Which projects should the corporation undertake Investment criteria 1. Investment into a new project generates a flow of cash and, therefore, a standard DPV rule should be the first choice under consideration. Note, that DPV gives you the value (the maximum price you would pay) of the project. Whether to make the investment or not you should compare the value of the project with the project cost. The difference between the DPV and the cost is called NPV (net present value) NPV = DPV Cost NPV rule: Any project with positive NPV should be implemented. In practice, other rules are also considered. 2. The payback period rule: investment is acceptable if its payback is less than some prespecified number of years. Payback is the minimum number of periods when undiscounted sum of payments becomes positive. Advantages Disadvantages 1. Easy to understand 2. Adjusts for uncertainty of later cash flows 3. Biased towards liquidity 1. Ignores the time value of money 2. Requires an arbitrary cut-off point 3. Ignores cash flow beyond the cutoff period 4. Biased against long-term projects such as R&D and new projects Some explanations. [a]. Adjusts for uncertainty of later cash flows: some of the actual cash flows exceed and some are lower than the projected cash flows. The fluctuations will cancel out as long as on average the projected cash flows are correct. [b.] Biased towards liquidity: the first reason for that is that 1
all cash flows after some cut-off period are disregarded. The second reason works in the opposite direction. Disregarding time makes the payback rule biased towards less liquid projects. Let s illustrated by the following example. Suppose there are only two periods and there are two projects that generate the payments (x 1, x 2 ) and (y 1, y 2 ). Suppose also that the two projects are equivalent with respect to NPV rule ( x 1 + x 2 = y 1 + y 2 ) and the 1+r (1+r) 2 1+r (1+r) 2 first project has more liquidity (x 1 > y 1 and x 2 < y 2 ). Then the payback rule would choose the second project if both have the same cut-off period. x 1 (1 + r) + x 2 = y 1 (1 + r) + y 2 x 1 + x 2 < y 1 + y 2 The main advantage of the payback rule is its simplicity. It is applied when a quick evaluation of the project with short horizon is needed. 3. Discounted payback period rule. The same as before, but now the sum of cash payments is discounted. This is a trade-off between NPV and payback period rule (though it is not clear why not to use NPV instead). 4. Average accounting return (AAR). AAR = average project earnings after taxes and depreciation average book value of the investment during its life Example: 2
AAR = 6+2+1 3 12+8+4+0 4 = 50% Problems: AAR is not a rate of return in any meaningful sense. Not clear how to specify the target return. Instead of cash flow and the market value of the firm AAR looks at the net income and book value of investment. One redeeming feature is that accounting information is available. 5. The internal rate of return (IRR) This is an analogue of the yield to maturity for bonds. The IRR is the rate at which the NPV is equal to zero. If the cost of the project is C and the flow of the dividends is (d 1, d 2,...) then the IRR is the solution of d 1 C + 1 + IRR + d 2 (1 + IRR) +... = 0 2 The investment rule based on IRR is to accept the project whenever IRR is greater than the market interest rate and reject otherwise. The rule assumes explicitly that this is an investment project. That is, the negative cash flow occurs immediately and then it is followed by positive cash flows. In the example, project A is an investment project and the IRR rule applies to it. Project B is a substitute for borrowing and it should be undertaken only if IRR < r. Finally, project C has multiple IRR and it should be undertaken only whenever IRR 1 = 10% < r < 20% = IRR 2. Ranking projects. Assign the priorities to the projects according to their IRR. If there are two mutually exclusive projects then the ranking may be not correct. 3
6. Profitability Index PV of cash flow P I = Initial investment = DP V Cost = NP V Cost + 1 The rule is equivalent to NPV rule. P I > 1 NP V > 0 However, P I (as IRR) is scale independent (if both investment and cash flows are rescaled then P I does not change). Therefore, if you compare two mutually exclusive projects ranking them by P I then you may come up with a wrong decision. When there is capital rationing (not sufficient funds for all positive NPV projects) P I may be a good ranking of which projects to choose. The ranking is by present value return per unit of invested capital. 4
Capital budgeting Strategy: 1. Construct Pro Forma financial statements. Sunk costs should be ignored and opportunity costs included in the statement. 2. Use NPV rule to decide whether to accep the project or reject it. Example 1: Suppose you are considering the following project. You plan to sell 50,000 cans of shark attractant for $4.30 per can. It costs $2.50 to produce a can. The new product as this one has only 3 year life time (because of competition or any other reason). The return on this type of projects is 20%. Operating costs on such projects are 12,000 per year. Furthermore, 90,000 must be invested in manufacturing equipment which will be 100% depreciated in three years (it will be worthless on the market). Finally, the project requires 20,000 investment into NWC. This amount is constant over the life of the project. Assume zero inflation rate. The first step is to construct the operating cash flow of the project. We need income statement for that. Income statement Sales (50,000 units at 4.30 / unit) $215,000 Variable cost (2.50 / unit) 125,000 Fixed cost 12,000 Depreciation (90,000/3) 30,000 EBIT $48, 000 Taxes (40%) 19,200 Net income $28, 000 Operating cash flow = EBIT Tax + Depreciation = 58, 000. Next step is to construct the cash flows associated with the project. Year 0 1 2 3 Operating cash flow 0 $ 58,800 $ 58,800 $ 58,800 Addition to NWC -$ 20,000 0 0 0 capital spending -90,000 0 0 0 Total cash flow -110,000 58,800 58,800 58,800 DPV -110,000 49,000 40,833 45,602 NPV $25, 435 5
Different equivalent ways to calculate the operating cash flows (OCF) Approach Basic Bottom-up Top-down Tax shield Formula OCF = EBIT + Depreciation Taxes OCF = Net income + Depreciation OCF = Sales Costs Taxes OCF = (Sales Costs) (1 T c )+ Depreciation T c Depreciation on a straight line If C is capital spending in period zero and the project lives for T years than depreciation is the same in every period of time: D t = C T Capital cost allowance (CCA) and depreciation The depreciation is exponential. If d is the rate at which capital is allowed to depreciate then in the first period D 1 = 1 Cd and in the other periods 2 [ C D t = 2 + C ] (1 d) d t 1 = C 2 d 2 2 d dt 6
Check the definition of CCA and details on depreciation calculations on page 40 of the textbook. 7
Investments of unequal life Consider a choice between two mutually exclusive projects that have different life periods. The projects do the same job, bring same revenues, but decisions lead to different operation costs. Simple NPV rule may lead to a wrong decision. The projects must be evaluated on an equal-life basis, taking into account all future replacement decisions. 8
Example: suppose that we are considering two machines with purchase price and maintenance cost shown in the table below. Assume discount 10%. Machine 0 1 2 3 4 A 500 120 120 120 0 B 600 100 100 100 100 P V A = 798.42 P V B = 916.99 but machine A must be replaced more frequently than machine B. There are two methods to compare the investments of unequal life. Method 1: matching cycles. First, find a common cycle for the two projects (in the example, it is 12). Machine A is replaced 4 times and machine B 3 times over the cycle. Find the NPV over the cycle. P V A = 798.42 + 798.42 1.1 3 + 798.42 1.1 6 + 798.42 1.1 9 = 2187.58 P V B = 916.99 + 916.99 + 916.99 = 1971.09 1.1 4 1.1 8 Therefore, the choice should be made in favor of project B. Method 2: equivalent annual costs (EAC). Find the PV of the machine and find an annuity that generates the same PV over the machine life-time. Intuition: the equivalent annuity shows how much the machine costs to us each year (transforms unequal cash payments into equal). The math formula for annuity PV is P V = C [ ] 1 1 r (1 + r) T In the example, C A = C B = rp V [ A ] = 321.06 1 1 (1+r) T rp V [ B ] = 289.28 1 1 (1+r) T 9
and we obtain the same result. Replacement decision The problem we address is when to replace an old machine with a new machine? Example: the maintenance cost and the market value (salvage value) of the old machine are shown in the table. Date Maintenance Salvage value 0 0 4,000 1 1,000 2,500 2 2,000 1,500 3 3,000 1,000 4 4,000 0 From the table we can derive the cost of using the machine for one more year. If we use the old machine the cost is 4,000 (opportunity cost) that we have to pay today + 1,000 that we pay next year and 2,500 that we obtain next year. Suppose also that the new machine B cost 9000, require annual maintenance of 1000, and would be sold for 2000 after 8 years. P V B = 12, 833 EAC B = 2, 860 By definition EAC is paid only starting next year. Date One-year carrying cost at the end of the year Yearly payment for the new machine at the end of the year 1 4,000*1.15 + 1,000-2,500 2,860 2 2,500*1.15 + 2,000-1,500 2,860 3 1,500*1.15 + 3,000-1,000 2,860 4 1,000*1.15 + 4,000-0 2,860 Example: a machine costs $12000, has annual year end operating costs of $6000, and lasts 4 years. It has $2000 salvage value. What is the PV of operating a series of such machines in perpetuity, if the appropriate discount rate is 6? 10
P V 1 cycle = 31, 206 EAC = 9, 006 P V = EAC r = 150, 099 Exercise: consider a machine with the following maintenance cost and market value Date Maintenance Salvage value 0 1,000 8,000 1 1,500 6,000 2 2,500 4,000 3 5,000 2,000 4 8,000 0 When should the machine be replaced by an identical machine? Example: A company wants to know the maximum price P it should be willing to pay for a new piece of equipment. I.e., the price that will give NPV=0 Facts: The new equipment would replace current equipment that has $20,000 market value. The new equipment would not affect revenues, but would reduce before tax operating costs by 10,000 per year for 8 years The old equipment is 5 years old, but is expected to last another 8 years, at which time it is expected to have no resale value. 11
The old machine was purchased for 40,000, and is being depreciated on a straight line basis for 10 years to a zero value. The new equipment will be depreciated to a zero value using straight line depreciation over 5 years, although it is expected to have a market resale value of 5,000 at the end of 8 years. The corporate tax rate is 34%. The company is profitable on going operations. The appropriate discount rate is 8%. Tax shield approach The NPV of purchasing new equipment = net capital spending in period zero + PV(OCF) + PV(Salvage value) of the new equipment. net capital spending in period zero = P + 20 (+20 because we sell the old equipment) OCF = (Sales Costs Opportunity cost)(1 T c ) + (Depreciation new Depreciation old ) T c = PV(annuity(10, 000 0.66, 0.08)) + PV(annuity(( P 5 4) 0.34, 0.08)) PV(Salvage value) = 5,000 3.4 1.08 8 Project Analysis 12