linda invested $1,000 at a continuously compounded rate of 10 percent for two years. $1,000 x e 0.10x2 = $1,221.

7 3.Annuity Formula for PV of Annuity: PV = C[1/r – {1/r(1+r) T }] 4.Growing Annuity Formula for PV of Growing Annuity: PV = C[1/(r-g) - 1/(r-g) x {(1+g)/(1+r)} T ] Example: Cash flow after expenses will be $100,000 next year. These cash flow are expected to rise at 5 percent per year. The relevant interest rate is 11 percent. So, PV of Growing Perpetuity = $100,000/(0.11 – 0.05) =$1,666,666.67

8 continue Example: Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value of the consol? PV = $100/0.08 = $1,250 Δ Example: Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000 = $50,000 x 20. If the interest rate is 8 percent, what is the true value of the lottery? PV = $50,000 x [1/0.08 – {1/0.08.(1.08) 20 }]

9 continue Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates salary increasing by 9 percent a year until his retirement in 40 years. Given interest rate of 20 percent, what is the present value of his lifetime salary? PV = $80,000 x [{1/( )} – 1/( ) {1.09/1.20} 40 ]= $711,731 Δ A Firm that is expected to generate net cash flow of $5,000 in the first year and $2,000 for each of the next five years. The firm can be sold for $10,000 seven years from now. NPV

10 SOME ALTERNATIVE INVESTMENT RULES 1.The Payback Period Rule : is the number of years required for a firm to recover its initial investment required by a project from the cash flow it generates. Consider a project with an initial investment of -$50,000. Cash flows are $30,000, $20,000 and $10,000 in the first three years, respectively. (-$50,000, $30,000, $20,000, $10,000) in this case two years is the payback period of the investment Problems with the Payback Method 1.Not consider the Timing of cash flow within the Payback Period. The NPV approach discounts the cash flows properly. 2.It ignores all cash flows occuring after the payback period. The NPV approach uses all cash flows of the project. 3.There is no comparable guide for choosing the payback period, so the choice is arbitrary to some extent

11 Table A. Epecteed Cash Flows to Projects A through C ($) YearABC Payback Period (years) , The Discounted Payback Period Rule Under this approach, we first discount the cash flows. Then, how long it takes for the discounted cash flows to equal the initial investment. For example, suppose that the discount rate is 10 percent, then, the cash flows look like: [-$100,$50/1.1,$50/(1.1) 2,$20/(1.1) 3 ] = (-$100.$45.45,$41.32,$15.03) $ ($45.45,$41.32,$15.03) is slightly less than three years. As long as the cash flows are positive, the discounted payback period will never be smaller than the payback period.

12 3.The Average Accounting Return The Average Accounting Return is the average project earnings after taxes and depreciation, divided by the average book value of the investment during its life. Example: Consider a company that is evaluating whether or not to buy a store in a newly built mall. The purchase price is $500,000. We will assume that the store has an estimated life of five years and will need to be completely scrapped or rebuilt at the end of that time.

13 Table B. Projected Yearly Revenue and Costs for Average Accounting Return Year 1Year 2Year 3Year 4Year 5 Revenue Expenses Before-tax Cash Flow Depreciation Earnings Before taxes Taxes (Tc) Net Income $100,000$150,000$50,000$0-$50,000 Average net income = ($100, , , – 50,000)/5 = $50,000 Average investment = ($500, , , , , ) / 6 = $250,000 AAR = $50,000/$250,000 = 20%

14 4.The Internal Rate of Return (IRR) A discount rate at which the net present value of an investment is zero. The IRR is a method of evaluating capital expenditure proposals. Example, consider the simple project (-$100,$110). For a given rate, the NPV of this project can be describe as NPV = -$100 + [$110/(1+r)] Accept the project if IRR is greater than the discount rate. Reject the project if IRR is less than the discounted rate.

15 5.The profitability Index (PI) A method used to evaluate projects. PI = PV of cash flow subsequent to initial investment / Initial Investment. Example: Hiram Finnegan Inc., applies a 12 percent discount rate to two investment opportunities. Cash Flows ($000,000) of CF S to I Invest ($000,000) ($000,000) ProjectC0C1C2PI

16 INFLATION AND CAPITAL BUDGETING Inflation is an important fact of economic life, and it must be considered in capital budgeting. Figure A. Calculation of Real Rate of Interest Date 0 Individual invests $1,000 in bank (Because hamburgers sell for $1 at date 0, $1,000 would have purchased 1,000 hambs) Interest rate Date 1 Individual receives $1,100 from bank Inflation rate has been 6% over year Because each humbur sells for $1.06 at date 1 1,038 (=1,100/1.06) hamburgers can be purchased. 3,8 % 10 % Interest Rates and Inflation

17 Hamburgers is used as illustrative good. 1,038 hamburgers can be purchased on date 1 instead 1,000 hamburgers at date 0. Real interest rate = 1.038/1,000 – 1 = 3.8% Real interest rate = [(1 + Nominal interest rate)/(1 + Inflation rate)] – 1 Example : Altshuler, Inc., used the following data for a capital budgeting project: Year012 Capital expenditure Revenues (in real terms) Cash expenses (in real terms) Depreciation (straight line) $1,210 $1, $2,000 1, Real interest rate Nominal interestrate – inflation rate (approximately true)

18 The president, David Altshuler, estimates inflation to be 10 percent per year over the next years. In addition, he believes that the cash flows of the project should be discounted at the nominal rate of 15.5 percent. His firm’s tax rate is 40 percent Mr. Altshuler forecasts all cash flows in nominal terms. Thus, he genarate the following spreadsheet: Year012 Capital Expenditure Revenues - Expenses - Depreciation Taxable income - Taxes (40%) Income after taxes + Depreciation Cash flow -$1,210 $2,090(=1,900x1.10) -1,045(=950x1.10) -605 (1.210/2) $2,420(=2,000x(1.10) 2 ) -1,210(=1,000x(1.10) 2 ) NPV = -$1,210 + ($869/1.155) + $968/(1.155) 2 = $268

19 Mr. Altshuler’s sidekick, Struar Weiss, prefers working in real terms. He first calculates the real rate to be 5 percent = [(1.155/1.10) – 1]. Next, he generates the following spreadsheet in real quantities: Year012 Capital Expenditure Revenues - Expenses - Depreciation Taxable income - Taxes (40%) Income after taxes + Depreciation Cash flow -$1,210 1, (605/1.1) $2,000 -1, (=605/1.1 2 ) NPV = -$1,210 + ($790/1.05) + $800/(1.05) 2 = $268