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Relevant cash flowsWorking capital treatmentUnequal project livesAbandonment valueInflation

CHAPTER 12Project Cash Flow Analysis

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Cost: $200,000 + $10,000 shipping + $30,000 installation.

Depreciable cost $240,000.Inventories will rise by $25,000 and

payables will rise by $5,000.Economic life = 4 years.Salvage value = $25,000.MACRS 3-year class.

Proposed Project

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Incremental gross sales = $250,000.

Incremental cash operating costs = $125,000.

Tax rate = 40%.

Overall cost of capital = 10%.

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0 1 2 3 4

InitialOutlay

OCF1 OCF2 OCF3 OCF4

+ Terminal CF

NCF0 NCF1 NCF2 NCF3 NCF4

Set up without numbers a time line for the project CFs.

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= Corporate cash flow with project

minus

Corporate cash flow without project

Incremental Cash Flow

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NO. The costs of capital are already incorporated in the analysis since we use them in discounting.

If we included them as cash flows, we would be double counting capital costs.

Should CFs include interest expense? Dividends?

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NO. This is a sunk cost. Focus on incremental investment and operating cash flows.

Suppose $100,000 had been spent last year to improve the production line

site. Should this cost be included in the analysis?

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Yes. Accepting the project means we will not receive the $25,000. This is an opportunity cost and it should be charged to the project.

A.T. opportunity cost = $25,000 (1 - T) = $15,000 annual cost.

Suppose the plant space could be leased out for $25,000 a year. Would

this affect the analysis?

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Yes. The effects on the other projects’ CFs are “externalities”.

Net CF loss per year on other lines would be a cost to this project.

Externalities will be positive if new projects are complements to existing assets, negative if substitutes.

If the new product line would decrease sales of the firm’s other products by

$50,000 per year, would this affect the analysis?

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Net Investment Outlay at t = 0 (000s)

EquipmentFreight + Inst.Change in NWC

Net CF0

EquipmentFreight + Inst.Change in NWC

Net CF0

($200)(40)(20)

($260)

($200)(40)(20)

($260)

NWC = $25,000 - $5,000= $20,000.

NWC = $25,000 - $5,000= $20,000.

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Basis = Cost + Shipping + Installation $240,000

Depreciation Basics

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Year1234

% 0.330.450.150.07

Depr.$ 79 108 36 17

x Basis =

Annual Depreciation Expense (000s)

$240

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Net revenueDepreciationBefore-tax incomeTaxes (40%)Net incomeDepreciationNet operating CF

$125 (79)$ 46 (18)$ 28 79$107

Year 1

Year 1 Operating Cash Flows (000s)

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Net revenueDepreciationBefore-tax incomeTaxes (40%)Net incomeDepreciationNet operating CF

Net revenueDepreciationBefore-tax incomeTaxes (40%)Net incomeDepreciationNet operating CF

$125 (79)$ 46 (18)$ 28 79$107

$125 (79)$ 46 (18)$ 28 79$107

$125 (17)$108 (43)$ 65 17$ 82

$125 (17)$108 (43)$ 65 17$ 82

Year 4Year 4Year 1Year 1

Year 4 Operating Cash Flows (000s)

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Net Terminal Cash Flow at t = 4 (000s)

Salvage valueTax on SVRecovery on NWCNet terminal CF

Salvage valueTax on SVRecovery on NWCNet terminal CF

$25 (10) 20 $35

$25 (10) 20 $35

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What if you terminate a project before the asset is fully depreciated?

Cash flow from sale = Sale proceeds- taxes paid.

Taxes are based on difference between sales price and tax basis, where:

Basis = Original basis - Accum. deprec.

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Original basis = $240.After 3 years = $17 remaining.Sales price = $25.Tax on sale = 0.4($25-$17)

= $3.2.Cash flow = $25-$3.2=$21.7.

Example: If Sold After 3 Years (000s)

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Project Net CFs on a Time Line

Enter CFs in CFLO register and I = 10.NPV = $81,573.IRR = 23.8%.

*In thousands.

0 1 2 3 4

(260)* 107 118 89 117

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What is the project’s MIRR? (000s)

(260)MIRR = ?

0 1 2 3 4

(260)* 107 118 89 117.0

97.9

142.8

142.4

500.1

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1. Enter positive CFs in CFLO:I = 10; Solve for NPV = $341.60.

2. Use TVM keys: PV = 341.60, N = 4I = 10; PMT = 0; Solve for FV = 500.10. (TV of inflows)

3. Use TVM keys: N = 4; FV = 500.10;PV = -260; PMT= 0; Solve for I = 17.8.

MIRR = 17.8%.

Calculator Solution

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What is the project’s payback? (000s)

Cumulative:

Payback = 2 + 35/89 = 2.4 years.

0 1 2 3 4

(260)*

(260)

107

(153)

118

(35)

89

54

117

171

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If this were a replacement rather than a new project, would the analysis

change?

Yes. The old equipment would be sold and the incremental CFs wouldbe the changes from the old to the new situation.

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Revenues.

Costs.

The relevant depreciation would be the change with the new equipment.

Also, if the firm sold the old machine now, it would not receive the salvage value at the end of the machine’s life.

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Coordination with other departments

Maintaining consistency of assumptions

Elimination of biases in the forecasts

What is the role of the financial staff in the cash flow estimation process?

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CF’s are estimated for many future periods.

If company has many projects and errors are random and unbiased, errors will cancel out (aggregate NPV estimate will be OK).

Studies show that forecasts often are biased (overly optimistic revenues, underestimated costs).

What is cash flow estimation bias?

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Routinely compare CF estimates with those actually realized and reward managers who are forecasting well, penalize those who are not.

When evidence of bias exists, the project’s CF estimates should be lowered or the cost of capital raised to offset the bias.

What steps can management take to eliminate the incentives for cash flow

estimation bias?

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Investment in a project may lead to other valuable opportunities.

Investment now may extinguish opportunity to undertake same project in the future.

True project NPV = NPV + value of options.

What is option value?

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No. Net revenues are assumed to be constant over the 4-year project life, so inflation effects have not been incorporated into the cash flows.

If 5% inflation is expected over the next 5 years, are the firm’s cash flow

estimates accurate?

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In DCF analysis, k includes an estimate of inflation.

If cash flow estimates are not adjusted for inflation (i.e., are in today’s dollars), this will bias the NPV downward.

This bias may offset the optimistic bias of management.

Real vs. Nominal Cash flows

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S and L are mutually exclusive and will be repeated. k = 10%. Which is

better? (000s)

0 1 2 3 4

Project S:(100)

Project L:(100)

60

33.5

60

33.5 33.5 33.5

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S LCF0 -100,000 -100,000CF1 60,000 33,500Nj 2 4I 10 10

NPV 4,132 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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Project S with Replication:

NPV = $7,547.

Replacement Chain Approach (000s)

0 1 2 3 4

Project S:(100) (100)

60 60

60(100) (40)

6060

6060

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Compare to Project L NPV = $6,190.Compare to Project L NPV = $6,190.

Or, use NPVs:

0 1 2 3 4

4,1323,4157,547

4,13210%

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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.

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EAA Calculator Solution

Project SPV = Raw NPV = $4,132.n = Original project life = 2.k = 10%.Solve for PMT = EAAS = $2,381.

Project LPV = $6,190; n = 4; k = 10%.Solve for PMT = EAAL = $1,953.

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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.

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If the cost to repeat S in two years rises to $105,000, which is best? (000s)

NPVS = $3,415 < NPVL = $6,190.Now choose L.NPVS = $3,415 < NPVL = $6,190.Now choose L.

0 1 2 3 4

Project S:(100)

60 60(105) (45)

60 60

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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.

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Year0123

CF ($5,000) 2,100 2,000 1,750

Abandonment Value $5,000 3,100 2,000 0

Consider another project with a 3-year life. If abandoned prior to Year 3, the

machinery will have positive abandonment value.

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1.751. No abandonment

2. Abandon 2 years

3. Abandon 1 year

(5)

(5)

(5)

2.1

2.1

5.2

2

4

0 1 2 3

CFs Under Each Alternative (000s)

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NPV(no) = -$123.

NPV(2) = $215.

NPV(1) = -$273.

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

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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.

Conclusions