10: Chapter 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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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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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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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?
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Payback for Franchise L (Long: Most CFs in out years)
0 CFt -100 Cumulative -100 PaybackL = 2 + 1 10 -90 30/80 2
2.4
3 80 50
60 100 -30 0
= 2.375 years
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Franchise S (Short: CFs come quickly)
0 CFt -100 1
1.6 2
3 20 40
70 100 50 -30 0 20
Cumulative -100 PaybackS
= 1 + 30/50 = 1.6 years
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Strengths of Payback: 1. Provides an indication of a project's risk and liquidity. 2. Easy to calculate and understand. Weaknesses of Payback: 1. Ignores the TVM. 2. Ignores CFs occurring after the payback period.
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Discounted Payback: Uses discounted rather than raw CFs.
0 CFt PVCFt -100 -100 10% 1 10 9.09 -90.91 2 60 49.59 -41.32 3 80 60.11 18.79
Cumulative -100 Discounted = 2 payback
+ 41.32/60.11 = 2.7 yrs
Recover invest. + cap. costs in 2.7 yrs.
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NPV: Sum of the PVs of inflows and outflows.
CFt NPV = . t t = 0 (1 + r )
Cost often is CF0 and is negative.
CFt NPV = - CF0 . t t =1 (1 + r )
n
n
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What's Franchise L's NPV?
Project L: 0 -100.00 10% 1 10 2 60 3 80
9.09 49.59 60.11 18.79 = NPVL
NPVS = $19.98.
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Calculator Solution Enter in CFLO for L: -100 10 60 80 10 CF0 CF1 CF2 CF3 I NPV = 18.78 = NPVL
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Rationale for the NPV Method NPV = PV inflows - 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 franchise(s) should be accepted?
If Franchise S and L are mutually exclusive, accept S because NPVs > NPVL . If S & L are independent, accept both; NPV > 0.
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Internal Rate of Return: IRR
0 CF0 Cost 1 CF1 2 CF2 Inflows 3 CF3
IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.
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NPV: Enter r, solve for NPV.
CFt (1 + r ) t = NPV . t =0
n
IRR: Enter NPV = 0, solve for IRR.
CFt t = 0. t = 0 (1 + IRR)
n
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What's Franchise L's IRR?
0
IRR = ?
1 10
2 60
3 80
-100.00 PV1 PV2 PV3 0 = NPV
Enter CFs in CFLO, then press IRR: IRRL = 18.13%. IRRS = 23.56%.
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Find IRR if CFs are constant:
0 -100
INPUTS OUTPUT 3
N I/YR IRR = ?
1 40
2 40
-100
PV
3 40
40
PMT
0
FV
9.70%
Or, with CFLO, enter CFs and press IRR = 9.70%.
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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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Decisions on Projects S and L per IRR
If S and L are independent, accept both. IRRs > r = 10%. If S and L are mutually exclusive, accept S because IRRS > IRRL .
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Construct NPV Profiles Enter CFs in CFLO and find NPVL and NPVS at different discount rates:
r 0 5 10 15 20 NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5
NPV ($)
60 50 40 30 20 10 0 0 -10 5 10 15 20 23.6
10 - 22 r 0 5 10 15 20 NPVL 50 33 19 7 (4) NPVS 40 29 20 12 5
Crossover Point = 8.7%
S L IRRS = 23.6%
Discount Rate (%)
IRRL = 18.1%
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NPV and IRR always lead to the same accept/reject decision for independent projects:
NPV ($) IRR > r and NPV > 0 Accept. r > IRR and NPV < 0. Reject.
IRR
r (%)
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Mutually Exclusive Projects
NPV
L
r < 8.7: NPVL> NPVS , IRRS > IRRL CONFLICT r > 8.7: NPVS> NPVL , IRRS > IRRL NO CONFLICT
S r 8.7 r
IRR
%
IRRL
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To Find the Crossover Rate
1. Find cash flow differences between the projects. See data at beginning of the case. 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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Two Reasons NPV Profiles Cross 1. 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. 2. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVS > NPVL.
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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.
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Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, 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.
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MIRR for Franchise L (r = 10%)
0 -100.0
10%
1 10.0
10% = MIRR 16.5%
2 60.0
10%
3 80.0 66.0 12.1 158.1 TV inflows
-100.0 PV outflows
$158.1 $100 = (1+MIRRL)3 MIRRL = 16.5%
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To find TV with 10B, enter in CFLO: CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80 I= 10 NPV = 118.78 = PV of inflows. Enter PV = -118.78, N = 3, I = 10, PMT = 0. Press FV = 158.10, = FV of inflows. = 0, Enter FV = 158.10 PV = -100, PMT N = 3. Press I = 16.50% = MIRR.
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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.
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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. Nuclear power plant, strip mine.
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Inflow (+) or Outflow (-) in Year
0 + 1 + + + + 2 + + + + 3 + + + 4 + + + + 5 + + N N NN N N NN NN
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Pavilion Project: NPV and IRR?
0 -800 1 5,000 2 -5,000
r = 10%
Enter CFs in CFLO, enter I = 10. NPV = -386.78 IRR = ERROR. Why?
We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs--two sign changes. Here's a picture:
NPV
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NPV Profile
IRR = 400%
450 0 -800 100 IRR1 = 25% 400 r
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Logic of Multiple IRRs 1. At very low discount rates, the PV of CF2 is large & negative, so NPV < 0. 2. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. 3. In between, the discount rate hits CF2 harder than CF1, so NPV > 0. 4. Result: 2 IRRs.
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Could find IRR 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 Now guess large IRR, say, 200: 200 STO IRR = 400% = upper IRR
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When there are nonnormal CFs and more than one IRR, use MIRR:
0 -800,000 1 5,000,000 2 -5,000,000
PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%
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Accept Project P?
NO. Reject because MIRR = 5.6% < r = 10%. Also, if MIRR < r, NPV will be negative: NPV = -$386,777.
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S and L are mutually exclusive and will be repeated. r = 10%. Which is better? (000s) 0 1 2 60 33.5 33.5 33.5 3 4
Project S: (100) 60 Project L: (100) 33.5
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CF0 CF1 Nj I NPV
S -100,000 60,000 2 10 4,132
L -100,000 33,500 4 10 6,190
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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Replacement Chain Approach (000s)
Franchise S with Replication:
0
1
2 60 (100) (40)
3
4
Franchise S: (100) 60 (100) 60
60 60
60 60
NPV = $7,547.
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Or, use NPVs: 0 4,132 3,415 7,547 1 10% 2 4,132 3 4
Compare to Franchise L NPV = $6,190.
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If the cost to repeat S in two years rises to $105,000, which is best? (000s) 0 1 2 60 (105) (45) 3 4
Franchise S: (100) 60
60
60
NPVS = $3,415 < NPVL = $6,190. Now choose L.
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Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value. Year 0 1 2 3 CF ($5,000) 2,100 2,000 1,750 Salvage Value $5,000 3,100 2,00...