Capital BudgetingRisk Considerations

Section 1Let’s Recap Capital Budgeting

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What is Capital Budgeting?

The process of identifying, analyzing, and selecting investment projects whose returns (cash flows) are expected to extend beyond one year;

The examples are;a. New products or expansion of existing products;b. Replacement of existing equipment or buildings;c. Research and development;d. Exploration;

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The Capital Budgeting Process

Generate investment proposals consistent with the firm’s strategic objectives;

Evaluate projected cash flows;

Select projects based on a value-maximizing acceptance criterion;

Reevaluate implemented investment projects continually and perform post audits for completed projects;

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Calculating Project Cash Flows

Initial cash outflow is the initial net cash investment;

Interim incremental net cash flows are those net cash flows occurring after the initial cash investment but not including the final period’s cash flow;

Terminal-year incremental net cash flows are the final period’s net cash flow;

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Project Evaluation: Alternative Methods

Payback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI)

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Potential Problems Under Mutual Exclusivity Ranking of project proposals may create

contradictory results;a.scale of investment;b.cash flow pattern;c.project life;

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Section 2An Illustration of Asset Replacement Decision

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 Asset Replacement Example

Kandy Corporation is considering a replacement investment. The machine currently in use was originally purchased two years ago for $65,000. Tax-allowable depreciation is $13,000 per year for five years. The current market value of this machine is $23,000. The new machine being considered would cost $140,000, and require $4,000 shipping cost and $2,000 installation costs. The economic life of the machine is estimated as three years. Tax-allowable depreciation is $70,000 per year for the first two years. If the new machine is acquired, the investments in accounts receivable is expected to increase by $9,000, the inventory by $13,000, and accounts payable by $15,000. The before-tax net operating cash flow is estimated as $120,000 per year for the next three years with the old machine and, $143,000 per year for the next three years with the new machine. The expected resale value of the old and new machines in three years’ time would be

$4,000 and $6,600, respectively. The corporate tax rate is 30%. 9

 Asset Replacement Example

Requireda.Calculate the cash flows of proposed replacement project.b.Compute the NPV of the replacement project assuming a discount rate of 6% per annum.c.What is the proposed investment’s IRR?d.Use the computed IRR and NPV results and discuss the project accept / reject decision

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Asset Replacement Solution

$+Purchase Price of New Asset 140 000+Shipping and Installation 6 000-Proceeds from the sale of old asset 23 000+Tax on sale of old asset*** -4800 +Change in NWC 7000Initial Investment 125 200*Tax Calculation(Sales Price-Book Value)TaxRate=(23000 -(65000-26000))*0.3=(23000-39000)*0.3=-4800

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Asset Replacement Solution

Operating Cash Flows(New Machine) Year 1 Year 2 Year 3Cash inflow $143 000 $143 000 $143 000Depreciation $70 000 $70 000 0Taxable Basis $73 000 $73 000 $143 000Tax Charge $21 900 $21 900 $42 900Result $121 100 $121 100 $100 100

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Asset Replacement Solution

Operating Cash Flows(Old Machine) Year 1 Year 2 Year 3Cash inflow $120 000 $120 000 $120 000Depreciation $13 000 $13 000 $13 000Taxable Basis $107 000 $107 000 $107 000Tax Charge $32 100 $32 100 $32 100Result $87 900 $87 900 $87 900

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Asset Replacement Solution

Incremental Cash Flows(New Machine-Less Old Machine) Year 1 Year 2 Year 3 $ 33 200 $33 200 $12 200

Terminal Year Cash InflowLast Year’s Cash Inflow $12 200-Proceeds from old machine $ 4000+Proceeds from new machine $6600+Tax saving on sale of old machine $1200 -Tax on sale of new machine $180+Recovery of working capital $7000

Total $ 22 820 14

Asset Replacement Solution

Projected Cash Flows0 Year 1 Year 2 Year 3 -$125 200 $ 33 200 $ 33 200 $22 820

NPV=33200/(1+0.06)1+33200/(1+0.06)2+22820/(1+0.06)3-

125200=-$45 171 ✖IRR=-16% which is below 6% ✖

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Section 3Evaluation of Project Risk

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An Illustration of Total Risk

ANNUAL CASH FLOWS: YEAR 1PROPOSAL APROPOSAL A

State ProbabilityProbability Cash FlowCash Flow

Deep Recession .05 $ -3,000Mild Recession .25 1,000Normal .40 5,000Minor Boom .25 9,000Major Boom .05 13,000

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An Illustration of Total Risk

ANNUAL CASH FLOWS: YEAR 1PROPOSAL BPROPOSAL B

State ProbabilityProbability Cash FlowCash Flow

Deep Recession .05 $ -1,000Mild Recession .25 2,000Normal .40 5,000Minor Boom .25 8,000Major Boom .05 11,000

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CFCF11 PP11 (CFCF11)(P)(P11))

$ -3,000 .05 $ -150 1,000 .25 250 5,000 .40 2,000 9,000 .25 2,250 13,000 .05 650

=1.001.00 CFCF11=$5,000$5,000

Expected Value of Year 1 Cash Flows (Proposal A)

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(CFCF11)(P)(P11)) (CF (CF11 - CF - CF11))22(P(P11) )

$ -150 ( -3,000 - 5,000)22 (.05) (.05) 250 ( 1,000 - 5,000)22 (.25) (.25) 2,000 ( 5,000 - 5,000)22 (.40) (.40) 2,250 ( 9,000 - 5,000)22 (.25) (.25) 650 (13,000 - 5,000)22 (.05) (.05)

$ 5,000$ 5,000

Variance of Year 1 Cash Flows (Proposal A)

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Variance of Year 1 Cash Flows (Proposal A)

(CFCF11)(P)(P11)) (CF (CF11 - CF - CF11))22*(P*(P11) )

$ -150 3,200,000 250 4,000,000 2,000 0 2,250 4,000,000 650 3,200,000

$5,000$5,000 14,400,00014,400,000

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Summary of Proposal A

The standard deviation standard deviation = SQRT (14,400,000) = $3,795$3,795

The expected cash flow expected cash flow = $5,000$5,000

Coefficient of Variation (CV) = $3,795 / $5,000 Coefficient of Variation (CV) = $3,795 / $5,000 = = 0.7590.759

CV is a measure of CV is a measure of relativerelative risk risk and is the ratio of and is the ratio of standard deviation to the mean of the distribution.standard deviation to the mean of the distribution.

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Expected Value of Year 1 Cash Flows (Proposal B)

CFCF11 PP11 (CFCF11)(P)(P11))

$ -1,000 .05 $ -50 2,000 .25 500 5,000 .40 2,000 8,000 .25 2,000 11,000 .05 550

=1.001.00 CFCF11=$5,000$5,00023

(CFCF11)(P)(P11)) (CF(CF11 - CF - CF11))22(P(P11))

$ -50 ( -1,000 - 5,000)22 (.05) (.05) 500 ( 2,000 - 5,000)22 (.25) (.25) 2,000 ( 5,000 - 5,000)22 (.40) (.40) 2,000 ( 8,000 - 5,000)22 (.25) (.25) 550 (11,000 - 5,000)22 (.05) (.05)

$5,000$5,000

Variance of Year 1 Cash Flows (Proposal B)

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Variance of Year 1 Cash Flows (Proposal B)

(CFCF11)(P)(P11)) (CF (CF11 - CF - CF11))22(P(P11))

$ -50 1,800,000 500 2,250,000 2,000 0 2,000 2,250,000 550 1,800,000

$5,000$5,000 8,100,000 8,100,000 25

Summary of Proposal B

The standard deviation of B < A ($2,846< $3,795), so B < A ($2,846< $3,795), so ““BB”” is is lessless risky than risky than ““AA””..

The coefficient of variation of B < A (0.569<0.759), so The coefficient of variation of B < A (0.569<0.759), so ““BB”” has has lessless relative risk than relative risk than ““AA””..

The standard deviation standard deviation = SQRT (8,100,000)= $2,846$2,846

The expected cash flow expected cash flow = $5,000$5,000Coefficient of Variation (CV) = $2,846 / $5,000 Coefficient of Variation (CV) = $2,846 / $5,000

= 0.569= 0.569

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Probability Tree Approach

A graphic or tabular approach for organizing the possible cash-flow

streams generated by an investment. The presentation resembles the

branches of a tree. Each complete branch represents one possible cash-

flow sequence.27

Probability Tree Approach

Basket Wonders is examining a project that will have an initial initial

cost cost today of $900$900. Uncertainty surrounding the first year cash

flows creates three possible cash-flow scenarios in Year 1Year 1.

-$900-$900

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Probability Tree Approach

Node 1: 20% chance of a $1,200$1,200 cash-flow.

Node 2: 60% chance of a $450$450 cash-flow.

Node 3: 20% chance of a -$600-$600 cash-flow.

-$900-$900

(.20) $1,200$1,200

(.20) -$600-$600

(.60) $450$450

Year 1Year 1

11

22

33

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Probability Tree Approach

Each node in Year 2 Year 2

represents a branchbranch of our

probability tree.

The probabilities

are said to be conditional conditional

probabilitiesprobabilities.

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

22

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(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2 30

Joint Probabilities [P(1,2)].02 Branch 1.12 Branch 2.06 Branch 3

.21 Branch 4

.24 Branch 5

.15 Branch 6

.02 Branch 7

.10 Branch 8

.08 Branch 9

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

11

22

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(.60) $1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2 31

Project NPV Based on Probability Tree Usage

The probability tree accounts for the distribution of

cash flows. Therefore,

discount all cash flows at only the risk-freerisk-free rate of

return.

The NPV for branch i NPV for branch i of the probability tree for two years

of cash flows is

NPV = (NPVNPVii)(PPii)

NPVNPVii = CFCF11

(1 + RRff )11 (1 + RRff )22

CFCF22

- ICOICO

+

i = 1

z

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NPV for Each Cash-Flow Stream at 5% Risk-Free Rate

$ 2,238.32 $ 1,331.29 $ 1,059.18

$ 344.90 $ 72.79-$ 199.32

-$ 1,017.91-$ 1,562.13-$ 2,106.35

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

11

22

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(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2 33

Calculating the Expected Net Present Value (NPV) Branch NPV NPVii

Branch 1 $ 2,238.32Branch 2 $ 1,331.29Branch 3 $ 1,059.18Branch 4 $ 344.90Branch 5 $ 72.79Branch 6 -$ 199.32Branch 7 -$ 1,017.91Branch 8 -$ 1,562.13Branch 9 -$ 2,106.35

P(1,2) P(1,2) NPVNPVii * P(1,2) P(1,2) .02 $ 44.77 .12 $159.75 .06 $ 63.55 .21 $ 72.43 .24 $ 17.47 .15 -$ 29.90 .02 -$ 20.36 .10 -$156.21 .08 -$168.51

Expected Net Present Value Expected Net Present Value = -$ 17.01-$ 17.0134

Calculating the Variance of the Net Present Value NPVNPVii

$ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79-$ 199.32-$ 1,017.91-$ 1,562.13-$ 2,106.35

P(1,2) P(1,2) (NPV(NPVii - NPVNPV )2[P(1,2)P(1,2)] .02 $ 101,730.27 .12 $ 218,149.55 .06 $ 69,491.09 .21 $ 27,505.56 .24 $ 1,935.37 .15 $ 4,985.54 .02 $ 20,036.02 .10 $ 238,739.58 .08 $ 349,227.33

Variance Variance = $1,031,800.31$1,031,800.3135

Section 3 Managerial Options

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Managerial (Real) Options

Management flexibility to make future decisions that affect a project’s

expected cash flows, life, or future acceptance.

Project Worth = NPV + Option(s) Value

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Managerial (Real) OptionsExpand (or contract)Expand (or contract)

– Allows the firm to expand (contract) production if conditions become favorable (unfavorable).

AbandonAbandon– Allows the project to be terminated early.

PostponePostpone– Allows the firm to delay undertaking a project

(reduces uncertainty via new information).38

Previous Example with Project Abandonment

Assume that this project can be abandoned at the end of the first year

for $200$200.

What is the project worthproject worth?

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

11

22

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(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2 39

Project AbandonmentNode 3Node 3:

(500500/1.05)(.1)+ (-100-100/1.05)(.5)+ (-700-700/1.05)(.4)=

($476.19)(.1)+ -($ 95.24)(.5)+ -($666.67)(.4)=

-($266.67)-($266.67)

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

11

22

33

(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2 40

Project Abandonment

--$900$900

(.20.20) $1,200$1,200

(.20.20) -$600-$600

(.6060) $450$450

Year 1Year 1

11

22

33

(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(.10) $ 500$ 500

(.50) -$ 100-$ 100

(.40) -$ 700-$ 700

Year 2Year 2

The optimal decision at the

end of Year 1 Year 1 is to abandon the

project for $200$200.

$200$200 >

-($266.67)-($266.67)

What is the ““newnew”” project value?

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Project Abandonment $ 2,238.32 $ 1,331.29 $ 1,059.18

$ 344.90 $ 72.79-$ 199.32

-$ 1,280.95

-$900-$900

(.20.20) $1,200$1,200

(.20.20) -$400*-$400*

(.6060) $450$450

Year 1Year 1

11

22

33

(.60) $1,200$1,200

(.30) $ 900$ 900

(.10) $2,200$2,200

(.35) $ 900$ 900

(.40) $ 600$ 600

(.25) $ 300 $ 300

(1.0) $ 0 $ 0

Year 2Year 2

*-$600 + $200 abandonment

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Summary of the Addition of the Abandonment Option

* For “True” Project considering abandonment option

The standard deviation*standard deviation* SQRT (740,326) = $857.56$857.56 The expected NPV* expected NPV* = $ 71.88 $ 71.88

NPV* NPV* = Original NPV + Abandonment OptionAbandonment Option

Thus, $71.88 Thus, $71.88 = -$17.01 + OptionOption Abandonment Option Abandonment Option = $ 88.89$ 88.89

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Thank You

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