Corporate Financial Management Professor James J. Barkocy There are three kinds of people: the ones that can count and the ones that can t. McGraw-Hill/Irwin Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Net Present Value Net Present Value - Present value of cash flows minus initial investments. Opportunity Cost of Capital - Expected rate of return given up by investing in a project. 2
Net Present Value Example Suppose we can invest $350,000 today and receive $400,000 in one year. What is our increase in value given a 7% expected return? Profit = -350,000 + 400,000 1.07 = $23,832 This is NPV $23,832 $350,000 Added Value Initial Investment 3
Net Present Value NPV = PV - required investment NPV = C 0 C t ( 1 r) t NPV = C 0 C1 C2 Ct... 1 2 ( 1 r) ( 1 r) ( 1 r) t 4
Example Net Present Value You have the opportunity to purchase an office building. You have a tenant lined up that will generate $25,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building? 5
Net Present Value $475,000 $450,000 Example - continued $25,000 $25,000 $25,000 Present Value 23,364 21,836 387,741 $432,942 0 1 2 3 FV=450,000 PMT= 25,000 N=3 I=7 6
Net Present Value Example - continued If the building is being offered for sale at a price of $375,000, would you buy the building and what is the added value generated by your purchase and management of the building? 7
Example - continued Net Present Value If the building is being offered for sale at a price of $375,000, would you buy the building and what is the added value generated by your purchase and management of the building? NPV NPV 25,000 25,000 475,000 = 375,000 1 2 3 (1.07) (1.07) (1.07) = $57,942 8
Net Present Value Net Present Value Rule Managers increase shareholders wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value. 9
Net Present Value Calculating the NPV can be a laborious task. Fortunately, financial calculators can perform this function easily. HP-10B HP-12C -375,000 CFj -375,000 g CF0 25,000 CFj 25,000 g CFj 25,000 CFj 25,000 g CFj 475,000 CFj 475,000 g CFj 7 i 7 i NPV f NPV Both produce NPV=57,941.95 10
The Net Present Value Rule Net Present Value (NPV) = Total PV of future CF s - Initial Investment Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV 11
Investment Timing Example: You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer? Year Cost PV Savings NPV at Purchase NPV Today 0 50 70 20 20.0 1 45 70 25 22.7 2 40 70 30 24.8 3 36 70 34 Date to purchase 25.5 4 33 70 37 25.3 5 31 70 39 24.2 12
Equivalent Annual Annuity (Cost) Equivalent Annual Annuity (Cost) - The payment per period with the same present value as the cash flows. Calculate the NPV of both projects. Use NPV as your present value and find the appropriate annuity payment. 13
Equivalent Annual Cost Example Given the following costs of operating two machines and a 10% cost of capital, select the lower cost machine using equivalent annual cost method. Year Annual 0 1 2 3 4 (N)PV@10% Cost A -500-120 -120-120 -798.42-321.05 B -600-100 -100-100 -100-961.99-289.28 14
Replacement Chain Method 0 1 2 3 4 5 6 7 8 9 10 11 12-500 -120-120 -120-500 -120-120 -120-500 -120-120 -120-500 -120-120 -120-500 -120-120 -620-120 -120-620 -120-120 -620-120 -120-120 NPV @10%= $-2,187.59 0 1 2 3 4 5 6 7 8 9 10 11 12-600 -100-100 -100-100 -600-100 -100-100 -100-600 -100-100 -100-100 -600-100 -100-100 -700-100 -100-100 -700-100 -100-100 -100 NPV @10%= $-1,971.08 15
Other Investment Criteria Internal Rate of Return (IRR) - Discount rate at which NPV = 0. Rate of Return Rule - Invest in any project offering a rate of return that is higher than the opportunity cost of capital. 16
Example Internal Rate of Return You can purchase a building for $375,000. The investment will generate $25,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? 0 = 375,000 25,000 (1 IRR) 1 25,000 (1 IRR) 2 475,000 (1 IRR) 3 IRR = 12.56% 17
Internal Rate of Return Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. HP-10B HP-12C -375,000 CFj -375,000 g CF0 25,000 CFj 25,000 g CFj 25,000 CFj 25,000 g CFj 475,000 CFj 475,000 g CFj {IRR/YR} f IRR Both produce IRR=12.56 18
NPV NPV Payoff Profile If we graph NPV versus discount rate, we can see the IRR as the x-axis intercept. Discount Rate NPV 0% $100.00 4% $71.04 8% $47.32 12% $27.79 16% $11.65 20% -$1.74 24% -$12.88 28% -$22.17 32% -$29.93 36% -$36.43 40% -$41.86 $120.00 $100.00 $80.00 $60.00 $40.00 $20.00 $0.00 -$20.00 -$40.00 -$60.00 9% 19% 29% 39% Discount rate IRR = 19.44% 19
The Internal Rate of Return (IRR) Rule IRR: the discount that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the required return. Ranking Criteria: Select alternative with the highest IRR Disadvantages: Does not distinguish between investing and borrowing. IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments Reinvestment assumption: All future cash flows assumed reinvested at the IRR. Advantages: Easy to understand and communicate 20
NPV Multiple IRRs There are two IRRs for this project: $200 $800 Which one should we use? 0 1 2 3 -$200 - $800 $60.00 $40.00 $20.00 $0.00-50% ($20.00) 0% 50% 100% 150% 200% ($40.00) ($60.00) ($80.00) ($100.00) ($120.00) 0% = IRR 1 100% = IRR 2 Discount rate 21
NPV $5,000.00 The Timing Problem The preferred project in this case depends on the discount rate $4,000.00 $3,000.00 $2,000.00 $1,000.00 $0.00 ($1,000.00) ($2,000.00) ($3,000.00) ($4,000.00) Project A Project B 10.55% = crossover rate 10% 20% 30% 40% 12.94% = IRR B 16.04% = IRR A Discount rate not the IRR. 22
Calculating the Crossover Rate Compute the IRR for either project A-B or B-A Year Project A Project B Project A-B Project B-A 0 ($10,000) ($10,000) $0 $0 1 $10,000 $1,000 $9,000 ($9,000) 2 $1,000 $1,000 $0 $0 3 $1,000 $12,000 ($11,000) $11,000 NPV $3,000.00 $2,000.00 $1,000.00 10.55% = IRR $0.00 ($1,000.00) 0% 5% 10% 15% 20% ($2,000.00) ($3,000.00) Discount rate A-B B-A 23
Example Internal Rate of Return You have two proposals to choice between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer? Project C 0 C 1 C 2 C 3 IRR NPV@7% Initial Proposal -350 400 14.29% $ 23,832 Revised Proposal -375 25 25 475 12.56% $ 57,942 24
The Payback Period Rule How long does it take the project to pay back its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria: set by management Ranking Criteria: set by management 25
Example Payback Method The three projects below are available. The company accepts all projects with a 2 year or less payback period. Show how this will impact our investment decision. Cash Flows Prj. C 0 C 1 C 2 C 3 Payback NPV@10% A -2000 +500 +1000 +10000 2+ +6,794 B -2000 +1000 +1000 0 2-264 C -2000 0 +2000 0 2-347 26
Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. Soft Rationing - Limits on available funds imposed by management. Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market. 27
Profitability Index Profitability Project PV Investment NPV Index L 4 3 1 1/3 =.33 M 6 5 1 1/5 =.20 N 10 7 3 3/7 =.43 O 8 6 2 2/6 =.33 P 5 4 1 1/4 =.25 28