Chapter 2Capital Budgeting Principles and

Techniques

Capital budgeting and investment Analysis by Alan Shapiro

Net Present Value (NPV)

• NPV is the present value of the project’s cash flows minus the cost of the project

• The value placed on an investment project must satisfy three criteria:– Focus on cash– Account for TVM– Account for Risk

NPV Decision Rule

• Invest in positive NPV projects• Reject negative NPV projects• Use the appropriate discount rate• If two projects are mutually exclusive, accept

the one with higher NPV• Cost of capital is the minimum acceptable rate

of return on projects with similar risk.

NPV cont.

• NPV=-Initial cash investment+ PV of future CFs• Initial investment includes any working capital

requirements• Net CF is after tax profit plus depreciation and

other non-cash charges such as deferred taxes less any additions to working capital during the period

• It is cash, and only cash that matters to shareholders

Example 1

• Plant and equipment of $6 million• 5 year contract• Sale of $10 per pound• 800,000 pounds of dye in the 1st year• 1,600,000 pounds per year in each of the next

4 years• Plant is expected to be sold at its book value

in end of year 5 for $1 million

Example 1 cont.

• Variable cost = $6.5 per pound• Fixed cost = $1,700,000 per year• Deprecation = $1,000,000 per year• Tax rate = 40%• Working capital requirement =$1,200,000 and

will be freed at end of year 5• Required return = 10%

Example 1 cont.

• Calculate the following:– Initial investment for this project– Net Cash Flow for years 1-5.– NPV– Decide whether you would accept or reject this

project and Why?

Example 2 (Contingent projects)• Purchase and transport mining equipment which

costs $90 million• Cost of extracting ore = $50 per ton• Expected to sell ore for $150 a ton• Produce 200,00 tons a year• 20 Years• Construct a rail line at cost of $30 million• Cost of transport = $10 per ton• Required rate of return= 15%• What are the NPVs for the mine and the railway?

Which project(s) should they take?

Strengths of NPV

• It evaluates investments in the same way that shareholders do

• It is a theoretically correct technique• It obeys the value additivity principle• The NPV of a set of independent projects is

just the sum of the NPVs of the individual projects

• It implies that the value of a firm equals the sum of the values of its component parts

Weakness of NPV

• Many corporate executives and non technical people have a tough time understanding the concept

• Applying the NPV has the problem of computing the proper discount rate.

Payback Period

• Payback period is the length of time necessary to recoup the initial investment from net cash flows

• Discounted payback period is the length of time it takes to the present value of CFs to equal the cost of the initial investment

• Find the payback period (PB) for example 1.

Payback period decision rule

• Projects with a payback less than a specified cutoff period are accepted whereas those with a payback beyond this figure are rejected

• The riskier the project is, the shorter the required payback will be

Payback period Strengths and Weaknesses

• Strength: It is simple to understand and easy to apply

• Weaknesses:– It ignores time value of money– It ignores cash flows beyond the payback period:

it is biased against longer projects

Accounting rate of return

• Also known as average rate of return or average return on book value

• It is the ratio of average after tax profit to average book investment (the initial investment less accumulated depreciation).

• Decision Rule– Investments yielding a return greater than this

standard are accepted, whereas those falling below it would be rejected.

Strengths and Weaknesses of Accounting rate of return

• Strength: It is simple to apply• Weakness:– It ignores the time value of money– It is based on accounting income rather than cash

flow. Cash flow and reported income often differ

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Internal Rate of Return (IRR)

• IRR is the discount rate that sets the present value of the project cash flow to the initial investment outlay

• It is the discount rate that equates the project NPV to zero

• Calculate the IRR of Example 1

IRR Decision Rule

• If the IRR exceeds the cost of capital, the firm should undertake the project; otherwise, the project should be rejected

IRR Strengths and Weaknesses

• Strengths:– Managers seem to visualize and understand more

easily the concept of a rate of return rather than they do the concept of a sum discounted dollars

– It permits an investment analysis without requiring advance specification of the discount rate

• Weaknesses:– When cash flows change more than once (Multiple

IRR)– When mutually exclusive projects are involved

Multiple IRRs

• IRR of 0%, 100%, and 200%

Year 0 1 2 3

Cash flow -$200 +$1,200 -$2,200 +$1,200

Mutually exclusive projects

• In case of mutually exclusive projects choices, NPV and IRR can favor conflicting projects

• When forced to choose between two mutually exclusive investments, the NPV will always provide the correct answer.

• When projects are substantially different in– Timing of cash flows

• Most of CFs coming in early years vs. later years– Scale differences

• Differences in the amount of the initial investment

Differences between rankings of NPV and IRR

Year X Y

0 -$100,000 -$1,000,000

1 $140,000 $1,250,000

NPV (k=15%) $21,739 $86,957

IRR 40% 25%

Year A B

0 -1,000,000 -1,000,000

1 800,000 100,000

2 300,000 400,000

3 200,000 500,000

4 100,000 800,000

NPV (k=17%) $81,154 $116,781

IRR 22.99% 21.46%

Profitability Index (PI)

• It is also called the benefit-cost ratio• It equals the present value of future cash

flows divided by the initial cash investment• Calculate Profitability Index (PI) for Example 1• The project returns a present value of $X for

every $1 of the initial investment

PI Decision Rule

• As long as the profitability index exceeds 1, the project should be accepted

• Strength:– NPV and PI give the same accept/reject signal

• Weakness:– NPV and PI sometimes disagree in the rank

ordering of acceptable projects– When there are mutually exclusive projects and

when there is capital rationing

Surveys of Capital budgeting used in practice

• Graham and Harvey (2002)– US companies– 75% of CFOs always or almost always use NPV– 75.7 always or almost always use IRR– Most popular secondary or supplemental method of

evaluation is the payback period due to its simplicity along with top management’s lack of familiarity with more sophisticated techniques

– Only about 20% of companies used accounting rate of return

What about Kuwait? Other international surveys?

Capital Rationing

• Some firms constrain the size of their capital budgets. Whenever such a constraint exist, we have the situation known as capital rationing

• Capital rationing may be self-imposed or externally imposed– Limit CapEx to internally generated cash flows– Limit # of attractive projects to undertake– Current lenders may restrict the amount of future

borrowing

Heuristic approach

• Calculate the PI for each project• Rank all projects in term of their PIs, from

highest to lowest• Starting with the project having the highest PI,

go down the list and select all projects having PI>1 until the capital budget is exhausted

Capital Rationing: NPV vs. PI

• The NPV method does not necessarily select the best combination of projects under capital rationing

• The PI approach will select the optimal combination of projects provided that:– The budget constraint is for 1 period only– The entire budget can be consumed by accepting

projects in descending order of PI.

Example on Capital RationingCapital budget of $5 million

Project Initial investment

NPV PI Ranking NPV

Ranking PI

A 500,000 100,000 1.20 1. D F

B 500,000 70,000 1.14 2. C A

C 2,000,000 300,000 1.15 3. E E

D 3,000,000 480,000 1.16 4. F D

E 1,000,000 170,000 1.17 5. A C

F 500,000 125,000 1.25 6. B B

Mutually exclusive projects with Different Lives

• Equivalent annual cost of an asset is an annuity that has the same life as the asset whose present value equals the cost of the asset

• Rule:– Compute the equivalent annual cost of each asset. • Select the asset with the lowest equivalent annual cost• For a revenue generating project, this rule becomes

select the project with the highest equivalent annual net cash flow

Example: Different LivesYear Dole Daihatsu

0 $12,000 $7,500

1 $3,000 $4,000

2 $3,000 $4,000

3 $3,000 $4,000

4 $3,000 $4,000

5 $3,000 -

Present value of cost at 8% $23,978.10 $20,740.40

Dole Truck Daihatsu truck

Initial cost $12,000 $7,500

Salvage Value 0 0

Life 5 years 4 years

Operating cost $3,000/year $4,000/year