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**Chapter 10: The Basics of Capital Budgeting: Evaluating Cash Flows**

Overview and “vocabulary” Methods Payback, discounted payback NPV IRR, MIRR Profitability Index Unequal lives Economic life

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MINICASE 10

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**What is capital budgeting?**

Analysis of potential projects. Long-term decisions; involve large expenditures. Very important to firm’s future.

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**Steps in Capital Budgeting**

Estimate cash flows (inflows & outflows). Assess risk of cash flows. Determine r = WACC for project. Evaluate cash flows.

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Digression: What is the difference between independent and 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.

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**An Example of Mutually Exclusive Projects**

BRIDGE VS. BOAT TO GET PRODUCTS ACROSS A RIVER.

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Normal Project Nonnormal Project

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Normal Project Cost (negative CF) followed by a series of positive cash inflows. Nonnormal Project One or more outflows occur after inflows have begun. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine.

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**Inflow (+) or Outflow (-) in Year**

1 2 3 4 5 N NN - + + + + + N - + + + + - NN - - - + + + N + + + - - - NN - + + - + - NN

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**c(1). What is the payback period?**

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**What is the payback period?**

The number of years required to recover a project’s cost, or how long does it take to get our money back?

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**Payback for Project L (Long: Most CFs in out years)**

1 2 2.4 3 CFt -100 10 60 80 Cumul -100 -90 -30 50 PaybackL = /80 = years. n.b. Assumes CF’s occur evenly over the year.

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**Project S (Short: CFs come quickly)**

1 1.6 2 3 CFt -100 70 50 20 Cumul -100 -30 20 40 PaybackS = /50 = 1.6 years. Payback is a type of breakeven analysis.

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Strengths of Payback Weaknesses of Payback

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**c(2). Strengths of Payback**

Provides an indication of a project’s risk and liquidity. Easy to calculate and understand. Weaknesses of Payback Ignores the TVM. Ignores CFs occurring after the payback period.

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**c(3):Discounted Payback: Uses discounted**

rather than raw CFs. Apply to Project L. 2.7 1 2 3 10% CFt -100 10 60 80 PVCFt -100 9.09 49.59 60.11 Cumul -100 -90.91 -41.32 18.79 Disc. payback = /60.11 = 2.7 years. Recover invest. + cap. costs in 2.7 years.

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**d(1) Net Present Value (NPV)**

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**Net Present Value (NPV)**

Sum of the PVs of inflows and outflows. n t=0 CFt (1 + k)t NPV = If one expenditure at t = 0, then n t=1 CFt (1 + k)t NPV = CF0.

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NET PRESENT VALUE NPV = CF0 + CF1/(1+k) + CF2/(1+k) CFn/(1+k)n

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**Project L: (Beware use of comp. fns)**

What is Project L’s NPV? Project L: (Beware use of comp. fns) 1 2 3 10% 10 60 80

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**What is Project L’s NPV? Project L: 18.78 = NPVL NPVS = $19.98. 1 2 3**

1 2 3 10% 9.09 49.58 60.11 18.78 = NPVL NPVS = $19.98. 10 60 80

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**Calculator Solution Enter in CFLO for L: = 18.78 = NPVL. -100 10 60 80**

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**d(2) Rationale for the NPV Method**

If NPV = 0, project breaks even; recovers cost of investment investors earn required rate of return (i.e. opportunity cost of capital) If NPV > 0; investors get above, plus additional $.

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**CONSIDER PROJECT L: SUM OF undiscounted CF’s = 150**

Investors get $100 back Cover their 10% cost of capital; and have $18.79 left over. Who does this $18.79 belong to? Stockholders.

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**Rationale for the NPV Method**

NPV = PV inflows - PV of Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.

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**Using NPV method, which project(s) should be accepted?**

If Projects S and L are mutually exclusive, ? If S & L are independent, ?

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**Using NPV method, which project(s) should be accepted?**

If Projects S and L are mutually exclusive,….. If S & L are independent, accept….. What happens to the NPV as the cost of capital changes?

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**e(1) What is the Internal Rate of Return (IRR)**

1 2 3 CF0 CF1 CF2 CF3 Cost Inflows

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**Internal Rate of Return (IRR)**

1 2 3 CF0 CF1 CF2 CF3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

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** NPV: Enter k, solve for NPV. CF k NPV 1 .**

1 . IRR: Enter NPV = 0, solve for IRR.

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**What is Project L’s IRR? 1 2 3 IRR = ? -100.00 10 60 80 PV1 PV2 PV3**

1 2 3 IRR = ? 10 60 80 PV1 PV2 PV3 0 = NPV

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**Enter CFs in CFLO, then press IRR:**

What is Project L’s IRR? 1 2 3 IRR = ? 10 60 80 PV1 PV2 PV3 Enter CFs in CFLO, then press IRR: 0 = NPV IRRL = 18.13%. IRRS = 23.56%.

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**e(2) How is a project’s IRR related to a bond’s YTM?**

1 2 10 IRR = ? 90 90 1090

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**How is a project’s IRR related to a bond’s YTM?**

They both measure percentage (rate of) return. A bond’s YTM is its IRR. 1 2 10 IRR = ? 90 90 1090 IRR = 7.08% (use TVM or CFLO).

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**e(3) Rationale for the IRR Method?**

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**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%. Profitable.

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**IRR Acceptance Criteria**

If IRR > k, accept project. If IRR < k, reject project.

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**Using IRR method, which project(s) should be accepted?**

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**Using IRR method, which project(s) should be accepted?**

If S and L are independent, ………. If S and L are mutually exclusive, accept…………. What effect does a change in the cost of capital have on the IRR?

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**f(1) Define Profitability Index (PI)**

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**Define Profitability Index (PI)**

PV of inflows PV of outflows PI = PI measures a project’s “bang for the buck”.

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**Calculate each project’s PI.**

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**Calculate each project’s PI.**

Project L: $ $ $60.11 $100 PIL = = 1.19. Project S: $ $ $15.03 $100 PIS = = 1.20.

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**PI Acceptance Criteria**

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**PI Acceptance Criteria**

If PI > 1, accept. If PI < 1, reject. The higher the PI, the better the project. For mutually exclusive projects, take the one with the highest PI. Therefore, accept L and S if independent; only accept S if mutually exclusive. Any problems with using PI?

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**g(1) Construct NPV Profiles**

Enter CFs in CFLO and find NPVL and NPVS at different discount rates: NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 k 5 10 15 20

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**NPV ($) Discount Rate (%) NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5 k 5**

5 10 15 20 50 40 Crossover Point = 8.7% 30 20 S IRRS = 23.6% 10 L Discount Rate (%) 5 10 15 20 23.6 -10 Vertical intercept horizontal intercept crossover point IRRL = 18.1%

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**NPV and IRR always lead to the same accept/reject decision for independent projects.**

IRR > k and NPV > 0 Accept. k > IRR and NPV < 0. Reject. k (%) IRR

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**g(2) Mutually Exclusive Projects**

NPV k < 8.7: NPVL > NPVS , IRRS > IRRL CONFLICT L k > 8.7: NPVS > NPVL , IRRS > IRRL NO CONFLICT S IRRs % k k IRRL

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**To Find the Crossover Rate**

1. Find cash flow differences between the projects. 2. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68, rounded to 8.7%. 3. Can subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.

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**How do you calculate the crossover point?**

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**Which project do you choose?**

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**h(1) Why do NPV profiles cross?**

Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opp. cost, the more valuable these funds, so high k favors small projects. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.

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**Reinvestment Rate Assumptions**

NPV assumes reinvestment at k (opportunity cost of capital). IRR assumes reinvestment at IRR. Reinvestment at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

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**i(1) Managers prefer IRR to NPV. Can we give them a better IRR?**

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**Managers prefer IRR to NPV. Can we give them a better IRR?**

Yes, modified IRR (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 forces cash inflows to be reinvested at WACC.

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**MIRR for Project L (k = 10%):**

1 2 3 10% 10.0 60.0 80.0 -100.0 10% 66.0 12.1 10% MIRR = 16.5% 158.1 -100.0 $158.1 (1+MIRRL)3 $100 = TV inflows PV outflows MIRRL = 16.5%

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**MIRR for Project L (k = 10%):**

1 2 3 10% 10.0 60.0 80.0 -100.0 10% 66.0 12.1 10% 158.1 -100.0 TV inflows PV outflows MIRRL = 16.5%

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**EXCEL HAS MIRR FUNCTION!**

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**Why use MIRR rather than IRR?**

MIRR correctly assumes reinvestment at opportunity cost = k. MIRR also avoids problems with multiple IRR’s with nonnormal projects. Managers like rate of return comparisons, and MIRR is better for this than IRR.

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**J: Pavillion Project: NPV and IRR?**

1 2 k = 10% -800 5,000 -5,000 What is NPV?, IRR? What is MIRR?

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**Pavillion Project: NPV and IRR?**

1 2 k = 10% -800 5,000 -5,000 Enter CFs in CFj, enter I/YR = 10. NPV = -$386.78 IRR = ERROR. Why?

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**How do we find the IRR on a 12c?**

Make a guess for i and key it in i. RCL g R/S.

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**We got IRR = ERROR because there **

are 2 IRRs. Nonnormal CFs with two sign changes. Here’s a picture: NPV NPV Profile IRR2 = 400% 450 k 100 400 IRR1 = 25% -800

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Logic of Multiple IRRs At very low disc. rates, the PV of CF2 is large & negative, so NPV < 0. At very high disc. rates, the PV of CF1 and CF2 are both low, so CF0 dominates and again NPV < 0. In between, the disc. rate hits CF2 harder than CF1 , so NPV > 0. Result: 2 IRRs.

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**When there are nonnormal CFs, use MIRR:**

1 2 -800,000 5,000,000 -5,000,000 PV 10% = -4,932, TV 10% = 5,500, MIRR = 5.6%

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j(2) Accept Project P?

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Accept Project P? NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.

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**NEW QUESTION: Which of the following mutually exclusive project’s is better? (000s)**

1 2 3 4 Project S: (100) Project L: 60 33.5 60 33.5 33.5 33.5 23

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S L CF , ,000 CF , ,500 Nj I NPV , ,190 NPVL > NPVS. But is L better? Can’t say yet. Need to perform common life analysis.

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**Note that Project S could be repeated after 2 years to generate additional profits.**

Can use either replacement chain or equivalent annual annuity analysis to make decision.

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**Franchise S with Replication:**

Replacement Chain Approach (000s) Franchise S with Replication: 1 2 3 4 Franchise S: (100) 60 60 (100) (40) 60 60 NPV = $7,547.

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Or, use NPVs: 1 2 3 4 4,132 3,415 7,547 4,132 10% Compare to Franchise L NPV = $6,190.

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**Equivalent Annual Annuity (EAA) Approach**

Finds the constant annuity payment whose PV is equal to the project’s raw NPV over its original life. 28

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**EAA Calculator Solution**

Project S PV = Raw NPV = $4,132. n = Original project life = 2. k = 10%. Solve for PMT = EAAS = $2,381. Project L PV = $6,190; n = 4; k = 10%. Solve for PMT = EAAL = $1,953. 29

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**The project, in effect, provides an annuity of EAA. **

EAAS > EAAL so pick S. Replacement chains and EAA always lead to the same decision if cash flows are expected to stay the same. 30

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**If the cost to repeat S in two years rises to $105,000, which is best**

If the cost to repeat S in two years rises to $105,000, which is best? (000s) 1 2 3 4 Franchise S: (100) 60 60 (105) (45) 60 60 NPVS = $3,415 < NPVL = $6,190. Now choose L.

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**Abandon because losing money, e.g., smokeless cigarette.**

Types of Abandonment Sale to another party who can obtain greater cash flows, e.g., IBM sold typewriter division. Abandon because losing money, e.g., smokeless cigarette. 31

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**Consider another project with a 3-year life**

Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value. Year 1 2 3 CF ($5,000) 2,100 2,000 1,750 Salvage Value $5,000 3,100 2,000

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**CFs Under Each Alternative (000s)**

1 2 3 1. No termination 2. Terminate 2 years 3. Terminate 1 year (5) 2.1 5.2 2 4 1.75

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**Assuming a 10% cost of capital, what is the project’s optimal, or economic life?**

NPV(no) = -$123. NPV(2) = $215. NPV(1) = -$273.

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Conclusions The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life.

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**The project is acceptable only if operated for 2 years. **

Conclusions The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life. The ability to abandon a project may make an otherwise unattractive project acceptable. Abandonment possibilities will be very important when we get to risk. 35

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**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

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**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...)

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If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.

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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...)

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**Reason: Companies want to avoid the direct costs (i. e**

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...)

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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...)

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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 post-audit process and tie the managers’ compensation to the subsequent performance of the project.

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11 - 1 Should we build this plant? CHAPTER 11 The Basics of Capital Budgeting.

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