Capital Budgeting (2)

What are Capital expenditures?

Such expenditures which are expected to provide benefits over a period of time greater than one year.

Plans for capital expenditure are summarized in a Capital Budget.

What is Capital Budgeting?What is Capital Budgeting?What is Capital Budgeting?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 process of identifying, analyzing, and selecting

investment projects whose returns (cash flows) are

expected to extend beyond one year.

Project ClassificationsProject Classifications1.Replacement: maintenance of business

2.Replacement: cost reduction

3.Expansion of existing products or markets

4.Expansion into new products or markets

5.Safety and/or environmental projects

6.Research and development

7. Long-term contracts

Project Evaluation: Project Evaluation: Alternative MethodsAlternative MethodsProject Evaluation: Project Evaluation: Alternative MethodsAlternative Methods

Payback Period (PBP)

Discounted Payback period

Internal Rate of Return (IRR)

Net Present Value (NPV)

Modified Internal Rate of Return (MIRR)

Profitability Index (PI)

Payback Period (PBP)

Discounted Payback period

Internal Rate of Return (IRR)

Net Present Value (NPV)

Modified Internal Rate of Return (MIRR)

Profitability Index (PI)

What is the payback period?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?

Proposed Project DataProposed Project DataProposed Project DataProposed Project Data

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW).

She has determined that the after-tax cash flows for the project will be

$10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of

the Years 1 through 5. The initial cash outlay will be $40,000.

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW).

She has determined that the after-tax cash flows for the project will be

$10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of

the Years 1 through 5. The initial cash outlay will be $40,000.

Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)

PBPPBP is the period of time required for the cumulative

expected cash flows from an investment project to equal

the initial cash outflow.

PBPPBP is the period of time required for the cumulative

expected cash flows from an investment project to equal

the initial cash outflow.

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K

Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of last negative cumulative cash flow

value.

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of last negative cumulative cash flow

value.

CumulativeCash Flows

-40 K 10 K 12 K 15 K 10 K 7 K

0 1 2 3 4 5

-40 K -30 K -18 K -3 K 7 K 14 K

PBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance Criterion

Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]

Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]

The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.

Should this project be accepted?

PBP Strengths PBP Strengths and Weaknessesand WeaknessesPBP Strengths PBP Strengths and Weaknessesand Weaknesses

StrengthsStrengths:: Easy to use and

understand

Can be used as a measure of liquidity

Easier to forecast ST than LT flows

StrengthsStrengths:: Easy to use and

understand

Can be used as a measure of liquidity

Easier to forecast ST than LT flows

WeaknessesWeaknesses:: Does not account

for TVM

Does not consider cash flows

beyond the PBP

Cutoff period is subjective

Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)

IRR is that discount rate that makes the present value of the future cash inflows from an investment project equal to the

present value of the cash outflows.

It is also the compound annual rate of return that the firm will earn if it invests in the project and receives the given cash inflows.

CF1 CF2 CFn (1+IRR)1 (1+IRR)2 (1+IRR)n

+ . . . ++ICO =

Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K

ABC. Co. wants to know whether it should invest in the project, if the minimum required rate of return on the project is 13%, calculate the IRR for the project ?

$15,000 $10,000 $7,000

IRR SolutionIRR Solution IRR SolutionIRR Solution

$10,000 $12,000

(1+IRR)1 (1+IRR)2

Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000.

+ +

++$40,000 =

(1+IRR)3 (1+IRR)4 (1+IRR)5

IRR Solution (Try 10%)IRR Solution (Try 10%)IRR Solution (Try 10%)IRR Solution (Try 10%)

$40,000$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $ 7,000(PVIF10%,5)

$40,000$40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621)

$40,000$40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347

= $41,444$41,444 [[Rate is too low!!Rate is too low!!]]

IRR Solution (Try 15%)IRR Solution (Try 15%)IRR Solution (Try 15%)IRR Solution (Try 15%)

$40,000$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $ 7,000(PVIF15%,5)

$40,000$40,000 = $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $ 7,000(.497)

$40,000$40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479

= $36,841$36,841 [[Rate is too high!!Rate is too high!!]]

The discount rate necessary to discount the cash flow stream to Rs.40,000 must therefore fall somewhere between 10 and 15%.

Present value at 10% > ICO > Present value at 15%

Rs.41,444 > ICO > Rs.36,841

=0.10 + (0.15 – 0.10) (41,444 – 40,000)

41,444-36,841

IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)

IRR = .10 +0.0157 = .1157 or 11.57%

The Decision CriteriaThe Decision Criteria

When IRR is used to make accept-reject decisions, the decision criteria are as follows:-

If the IRR is greater than the cost of capital (RRR) ,accept the project.

If the IRR is less than the cost of capital (RRR), reject the project.

IRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance Criterion

No! The firm will receive 11.57% for each dollar invested in this project at

a cost of 13%. [ IRR < RRR ]

No! The firm will receive 11.57% for each dollar invested in this project at

a cost of 13%. [ IRR < RRR ]


IRR Strengths IRR Strengths and Weaknessesand WeaknessesIRR Strengths IRR Strengths and Weaknessesand Weaknesses

StrengthsStrengths: : Accounts for

TVM

Considers all cash flows

Less subjectivity

StrengthsStrengths: : Accounts for

TVM

Considers all cash flows

Less subjectivity

WeaknessesWeaknesses: : Assumes all cash

flows reinvested at the IRR

Difficulties with project rankings

and Multiple IRRs

What is the difference between What is the difference between independent and mutually independent and mutually exclusive projects?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.

Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)

NPV is the present value of an investment project’s net cash

inflows minus the project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ - ICOICONPV =

ABC. Co. wants to know whether it should invest in the project, if the minimum required rate of return on the project is 13%, calculate the NPV for the project ?

$10,000 $7,000

NPV SolutionNPV Solution NPV SolutionNPV Solution

$10,000 $12,000 $15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - $40,000$40,000(1.13)4 (1.13)5

NPVNPV = +

NPV SolutionNPV SolutionNPV SolutionNPV Solution

NPVNPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $ 7,000(PVIF13%,5) - $40,000$40,000

NPVNPV = $10,000(.885) + $12,000(.783) + $15,000(.693) + $10,000(.613) + $ 7,000(.543) - $40,000$40,000

NPVNPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000$40,000

= - $1,428$1,428


If the present value of cash inflows exceeds the present value of cash outflows – the firm should accept a proposal – i.e. with a NPV equal to zero or more (positive)

If NPV is negative, the project should be rejected.

NPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance Criterion

No! The NPV is negative. [Reject Reject as NPVNPV < 00 ]

No! The NPV is negative. [Reject Reject as NPVNPV < 00 ]

the required rate is 13% for projects of this type.


NPV Strengths NPV Strengths and Weaknessesand WeaknessesNPV Strengths NPV Strengths and Weaknessesand Weaknesses

StrengthsStrengths:: Cash flows assumed to be reinvested at the required rate of return. Accounts for TVM. Considers all

cash flows.

StrengthsStrengths:: Cash flows assumed to be reinvested at the required rate of return. Accounts for TVM. Considers all

cash flows.

WeaknessesWeaknesses:: May not preferred

for managerial decisions.

What is an NPV Profile?What is an NPV Profile?

A graph that plots a project’s NPV against the cost of capital rates is defined as the project’s net present value profile.

Net Present Value ProfileNet Present Value Profile

Shows a curvilinear relationship between present value for a project and the discount rate employed.

IRR can be determined very easily form an NPV profile at the point where the curve cuts the horizontal axis.

Expected After tax Net cash flows

Year Project S Project L

0 ($1,000) ($1,000)

1 500 100

2 400 300

3 300 400

4 100 600

-100

300

0 5 10 15

NPV ($)

Discount Rate (%)IRRL = 11.8%

IRRS = 14.5%

r

0

5

10

15

NPVL

400

206.5

49.18

(80.14)

NPVS

300

180.42

78.82

(8.33)

S

L

If projects are ranked differently using these methods, conflict in rankings will be due one or combination of the following three project differences:-

1.Scale of investment – cost of project differs

2.Cash flow Pattern – time of cash flows differs

3.Project life- projects have unequal useful lives

Ranking ProblemsRanking Problems When Projects are mutually exclusive,

ranking enables the firm to determine which project is acceptable.

For example:

Project NPV IRR Rank

S $78.82 14.5% 1

L $49.18 11.8% 2

In ranking mutually exclusive projects ,NPV and IRR can lead to conflicting decisions.

Whether or not a conflict occurs depends on the cost of capital and the cross over rate.

Project NPV Rank

S $180.42 2

L $206.50 1

Modified Internal Rate of ReturnModified Internal Rate of Return PV costs =Terminal Value

(1+ MIRR)n

PV= Investment outlays

TV = compounded value of all cash

inflows

MIRR= Interest rate that causes TV equal to PV.

PV= TV

(1+ MIRR)n

40,000 = 71,071

(1+MIRR)5

(1+MIRR)5 =1.7768

1+MIRR=1.77681/5

MIRR=1.1218-1

MIRR=0.1218 or 12.18%


When MIRR is used to make accept-reject decisions, the decision criteria are as follows:-

If the MIRR is greater than the cost of capital (RRR) ,accept the project.

If the MIRR is less than the cost of capital (RRR), reject the project.

MIRR Strengths MIRR Strengths and Weaknessesand WeaknessesMIRR Strengths MIRR Strengths and Weaknessesand Weaknesses

StrengthsStrengths: : Cash flows

assumed to be reinvested at the cost of capital.

Better indicator of projects true profitability.

StrengthsStrengths: : Cash flows

assumed to be reinvested at the cost of capital.

Better indicator of projects true profitability.

WeaknessesWeaknesses: : Conflict may occur

if the projects differ in size.

Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)

PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ ICOICOPI =


As long as the Profitability index is 1.0 or greater, the investment proposal is acceptable.

Profitability index less than 1.0 , the investment proposal is rejected.

PI Acceptance CriterionPI Acceptance Criterion PI Acceptance CriterionPI Acceptance Criterion

No! The PIPI is less than 1.00. This means that the project is not profitable.

[Reject Reject as PIPI < 1.001.00 ]

No! The PIPI is less than 1.00. This means that the project is not profitable.

[Reject Reject as PIPI < 1.001.00 ]

PIPI = $38,572 / $40,000

= .9643


PI Strengths PI Strengths and Weaknessesand WeaknessesPI Strengths PI Strengths and Weaknessesand Weaknesses

StrengthsStrengths:: Same as NPV

Allows comparison of different scale projects

StrengthsStrengths:: Same as NPV

Allows comparison of different scale projects

WeaknessesWeaknesses:: Same as NPV

Provides only relative profitability

Potential Ranking Problems

Evaluation SummaryEvaluation Summary

Method Project Comparison Decision

PBP 3.3 3.5 Accept

IRR 11.47% 13% Reject

NPV -$1,424 $0 Reject

MIRR

PI

12.18%

.96

13%

1.00

Reject

Reject

Capital RationingCapital Rationing

Capital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures

during a particular period.

Example: Mr.A must determine what investment opportunities to undertake. He is limited to a maximum expenditure of $65,000 only for this capital budgeting period.

Summary of ComparisonSummary of Comparison

Method Projects Accepted Value Added

PI C, E, F, and G $76,000

NPV C and B $57,000

IRR C, D, and F $54,000

PIPI generates the greatestgreatest increaseincrease in shareholder wealth shareholder wealth when a limited capital

budget exists for a single period.

Documents

Capital Budgeting (2)