# Chapter 10. What is capital budgeting? Topics. The Basics of Capital Budgeting: Evaluating Cash Flows

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1 Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows 1 Topics Overview and vocabulary Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life 2 What is capital budgeting? Analysis of potential projects. Longterm decisions; involve large expenditures. Very important to firm s future. 3

2 Steps in Capital Budgeting Estimate cash flows (inflows & outflows). Assess risk of cash flows. Determine r = WACC for project. Evaluate cash flows. 4 Independent versus Mutually Exclusive Projects Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other. 5 Cash Flows for Franchise L and Franchise S L s CFs: % S s CFs: %

3 NPV: Sum of the PVs of all cash flows. NPV =Σ N CF t (1 r) t t = 0 Cost often is CF 0 and is negative. NPV =Σ N CF t CF (1 r) t 0 t = 1 7 What s Franchise L s NPV? L s CFs: % = NPV L NPV S = \$ Calculator Solution: Enter values in CFLO register for L. 100 CF 0 10 CF 1 60 CF 2 80 CF 3 10 I/YR NPV = = NPV L 9

4 Rationale for the NPV Method NPV = PV inflows Cost This is net gain in wealth, so accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value. 10 Using NPV method, which franchise(s) should be accepted? If Franchise S and L are mutually exclusive, accept S because NPV s > NPV L. If S & L are independent, accept both; NPV > Internal Rate of Return: IRR CF 0 CF 1 CF 2 CF 3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0. 12

5 NPV: Enter r, solve for NPV. = NPV Σ N CF t (1 r) t t = 0 IRR: Enter NPV = 0, solve for IRR. Σ N CF t = (1 IRR) t= 0 t = 0 13 What s Franchise L s IRR? 0 IRR =? PV 1 PV 2 PV 3 0 = NPV Enter CFs in CFLO, then press IRR: IRR L = 18.13%. IRR S = 23.56%. 14 Find IRR if CFs are constant: INPUTS N I/YR PV PMT FV OUTPUT 9.70% Or, with CFLO, enter CFs and press IRR = 9.70%. 15

6 Rationale for the IRR Method If IRR > WACC, then the project s rate of return is greater than its cost some return is left over to boost stockholders returns. Example: WACC = 10%, IRR = 15%. So this project adds extra return to shareholders. 16 Decisions on Projects S and L per IRR If S and L are independent, accept both: IRR S > r and IRR L > r. If S and L are mutually exclusive, accept S because IRR S > IRR L. 17 Construct NPV Profiles Enter CFs in CFLO and find NPV L and NPV S at different discount rates: r NPV L (4) NPV S

7 NPV Profile 50 L Crossover Point = 8.7% NPV (\$) S IRR S = 23.6% Discount rate r (%) IRR L = 18.1% 19 NPV and IRR: No conflict for independent projects. NPV (\$) IRR > r and NPV > 0 Accept. r > IRR and NPV < 0. Reject. IRR r (%) 20 Mutually Exclusive Projects NPV L r < 8.7: NPV L > NPV S, IRR S > IRR L CONFLICT r > 8.7: NPV S > NPV L, IRR S > IRR L NO CONFLICT S IRR S 8.7 IRR L % 21

8 To Find the Crossover Rate Find cash flow differences between the projects. See data at beginning of the case. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. Can subtract S from L or vice versa, but easier to have first CF negative. If profiles don t cross, one project dominates the other. 22 Two Reasons NPV Profiles Cross Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPV S > NPV L. 23 Reinvestment Rate Assumptions NPV assumes reinvest at r (opportunity cost of capital). IRR assumes reinvest at IRR. Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. 24

9 Modified Internal Rate of Return (MIRR) MIRR is the discount rate which causes the PV of a project s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash inflows are reinvested at WACC. 25 MIRR for Franchise L: First, find PV and TV (r = 10%) % PV outflows % % TV inflows 26 Second, find discount rate that equates PV and TV PV outflows MIRR = 16.5% \$100 = \$158.1 (1MIRR L ) TV inflows MIRR L = 16.5% 27

10 To find TV with 10B: Step 1, find PV of Inflows First, enter cash inflows in CFLO register: CF 0 = 0, CF 1 = 10, CF 2 = 60, CF 3 = 80 Second, enter I/YR = 10. Third, find PV of inflows: Press NPV = Step 2, find TV of inflows. Enter PV = , N = 3, I/YR = 10, PMT = 0. Press FV = = FV of inflows. 29 Step 3, find PV of outflows. For this problem, there is only one outflow, CF 0 = 100, so the PV of outflows is 100. For other problems there may be negative cash flows for several years, and you must find the present value for all negative cash flows. 30

11 Step 4, find IRR of TV of inflows and PV of outflows. Enter FV = , PV = 100, PMT = 0, N = 3. Press I/YR = 16.50% = MIRR. 31 Why use MIRR versus IRR? MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR. 32 Normal vs. Nonnormal Cash Flows Normal Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. For example, nuclear power plant or strip mine. 33

12 Inflow () or Outflow () in Year N NN N NN N N NN 34 Pavilion Project: NPV and IRR? r = 10% 800 5,000 5,000 Enter CFs in CFLO, enter I/YR = 10. NPV = IRR = ERROR. Why? 35 Nonnormal CFstwo sign changes, two IRRs. NPV NPV Profile 450 IRR 2 = 400% r 800 IRR 1 = 25% 36

13 Logic of Multiple IRRs At very low discount rates, the PV of CF 2 is large & negative, so NPV < 0. At very high discount rates, the PV of both CF 1 and CF 2 are low, so CF 0 dominates and again NPV < 0. In between, the discount rate hits CF 2 harder than CF 1, so NPV > 0. Result: 2 IRRs. 37 Finding Multiple IRRs with Calculator 1. Enter CFs as before. 2. Enter a guess as to IRR by storing the guess. Try 10%: 10 STO IRR = 25% = lower IRR (See next slide for upper IRR) 38 Finding Upper IRR with Calculator Now guess large IRR, say, 200: 200 STO IRR = 400% = upper IRR 39

14 When there are nonnormal CFs and more than one IRR, use MIRR: ,000 5,000,000 5,000,000 PV 10% = 4,932, TV 10% = 5,500, MIRR = 5.6% 40 Accept Project P? NO. Reject because MIRR = 5.6% < r = 10%. Also, if MIRR < r, NPV will be negative: NPV = \$386, Profitability Index The profitability index (PI) is the present value of future cash flows divided by the initial cost. It measures the bang for the buck. 42

15 Franchise L s PV of Future Cash Flows Project L: 0 10% Franchise L s Profitability Index PI L = PV future CF Initial Cost = \$ \$100 PI L = PI S = What is the payback period? The number of years required to recover a project s cost, or how long does it take to get the business s money back? 45

16 Payback for Franchise L CF t Cumulative Payback L = 2 30/80 = years 46 Payback for Franchise S CF t Cumulative Payback S = 1 30/50 = 1.6 years 47 Strengths and Weaknesses of Payback Strengths: Provides an indication of a project s risk and liquidity. Easy to calculate and understand. Weaknesses: Ignores the TVM. Ignores CFs occurring after the payback period. 48

17 Discounted Payback: Uses discounted rather than raw CFs. 0 10% CF t PVCF t Cumulative Discounted payback = /60.11 = 2.7 yrs Recover invest. cap. costs in 2.7 yrs. 49 S and L are mutually exclusive and will be repeated. r = 10% Project S: (100) Project L: (100) Note: CFs shown in \$ Thousands NPV L > NPV S. But is L better? CF 0 CF 1 N J I S L NPV

18 Equivalent Annual Annuity Approach (EAA) Convert the PV into a stream of annuity payments with the same PV. S: N=2, I/YR=10, PV=4.132, FV = 0. Solve for PMT = EAA S = \$2.38. L: N=4, I/YR=10, PV=6.190, FV = 0. Solve for PMT = EAA L = \$1.95. S has higher EAA, so it is a better project. 52 Put Projects on Common Basis Note that Project S could be repeated after 2 years to generate additional profits. Use replacement chain to put on common life. Note: equivalent annual annuity analysis is alternative method. 53 Replacement Chain Approach (000s). Franchise S with Replication: Franchise S: (100) 60 (100) (100) (40) NPV = \$7,

19 Or, use NPVs: ,132 3,415 7,547 10% 4,132 Compare to Franchise L NPV = \$6, Suppose cost to repeat S in two years rises to \$105, Franchise S: (100) (105) (45) NPV S = \$3,415 < NPV L = \$6,190. Now choose L. 56 Economic Life versus Physical Life Consider another project with a 3year life. If terminated prior to Year 3, the machinery will have positive salvage value. Should you always operate for the full physical life? See next slide for cash flows. 57

20 Economic Life versus Physical Life (Continued) Year CF (\$5000) 2,100 2,000 1,750 Salvage Value \$5000 3,100 2, CFs Under Each Alternative (000s) No termination (5) Terminate 2 years (5) Terminate 1 year (5) NPVs under Alternative Lives (Cost of capital = 10%) NPV(3) = \$123. NPV(2) = \$215. NPV(1) = \$

21 Conclusions The project is acceptable only if operated for 2 years. A project s engineering life does not always equal its economic life. 61 Choosing the Optimal Capital Budget Finance theory says to accept all positive NPV projects. Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital. Capital rationing 62 Increasing Marginal Cost of Capital Externally raised capital can have large flotation costs, which increase the cost of capital. Investors often perceive large capital budgets as being risky, which drives up the cost of capital. (More...) 63

22 If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital. 64 Capital Rationing Capital rationing occurs when a company chooses not to fund all positive NPV projects. The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year. (More...) 65 Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. (More...) 66

23 Reason: Companies don t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing. (More...) 67 Reason: Companies believe that the project s managers forecast unreasonably high cash flow estimates, so companies filter out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a postaudit process and tie the managers compensation to the subsequent performance of the project. 68

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