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Gitman, Juchau, Flanagan, Principles of Managerial Finance 5e: © 2008 Pearson Education Australia 1

BFA281 Financial Management

Tony Stanger

Weeks 5 & 6

Capital Budgeting Techniques

(Chapter 9)


Learning Objectives

• Discuss the role of capital project evaluation techniques

• Apply the payback period method

• Apply the net present value method

• Apply the internal rate of return method

• Compare NPV and IRR

• Describe some other methods


Overview

• Capital budgeting is used to accept or rank capital projects

• The techniques employed need to integrate - time value (chapter 4) - risk and return (chapter 5) - valuation (chapters 6 and 7)

• The goal is to maximise shareholder wealth i.e. share price


Payback period

• Definition: the ‘payback period’ is the exact amount of time required for the firm to recover its initial investment

• Payback is calculated from net (after-tax) cash inflows

• Decision criterion:• Independent projects – acceptance of one project

does not exclude the acceptance of other projects• accept if payback period < maximum acceptable• reject if payback period > maximum acceptable

• Mutually exclusive projects – acceptance of one project excludes the acceptance of other projects

• accept project with shortest payback period if < maximum acceptable


Payback period

Example:

Project A Project B

Initial cash outlay ($10,000) ($10,000)

Annual net cash-flows

Year 1 $6,000 $5,000

Year 2 $4,000 $5,000

Year 3 $3,000 -

Year 4 $2,000 -

Year 5 $1,000 -

These projects have the same payback period which is two years


Payback period

Reasons for popularity:• Simple to calculate and easy to understand

• Widely used in practice• inconjuction with other techniques e.g. NPV and IRR• especially with small projects

• Deals with cash flows, not accounting profits• Used as a risk indicator

• The longer the payback period, the riskier the project

• Places emphasis on liquidity• Favours projects that alleviate liquidity problems


Payback period

Disadvantages• Unsophisticated as fails to properly account for

timing of project’s cash flows• does not discount cash flows i.e. ignores time value of

money

• Fails to take full account of project’s economic life• ignores cash flows after payback period

• Maximum acceptable period is arbitrarily chosen• In general, discriminates against projects with

long gestation periods


Discounted (sophisticated) cash flow methods of capital project evaluation• Net present value method (NPV) and

internal rate of return method (IRR)• Not as simple to calculate and easy to

understand as payback period method• However, increasingly used in practice because:

• focus on cash-flows, not accounting profits• take full account of timing of cash-flows and

time value of money

• If required rate of return for capital projects is properly determined, both methods result in shareholder wealth maximisation


Net present value (NPV)

• Difference between present value of project’s net cash receipts and present value of initial cash outlay, both calculated using business’s required rate of return for capital projects as discount rate

• NPV = (present value of net cash inflows) –

(initial investment)

= CF1/(1+k)1 + … + CFt/(1+k)t - CF0

= Σ [ CFt / (1 + k)t ] - CF0 from t = 1n

If CFt is an annuity

= (CFt)(PVIFAk,t) – CF0


Net present value (NPV)

• Decision criterion• For independent projects:

• accept if NPV > 0

• reject if NPV < 0

• indifferent if NPV = 0

• For mutually exclusive projects:• project with highest positive NPV should be preferred

• Value additivity principle• Value of business is sum of NPVs of its capital projects

• If the NPV is positive, the firm will earn a greater return than its cost of capital


Internal rate of return (IRR)

• The discount rate that equates the PV of net cash inflows with the initial investment

• Alternatively, the highest interest rate a business could afford to pay if it borrowed all funds needed for project, and used proceeds when received to pay interest and repay loan

• The IRR test guarantees the firm will earn at least its required return

• The IRR implies NPV = $0• More difficult than NPV to calculate



• Decision criterion:• For independent projects

• accept if IRR ≥ cost of capital• reject if IRR < cost of capital• indifferent if IRR = cost of capital

• For mutually exclusive projects• project with the highest IRR above the cost of

capital should be preferred



• Multiple or no IRRs• There may be as many IRRs as there are

sign changes in the cash flows e.g.

A project has the following cash flows:Initial investment ($14,545)Year 1 $34,182Year 2 ($20,000)

Solve for IRR: $14,545 = 34,182/(1+IRR) – 20,000/(1+IRR)2

IRR = 10% and 25%

If Required Rate of Return is 15%, it is unclear whether the project should be accepted



• Calculating IRR• Set NPV = $0 = CF1/(1+IRR)1 +…+ CFt/(1+IRR)t - CF0 for

t = 1n, where IRR = k, or

• Set NPV = $0 = Σ [ CFt / (1 + IRR)t ] - CF0 for t = 1n, where IRR = k

• If net cash flows CFt are constant i.e. an annuity• NPV = $0 = (CFt)(PVIFAIRR,t) – CF0

=> (PVIFAIRR,t) = CF0/CFt use Table A-4 to solve for IRR

• E.g. Bennett Company, Figure 9.3, p.395 • PVIFAIRR,5 = $42,000/$14,000 = 3• From Table A-4 IRR is 19 to 20%, approx. 20%



• Calculating IRR• set NPV = $0 = Σ [ CFt / (1 + IRR)t ] - CF0

from t = 1n, where IRR = k

• if net cash flows CFt are not an annuity• manually finding IRR from the above equation involves

trial and error and is time consuming• use financial calculator with IRR program or spreadsheet• graphically – plot NPV for various required rates of return• Interpolation (not covered in Gitman et al.)


Example

Kentiki Fast Food is developing an extra fast-food outlet. Costs and income flows are: $2 million site acquisition and development costs (this includes plant

and equipment) $400,000 plant & equipment straight line depreciable over 5 years (assume

no salvage value) Sales in year 1 of $600,000, $700,000 per year thereafter Cost of labour & materials = 40% of sales Policy is to sell outlet in 3 years, estimated sale price is 20% more than

initial cost including equipment at book value (ignore capital gains tax consequences for this example)

Sales in a similar outlet of ours to decline by $70,000 in year 1 only due to loss of customers and experienced staff to new outlet

Other costs: $150,000 annually (salaries, wages, training, power, cleaning, advertising)

Investment in working capital = 10% of annual sales The required rate of return is 10% Tax rate 47%


Example: cash flows in year 0

Initial development costs

Incremental working capital

Net cash flow, after tax

Net cash flow, pre tax

-$2,000,000

-$53,000

-$2,053,000

-$2,053,000



Sales Less: Cost of sales Gross profit Less: Operating costs Depreciation Net profit before tax Less: Tax Net profit after tax Add: Depreciation Operating cash flow after tax Incremental working capital Net cash flow, after tax Net cash flow, pre tax

$530,000 212,000 318,000 150,000 80,000 88,000 41,360 46,640 80,000 126,640 -17,000 109,640 151,000



Sales Less: Cost of sales Gross profit Less: Operating costs Depreciation Net profit before tax Less: Tax Net profit after tax Add: Depreciation Operating cash flow after tax Incremental working capital Net cash flow, after tax Net cash flow, pre tax

700,000 280,000 420,000 150,000 80,000 190,000 89,300 100,700 80,000 180,700 0 180,700 270,000



Sales Less: Cost of sales Gross profit Less: Operating costs Depreciation Net profit before tax Less: Tax Net profit after tax Add: Depreciation Operating cash flow after tax Proceeds of sale Recovery of working capital Net cash flow, after tax Net cash flow, pre tax

$700,000 280,000 420,000 150,000 80,000 190,000 89,300 100,700 80,000 180,700 2,400,000 70,000 2,650,700 2,740,000


Example: summary

Pre tax cash flowsPre tax cash flows

00 11 22 33

-$2,053,000-$2,053,000 $151,000$151,000 $270,000$270,000 $2,740,000$2,740,000

After tax cash flowsAfter tax cash flows

00 11 22 33

-$2,053,000-$2,053,000 $109,640$109,640 $180,700$180,700 $2,650,700$2,650,700


Example: calculating NPV and IRR

NPV = $109,640 + $180,700 + $2,650,700 - $2,053,000 (1.1) (1.1)2 (1.1)3

= 99,672.73 + 149,338.84 + 1,991,510.14 – 2,053,000 = 2,240,521.71 – 2,053,000 = $187,521.71

⇒ Accept project as NPV is > o

IRR (using IRR calculator function)

$2,053,000 = $109,640 + $180,700 + $2,650,700 (1 + IRR) (1 + IRR)2 (1 + IRR)3

⇒ IRR = 0.1344 or 13.44%

Accept project as IRR > 0.10 or 10%


Comparing NPV and IRR

Example: Bennett Company



Example: Bennett Company (Gitman et al)

NPVdiscount rate project A project B0% $28,000 $25,00010% 11,084 10,91419.9% 0 > 021.7% < 0 0

see next slide



• the NPV profile is a graph that depicts the NPV of a project at various discount rates



Example: Bennett Company (continued) we observe from Figure 9.4 (previous slide) that:

- NPV (A) > NPV (B) for any discount rate below 10.7%

- NPV (A) < NPV (B) for any discount rate above 10.7%



Conflicting rankings

• Bennett Company example gives conflicting rankings between NPV and IRR for discount rates below 10.7%• At 10%, NPV(A) > NPV(B), but IRR(B) > IRR(A)• At > 10.7% NPV(B) > NPV(A) and IRR(B) > IRR(A)

• Ranking is necessary when - projects are mutually exclusive OR - capital is limited and must be rationed

• Assume in the following examples ranking is necessary as projects are mutually exclusive



Conflicting rankings (continued)

• Conflicts between NPV and IRR can arise due to differences in the magnitude and/ or timing of project cash flows which can arise due to the following project differences:

• Size disparity - projects of unequal size (initial investment), e.g. if k = 10%, then for:

• Project A: CF0 = ($200), CF1 = $300• NPV=$72.70, IRR = 50%

• Project B: CF0 = ($1,500), CF1 = $1,900• NPV=$227.10, IRR= 27%

• Conflict: NPVB > NPVA, but IRRA > IRRB


Comparing NPV and IRRConflicting rankings (continued)

• Time disparity – projects of equal size have significantly different cash flow patterns over the lives of the projects, e.g. if k = 10%, then for:

• Project E: CF0 = ($1,000), CF1 = $100, CF2 = $200, CF3 = $2,000• NPV = $758.10, IRR = 35%

• Project F: CF0 = ($1,000), CF1 = $650, CF2 = $650, CF3 = $650• NPV = $616.55, IRR = 42%

• Conflict: NPVE > NPVF, but IRRF > IRRE

• Unequal lives – projects have different life spans• Project J: CF0 = ($1,000), CF1 = $500, CF2 = $500 CF3 = $500

• NPV = $243.43, IRR = 23%• Project K: CF0 = ($1,000), CF1 to CF6 = $300

• NPV = $306.58, IRR = 20%• Conflict: NPVK > NPVJ, but IRRJ > IRRK




• Reason why size, timing and life disparities between projects can lead to conflicting rankings

• NPV and IRR make different assumptions about the rate (%) intermediate cash flows are reinvested at

• ‘intermediate cash flows’ are net cash inflows received prior to the termination of the project

• They have an opportunity cost or a rate at which they can be invested somewhere




• NPV assumes minimum opportunity cost (= the return on a hypothetical alternative project) i.e. the discount rate• Intermediate cash flows are reinvested at the discount rate• This is usually a more reasonable reinvestment assumption

• IRR assumes maximum opportunity cost (= IRR): - as the maximum cost of capital a project could sustain and still be acceptable, OR - as the opportunity cost on a hypothetical alternative project with return = IRR




• Projects with lower net cash inflows in the early years (and higher in later years) tend to be preferred at lower discount rates by NPV, increasing likelihood of conflicting rankings

• Projects with higher net cash inflows in the early years (and lower in later years) tend to be preferred at higher discount rates by NPV, reducing likelihood of conflicting rankings (as per Bennett example slides 23-4)



Which is better, NPV or IRR?

• Despite conflicting rankings, both NPV and IRR give same accept-reject decisions

• Theoretically speaking, NPV is better: - it assumes intermediate flows are reinvested at the firm’s cost of capital - it directly reflects the actual project return

• Practically speaking, many financial managers prefer IRR: - it works with rates of return not dollars - NPV does not measure benefits relative to the amount invested


Other techniques

• Accounting Rate of Return (ARR) = average accounting profit generated by project as percentage of average investment outlay

• ARR can be calculated in a number of ways e.g. ROA

• ROA = (net profit after tax) / (total assets) = (average net profit) / (average book value)

2/

/1

uesalvagevallayinitialout

nprofitaccountingn

tt


Other techniques

• Accounting Rate of Return (ARR) measures return on investment, for example ROA

• Return on Assets (ROA) = (net profit after tax)/(total assets)

• Decision criterion: accept if ROA > reference rate of return reject if ROA < reference rate of return

• Weakness: ignores cash flows and time value of money• Example

• A machine will cost $62,000 and have a useful life of 5 years with a salvage value of $2,000. It will provide a net cash inflow of $22,000 p.a. Depreciation will be $12,400 p.a. The required rate of return on investments of this type is 17% p.a. What is the accounting rate of return?


Other techniques

• Accounting Rate of Return (ARR) - example

Average Accounting profit = $22,000 – $12,400

= $9,600

Average investment = ($62,000 + $2,000) / 2

= $32,000

ARR = $9,600 / $32,000

= 30%


Other techniques

• Profitability Index (PI) uses the ratio of PV of annual net cash inflows to the initial investment

• PI = [ Σ (CFt/(1+k)t) ] / CF0 for t=1n

• Decision criterion: Independent projects: accept if PI > 1 Mutually exclusive projects: accept largest PI > 1

• Strength: useful where funds are limited

• Weakness: can give an incorrect ranking for mutually exclusive projects (see next slide)


Other techniques

• Profitability Index (PI) – example

• Using the data from the earlier example on projects A & B (slides 28):

PI = PV of net cash inflows Initial Investment

PIA = $300/1.1 = 1.36 Accept (NPV = $72.73)$200

PIB = $1,900/1.1 = 1.15 Accept (NPV = $227.30) $1,500

Conflict: PIA > PIB , but NPVB > NPVA


Other techniques

• Discounted Payback Period (DPP) uses exact amount of time required for a project to recover its initial investment

• Decision criterion: accept if DPP < maximum acceptable period reject if DPP > maximum acceptable period

• Weakness: ignores cash flows after payback period & therefore ranking conflict with NPV possible


Quiz1. Unsophisticated capital budgeting techniques do NOT:

A) use net profits as a measure of return.

B) explicitly consider the time value of money.

C) take into account an unconventional cash flow pattern.

D) examine the size of the initial outlay.

2. Among the reasons many firms use the payback period as a guideline in capital investment decisions are all of the following EXCEPT:

A) it is easy to calculate.

B) it gives an implicit consideration to the timing of cash flows.

C) it is a measure of risk exposure.

D) it recognises cash flows which occur after the payback period.

3. The minimum return that must be earned on a project to leave the firm's market value unchanged is all of the following EXCEPT:

A) average rate of return.

B) discount rate.

C) cost of capital.

D) opportunity cost.


Quiz4. A firm would accept a project with a net present value of zero because:

A) the return on the project would be zero.

B) the return on the project would be positive.

C) the project would enhance the wealth of the firm's owners.

D) the project would maintain the wealth of the firm's owners.

5. The __________ is the discount rate that equates the present value of the cash inflows with the initial investment.

A) payback period

B) internal rate of return

C) average rate of return

D) cost of capital

6. The underlying cause of conflicts in ranking for projects by internal rate of return and net present value methods is:

A) that neither method explicitly considers the time value of money.

B) the reinvestment rate assumption regarding intermediate cash flows.

C) the assumption made by the NPV method that intermediate cash flows are reinvested at the internal rate of return.

D) the assumption made by the IRR method that intermediate cash flows are reinvested at the cost of capital.


Week 7 Tutorial

• Review Questions and Problems to be covered in the Week 7 Tutorial:

• Review Questions 9.1, 9.3, 9.5, 9.7, 9.8, 9.9 & 9.10

• Problems 9.36 & 9.38

gitman ch09 01 student

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