Lectures 3-4

Lectures 3-4: Investment decision rules and capital budgeting Alex Kostakis Manchester Business School Semester 1, 2013-2014 Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 1 / 27 Overview of Lectures 3-4 Investment decision rules Net Present Value (NPV), Internal Rate of Return (IRR) and Payback investment rules Pitfalls when not using NPV Investment decision between mutually exclusive projects Investment decision with resource constraints Capital budgeting Determining incremental cash ‡ows Applying the NPV rule Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 2 / 27 NPV and stand-alone projects Consider a take-it-or-leave-it investment involving a stand-alone project investment outlay (out‡ow): $250m incurred today (t = 0) expected cash in‡ows: $35m for every year starting next year (t = 1) The expected cash ‡ows constitute a perpetuity. Its PV is given by: PV = C r = 35 r Subtract the initial out‡ow to obtain the NPV of the project: NPV = �250+ 35 r The sign of NPV crucially depends on the discount rate (opportunity cost of capital) r . Remember: Accept project if and only if NPV > 0. Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 3 / 27 NPV and the discount rate Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 4 / 27 The Internal Rate of Return (IRR) Recall that the Internal Rate of Return (IRR) is the discount rate for which NPV = 0. In the previous example, IRR = 14% IRR-based decision rule: If IRR > r , then accept the project If IRR < r , then reject the project The term IRR comes from the fact that at this rate PV (cash in‡ows) = PV (cash out‡ows) IRR rule appears equivalent to NPV rule in the previous example. However, there are various cases where the two rules will disagree: i) delayed investments, ii) nonexistent IRR, iii) multiple IRRs Always use the NPV rule Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 5 / 27 Pitfall 1: The Delayed Investment Fallacy Example: Mr Right is o¤ered $1m upfront for writing a book. Writing the book would take him 3 years, and in each year he would forgo cash in‡ows of $0.5m. The discount rate is r = 10%. The NPV of this investment is: NPV = 1+ �0.5 (1+ r) + �0.5 (1+ r)2 + �0.5 (1+ r)3 Solving NPV = 0 for r , we get that IRR = 23.38% Since IRR > r , then IRR rule would wrongly advise us to accept the o¤er. That is wrong because the NPV of the project is: NPV = 1+ �0.5 (1.1) + �0.5 (1.1)2 + �0.5 (1.1)3 = �0.2434 < 0 We should not accept a negative NPV investment. Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 6 / 27 Pitfall 1: The Delayed Investment Fallacy This fallacy derives from the fact that in this example the in‡ow precedes the out‡ows. As a result, it is as if Mr. Right borrows money, receiving cash today in exchange for a future liability, and IRR is best interpreted as the rate he pays rather than earns. Therefore, IRR and NPV give the opposite recommendations. He should accept such a deal only when IRR < r . Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 7 / 27 Pitfall 2: The Multiple IRRs Fallacy Mr. Right is o¤ered now a new improved deal: To receive now $0.55m at t = 0 and $1m in 4 years time (t = 4) Plotting the NPV of the new deal for various discount rate levels... we see that there are 2 solutions (roots) to the equation NPV = 0. Fallacy: Which IRR should we compare with r? General rule: There may be as many IRRs as the number of sign changes in the CF stream Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 8 / 27 Pitfall 3: Nonexistent IRR Finally, Mr. Right convinces the publisher to increase the initial (t = 0) payment to $0.75m. NPV is now given by: NPV = 0.75+ �0.5 (1.1) + �0.5 (1.1)2 + �0.5 (1.1)3 + 1 (1.1)4 In this case, there is no solution for NPV = 0. Graphically: Here we cannot use the IRR rule to make an investment decision General lesson: Always use the NPV rule Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 9 / 27 The Payback Rule The payback investment rule states that you should only accept a project if its cash ‡ows pay back its initial investment within a prespeci…ed period. Payback rule is simple and provides info regarding the length of time capital will be committed to a project. However, it is not as reliable as the NPV rule because it 1 Ignores the project’s cost of capital and the time value of money 2 Ignores the cash ‡ows after the payback period 3 Relies on an ad hoc decision criterion (choice of payback period) Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 10 / 27 Mutually exclusive projects Till now we have assumed we can evaluate each project independently In practice businesses have to choose among mutually exclusive projects: Investing in one project excludes the other. NPV rule: Choose the project with the highest NPV IRR rule: Choose the project with the highest IRR (again this can lead to wrong decision) Example initial cash flow growth cost of project investment (year 1) rate capital NPV IRR Book store 300,000 63,000 3.00% 8.00% 960,000 24% Coffee shop 400,000 80,000 3.00% 8.00% 1,200,000 23% Music store 400,000 104,000 0.00% 8.00% 900,000 26% Electronics store 400,000 100,000 3.00% 11.00% 850,000 28% For each project NPV = �Investment + CFr�g Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 11 / 27 Fallacies of IRR rule for mutually exclusive projects 1 Di¤erences in scale (co¤ee shop vs book store) Would you prefer a 100% return on $1 investment or a 1% return on a $1m investment? IRR shows the relative (%) increase in value, while NPV shows the absolute increase in value 2 Di¤erences in timing (co¤ee shop vs music store) Would you prefer a high rate of return for several years or only for a few days? Music store o¤ers high CFs from the start, while for the co¤ee shop CFs are initially low but with higher growth rate g The delay in its high CFs makes the co¤ee shop an e¤ectively longer-term investment 3 Di¤erences in risk (cost of capital) (co¤ee shop vs electronics) A project’s IRR should be adjusted for its cost of capital (risk) Electro store o¤er a higher IRR but has a higher cost of capital (riskier) Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 12 / 27 IRR rule for incremental cash ‡ows IRR rule can be applied at incremental cash ‡ows of mutually exclusive projects. Example: As stand-alone projects: IRR(L)=18.92% and IRR(S)=25% Subtract the CFs of the 2nd project from the CFs of the 1st Compute the IRR for these incremental CFs (IRR=12.47%) Rule: If IRR > r , choose the 1st project over the 2nd Previous pitfalls regarding IRR rule still apply NPV rule is much simpler and works always! Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 13 / 27 Resource constraints Till now, we have assumed that we can always raise new capital to invest into projects. In reality there are resource constraints Example: Choice among 3 projects which will take up space in our warehouse: NPV Fraction of (in millions) Warehouse (\%) Project 1 100 100 Project 2 75 60 Project 3 75 40 Choosing the highest NPV project (P1) is incorrect because it makes full use of our warehouse Check that you can instead choose P2 and P3, because they are within the warehouse capacity and together lead to higher NPV Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 14 / 27 The Bang for the Buck Rule To identify the optimal combination of projects under resource constraints we use the pro…tability index This is given by the NPV per unit of the constrained resource (bang for the buck) NPV Fraction of Profitability (in millions) Warehouse (\%) Index Project 1 100 100 1 Project 2 75 60 1.25 Project 3 75 40 1.875 Choose progressively projects with the highest pro…tability index until the resource is exhausted This rule does not work well 1 when the set of projects do not exhaust the available resource 2 there are multiple resource constraints Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 15 / 27 Capital Budgeting Capital budgeting is the process through which we analyze alternative investments and decide which ones to accept Usually, capital budgeting starts from earnings because they are (seem) easier to forecast and understand But we are ultimately interested in the project’s cash ‡ows Golden rule: Consider only incremental cash ‡ows= changes in cash ‡ows that occur due to the investment project 1 Consider the opportunity cost of resources used in the project (e.g. land or o¢ ces that could be alternatively rented out) 2 Ignore sunk or …xed costs that are independent of the investment decision and cannot be recovered 3 Consider the e¤ect of the project on the cash ‡ows of existing projects (cannibalization) Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 16 / 27 An Example LinkSys has already completed a $300,000 feasibility study to assess a new product, HomeNet. The product has an expected life of 4 years and its riskiness corresponds to a discount rate of 12%. The marginal tax rate is 40%. Revenue estimates: Sales of 100,000 units per year Price per unit: $260 Cost estimates: Variable cost per unit of $110 Up-front R&D expenditure of $15m (R&D not depreciated) New equipment of $7.5m up-front with expected life of …ve years (straight-line depreciation) Additional annual overheads (marketing etc.) of $2.8m Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 17 / 27 Capital Budgeting Sheet 1 Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 18 / 27 Some Further Complications The new product is housed in an existing production lab Our wrong intuition is that the lab does not imply any costs because we already own it However, the lab could be rented out for $200,000 per year and we should take into account this opportunity cost Project externalities (cannibalization) 25% of sales (i.e. 25,000 units) come from customers who would otherwise purchase an existing product at a price of $100 and whose production cost is $60 per unit. We need to subtract these lost sales (25,000x$100=$2.5m) from our sales estimates and add back the forgone variable cost (25,000x60=$1.5m) to our cost estimates Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 19 / 27 Capital Budgeting Sheet 2 Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 20 / 27 Computing Cash Flows Recall that we want to discount cash ‡ows, not earnings. We had to compute the unlevered income in order to compute the tax liability (out‡ow). Having computed tax liability, we need to adjust the unlevered income for non-cash ‡ow items: 1 Capital expenditures are paid immediately, while they are subtracted from earnings over the lifetime of the project through depreciation. We need to deduct capital expenditures when they occur and to add back depreciation in the rest years 2 Change in the net working capital (∆NWC ) NWC is cash needed to keep the project running and it is not included in unlevered net income. NWC = Cash + Inventory + Receivables � Payables Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 21 / 27 Capital Budgeting Sheet 3 Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 22 / 27 Calculating the NPV We are now ready to calculate the NPV of Free CFs NPV > 0, so LinkSys should invest in the new product. Free Cash Flow directly: unlevered net income FCF = z }| { (Revenues� Costs�Dep) (1� τc ) +Dep� CapEx� ∆NWC We initially compute the NPV as if the project were all-equity …nance, even if it is not. We can then adjust for the e¤ects of external …nancing. Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 23 / 27 Uncertainty about cash ‡ows and discount rate 1 Break-even analysis Calculate for each input the level for which the project’s NPV = 0 (break-even level) 2 Sensitivity analysis Calculate how much the project’s NPV varies due to a change in an input parameter, holding the rest constant 3 Scenario analysis Calculate the e¤ect of simultaneously changing more than one input parameters on the project’s NPV Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 24 / 27 Break-even analysis The following graph shows how the project’s NPV varies for a range of values for each of the input parameters Some input parameters have a far greater impact on project’s NPV than others (more attention required) Conclusion: Only low sales can render the project unacceptable Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 25 / 27 Scenario analysis Here we examine the e¤ect of a change in the pricing strategy Since the pricing strategy also a¤ects the number of units sold, then it’s more appropriate to consider these two e¤ects simultaneously (scenario rather sensitivity analysis) Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 26 / 27 Reading and Homework This week: Berk and DeMarzo (3rd ed.): 3.3, 4.9, Chapters 7 and 8. Homework uploaded on Blackboard Next week (advance reading): Valuation of bonds. Berk and Demarzo (3rd ed.): 5.3 and Chapter 6. Alex Kostakis (Manchester Business School) BMAN 23000: Foundations of Finance Semester 1, 2013-2014 27 / 27 Lectures 3-4 Overview NPV NPV IRR IRR IRR IRR IRR Payback rule Mutually exclusive projects Mutually exclusive projects Mutually exclusive projects Resource constraints Resource constraints Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Capital Budgeting Reading and Homework