PV of Cash Flows Initial Investment

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1 The Basics of Capital Budgeting: Evaluating Cash Flows Topics to be covered 1. Net Present Value (NPV) 2. Internal Rate of Return (IRR) 3. Payback Period 4. Book Rate of Return 5. Profitability Index (PI) 6. Project Interactions -(6.1) Investment Timing -(6.2) Long-Lived versus Short-Lived Equipment (EAC) -(6.3) Replacing an old machine Firm possesses a huge number of investments. These investments are options available to the firms. Some are valuable and some are not. The successful financial manager should be able to identify which one is valuable and which one is not. Capital Budgeting Decision: is the process of choosing investment projects. Capital Investment project: Any expenditure made in hope of generating more cash later, regardless of whether cash outlay goes to tangible or intangible assets (e.g. R & D for medicines, design & testing for cars, laying of pipeline to carry oils) Net Present Value (NPV) is the difference between an investment s market value and its cost. It is a measure of how much value is created or added today by undertaking an investment. So, the basic idea is to undertake the project that has a positive NPV since it creates the value for its owners or shareholders. NPV = PV of Cash Flows Initial Investment Opportunity Cost of Capital is the expected rate of return given up by investing in a project. Discounting should be done by taking the opportunity cost equal to that of similar risk projects. Example 1: You buy a house for $25,000 and spend another $25,000 for fixing and painting. When the work is completed, you place the house in the market and find that it is worth $60,000. What is the value created or added? Profit = -50,000+60,000 = $10,000 Example 2: Using the same example, suppose a year later you place the house in the market and it is worth 60,000. What is our increase in value given a 10% expected return? Profit = -50, ,000/(1.10) = $4, n 1. NPV = C 0 + C t /(1+r) t t =1 2. NPV = C 0 + C 1 /(1+r) 1 + C 2 /(1+r) 2 + C t /(1+r) t Where C t = Cashflow at time t t = Time period of investment r = Opportunity Cost of Capital (Discount Rate) 1

2 Two types of Project 1. Non-mutually exclusive project: Two or more projects that can be pursued simultaneously. 2. Mutually exclusive project: Two or more projects that cannot be pursued simultaneously. NPV Decision Rule for non-mutually exclusive project. NPV > 0 (Positive NPV) Accept the project NPV < 0 (Negative NPV) Reject the project Managers increase shareholders wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all the projects with a positive NPV. NPV Decision Rule for mutually exclusive projects When you have to choose between mutually exclusive projects, first calculate the NPV of each project, from those options that have a positive NPV, choose the one whose NPV is highest. NPV Process 1. Forecast the project cash flow (C t ) 2. Estimate the opportunity cost of capital (r) 3. Calculate the PV of future cash flows discounted at the opportunity cost of capital 4. NPV = PV of future CF Cost 5. NPV decision rule Example 3: You have an opportunity to buy an office building. You have a tenant lined up that will generate $16,000 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 if the discount rate is 7%? T=0 t=1 t=2 t=3 Price =? 16,000 16,000 16, ,000 Price = 16000/ /(1.07) /(1.07) /(1.07) 3 = = Example 4: If the building in example 3 is being offered for sale at a price of $350,000, would you buy the building and what is the value added if the discount rate is 7%? Value added = = $

3 Example 5: You are considering two investments A and B. T=0 (Today) T=1 T=2 T=3 T=4 Project A -50,000 22,000 22,000 22,000 Project B -50,000 18,000 18,000 18,000 18,000 1) Assume that the discount rate is 9%, what is the NPV of project A and B? (5,688.48, 8,314.95) For Project A: CF0= C01=22000 F01=3 then Press NPV and put I=9 Press CPT to get NPVA=$ For Project B: CF0= C01=18000 F01=4 then Press NPV and put I=9 Press CPT to get NPVB= ) According to NPV rule, which project would you accept if they are not mutually exclusive and why? Both projects as NPV of both is positive 3) Which project would you accept if they are mutually exclusive projects and why? Project B as its NPV is higher than the NPV of Project B Note: A risky dollar is worth less than a safe one! The expected rate of return which is used to discount the expected payoffs depends on the risk of the project. NPV calculations are only as good as the underlying cash-flow forecasts. II Internal Rate of Return (IRR) Deciding whether the projects return>the opportunity cost of capital. IRR is the discount rate at which NPV equals zero. In other words, IRR is the discount rate that will produce present value equal to the cost of the project. NPV = -C 0 +C 1 /(1+IRR) 1 + C 2 /(1+IRR) = -C 0 +C 1 /(1+IRR) 1 + C 2 /(1+IRR) 2 + It implies that C 0 = C 1 /(1+IRR) 1 + C 2 /(1+IRR) 2 + Cost = PV of cash flows NPV IRR Discount rate 3

4 Example 6: You invest $ now and receive $ one year later. Calculate the rate of return. If the opportunity cost of capital were 15%, would you pursue the project? ROR = Profit/ Investment = 20000/ = 20% Example 7: You invest $ now and get a payment of $16,000 for the next three years. At the end of three years you get back $450000, Calculate the IRR. NPV = /(1+r) /(1+r) /(1+r) 3 = 0 Trial and Error Try with r = 15% NPV is positive With r= 10 % NPV is negative R should lie in between %! IRR decision rule: invest in any project offering a rate of return higher than the opportunity cost of capital (or discount rate). IRR > discount rate => NPV > 0 Accept the project IRR < discount rate => NPV < 0 Reject the project 1) Do not confuse IRR with the opportunity cost of capital (discount rate). IRR is the rate of Return on the cash flows of the investment. 2) The opportunity rate of return is an estimate of the minimum acceptable rate of return demanded by an investor on similar risk investments. *** Both IRR and NPV rules consider the timing of cash flows and the opportunity rate of return of shareholders. Hence, they are preferred investment criteria decision. Both IRR and NPV give same answers as long as the NPV of project declines smoothly with the rise in discount rate. However, NPV is a preferred criterion over IRR because 1) Multiple IRRs For a project, which has cash flow that alternates in sign, there is a multiple IRRs For example, IRR for project is 12% and 22%, while the discount rate is 15%. It provides the misleading result because the first IRR < discount rate Reject the project The second IRR > discount rate Accept the project. Example 8: C0 C1 C2 C3 C4 C NPV = 0 = /(1+r) + 15/(1+r) /(1+r) 5 NPV =0 for R=6% and 28% Example 9: C0 C1 C2-10, NPV=0 for R=2% and 4% There are as many different IRRs as the changes in cash flow signs. When there are multiple changes in the sign of cash flows, the IRR rule doesn t work. Apply NPV rule. 4

5 2) Lending vs. Borrowing Lending T=0 C IRR = 50% NPV at 6% is $41.51 Borrowing T=0 C IRR = 50% NPV at 6% is -$41.51 In this case, if you are lending money, you prefer higher IRR. If you are borrowing money, you prefer lower IRR. When NPV rises as the interest rate rises, the rate of return rule is reversed. 3) Mutually exclusive projects: Given a choice choose the project that adds maximum value to the shareholder s wealth. C0 C1 C2 C3 C4 Project A Project B Calculate the IRR for the above two projects and decide which project you would choose if the opportunity cost of capital is 6%. What happens if the cost of capital rises to 18%? Using BA II plus Project A C0 = -200 C1 = 150 F1 =1 C2 = 150 F2=1 Compute IRR to get Project B C0=-200 C1=90 F1=1 C2=90 F2=1 C3=90 F3=1 C4=90 F4=1 Compute IRR to get If we choose the project with greater IRR we choose Project A But NPV of A at 6% = NPV of B at 6% = So in this example IRR gives us an incorrect decision for mutually exclusive project. Hence we use NPV rule for mutually exclusive projects 5

6 Example 10: Using the information from Example 5 1) What are the IRRs of project A and project B? (15.28%, 16.37%) For Project A: CF0= C01=22000 F01=3 then Press IRR button and Press CPT to get IRR=15.28% For Project B: CF0= C01=18000 F01=4 then Press IRR button and Press CPT to get IRR=16.37% 2) According to IRR rule, which project would you accept if the discount rate is 9%. And Why? Accept both projects as the IRR for both is greater than 9%. NPV Profile Project A NPV NPV Profile Project B NPV 8, ,688 IRR A IRR B 15.28% 16.37% 0 Discount Rate (%) 9% 9% Example 11 Crossover point or crossover rate is the discount rate at which NPV of two projects are equal. NPV 14% 19% 0 Discount Rate (%) Project 2 16% Project 1 1) What are the IRRs of project 1 and project 2? IRR 1 = 16% IRR 2 = 19% 2) What is the crossover rate and what does it represent? Cross over rate = 14% 3) If the discount rate is 18%, which project would you accept according to IRR rule? Why? Project 2 4) If the discount rate is 20%, according to IRR rule, would you accept any project? If not, why? No project is accepted 5) Label in the graph what are the NPVs of project 1 and 2, if the discount rate is 0%? 6

7 III Modified IRR: The MIRR is similar to IRR except it is based on assumption that cash flows are reinvested at the WACC or some other reasonable rate. Ex: Calculate the MIRR for Project A and Project B in example Solution: Project A 26, K 22K 22K 23,980-50K = FV = PV= -50 K Payment=0 N=4 I/Y=11.98 % 23, Project B: 21, ,620 18K 18K 18K 18K -50K FV=82, PV= -50K Payment=0 N=4 I/Y=13.27% IV Payback Period: The time until cash flows recovers the initial investment of the project. Example 12: Using information from example 5, what are the payback periods for project A and project B? Project A: 2 Years + 6,000/22,000 = 2.27 years Project B: 2 Years + 14,000/18,000 = 2.78 years Decision Rule: The investment should proceed if the payback period is less than the specified cutoff period. ** While cash flows are considered, the timing of cash flows and cash flows beyond the payback period are not considered. The payback ignores the risk of project cash flows and opportunity rate of return of investors. 7

8 V. Profitability Index: = Net Present Value Investment If you are subject to capital rationing, then you are required to select projects subject to a budget constraint. You must first rank the project according to the profitability index and accept the project, with the highest PI so as to maximize the firm value. Capital rationing: Limit set on the amount of funds available for investments. Soft rationing: When capital rationing is imposed by management Hard rationing: Firm actually can t raise the money it needs. Example 13: Using information from example 5, what is the profitability index of each project? PIA= NPVA/Investment A= $ /50000 = PIB= NPVB/Investment B= $ /50000= Example 14: You are in charge of one department of Company Y. The department has five projects available below. If your department is subject to capital rationing, and you must select projects subject to a budget constraint of $20 million dollars, which set of projects should be accepted so as to maximize firm value? From the following table you will choose the third project first (PI=.43), then choose the fourth project (PI=.33) and then choose the first project (PI=.33) and lastly choose the fifth project (PI=.25). You will consume all your money and will not pursue the project with least PI. PV Investment NPV PI

9 VI Project Interaction: 6.1) The investment time decision: When is it best to commit to a positive NPV investment? Investment timing problems all involve choices amongst mutually exclusive investments. Buy now or wait? You can t do both! The right time to choose the investment date that result in the highest NPV today. Example 15: You are considering buying a new fax machine and the cost of the machine is $350. If you use your own machine, then you save $75 each year. The machine will last about 5years. Assume that the price the machine decreases by 15% each year. Should you immediately buy this machine if the discount rate is 12%? Year of Cost of Machine PV NPV at the year of NPV today Purchase Savings purchase 0 $ = $350*0.85 = $ = $297.5 *.85=$ = PV of Savings: 75 PMT 5 N 12 %I CPT PV NPV today: FV 1 N 12 %I CPT PV From the table you find out that the NPV today is maximum when you purchase the machine in year 7. Beyond which the NPV starts decreasing, so the optimal time to purchase the machine is year7. EX15B: OB Inc. is considering the purchase of a new computer system. The system costs $50,000, is expected to last for 4 years and would reduce costs of operation by $22,000 per year. If the cost of capital is 10%, should OB purchase the system? If the cost of the computer system is reducing by 10% each year what is the best time to buy this machine. Year of Purchase Cost of Machine PV Savings NPV at the year of purchase NPV today 0 $ = $50*0.90 = $ = = = = From the above table you find that NPV today is maximized when you purchase the compute in year4. Both the above examples are hypothetical and you can replace fax machine and computer with any other machine and the year of purchase can be month of purchase or day of purchase. 9

10 6.2) Long-Lived vs. Short-Lived Equipment : 1) When comparing mutually exclusive projects that have unequal project lives, one must analyze the costs of the project. 2) Calculate the equivalent annual cost (EAC) of both machines. Decision Rule: Accept the project with the lowest equivalent annual cost. 3) EAC is the annual project cost per period that equates the present value of cost of buying and operating a machine. Example 16: Machine A costs $15000, will last for 3 years and costs $4000/year in maintenance, machine B costs $10,000 will last for 2 years and costs $6000/year in maintenance. Which machine would you chose if cost of capital is 6%. Solution: EAC for Machine A: PV of Maintenance cost: Payment=4000, N=3, I/Y=6, FV=0 CPT PV=10, Total cost = = EAC A=? PV= -25, N=3 I/Y=6 FV=0 CPT Pmt= $ EAC A EAC for Machine B: PV of Maintenance cost: Payment=6000, N=2, I/Y=6 FV=0 CPT PV= Total cost = = EAC B =? PV = N=2 FV=0 CPT Pmt= 11, EAC B EAC A < EAC B Hence Choose Machine A. Example 17: You are considering buying a photocopying machine. If the discount rate is 10%, what are the equivalent annual costs of Brand A vs. B? Which machine is more cost effective? Machine Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Price Operating Operating Operating Operating Operating Operating Operating Cost Cost Cost Cost Cost Cost Cost A -$10,000 -$1,100 -$1,100 -$1,100 -$1,100 -$1,100 B -$11,500 -$700 -$700 -$700 -$700 -$700 -$700 -$700 Solution: PV of operating Cost A =? Total cost = 10, = 14, EAC A =? PV= N=5 FV= 0 I/Y=10 CPT Payment = $ EAC A PV of operating Cost B =?

11 Total cost = = EAC B =? PV= N= 7 FV= 0 I/Y= 0; CPT Payment = $ EAC A > EAC B, Hence choose Machine B. EAC B 6.3 Replacing an old machine Example 18: You are operating an old machine that will last only 2 more years. It costs $12,000 per year to operate. You can replace it now with a new machine, which costs $25,000 but it much more efficient with $8,000 operating costs per year and will last for 5 years. Should you replace now or wait if the opportunity cost of capital is 6%? Solution: New Machine: PV of operating cost: Amount=8000, N=5, I/Y=6, FV=0 CPT PV= Total Cost = =58, EAC New Machine =? PV= ; N= 5; I/Y = 6; FV=0; CPT Pmt= 13, EAC New Machine > Maintenance cost on old machine Hence we should not replace the old machine. Decision: If the EAQ of new project is less than the period cost of the old project =>Accept new If the EAQ of new project is greater than the period cost of the old project =>Delay Investment Criteria Cash Flow Timing of Cash Flow Opportunity cost of capital NPV Yes Yes Yes IRR Yes Yes Comparing IRR with opportunity cost of capital Payback Period Not consider after a cutoff No No period MIRR Yes Yes Yes Profitability Index Yes Yes Yes 11