Chapter 15Capital Budgeting

Typical Capital Budgeting Decisions

Capital budgeting tends to fall into two broad categories . . .

Screening decisions. Does a proposed project meet some present standard of acceptance?

Preference decisions. Selecting from among several competing courses of action.

Capital Budgeting Methods

We will consider four Capital Budgeting methods :

1. Net Present Value Method2. Internal Rate of Return Method3. Cash Payback Method4. Average Rate of Return Method

The Mathematics of InterestA dollar received

today is worth more than a dollar received

a year from now because you can put it in the bank today

and have more than a dollar a year from

now.

The Mathematics of Interest – An Example

Assume a bank pays 10% interest on a $100 deposit made today. How much

will the $100 be worth in one year?

Fn = P(1 + r)n

Computation of Present Value

Present Value

Future Value

An investment can be viewed in two ways—its future value or its present

value.

Let’s look at a situation where the future value is known and the present

value is the unknown.

Present Value – An ExampleIf a bond will pay $100 in two years, what

is the present value of the $100 if an investor can earn a return of 12% on

investments?

(1 + r)nP =Fn

Present Value of a Series of Cash Flows

1 2 3 4 5 6

$100 $100 $100 $100 $100 $100

An investment that involves a series of identical cash flows at the end of each year is called an annuity.

Expected returnsYear 1 10,000$ 150,000$ 100,000$ 325,000$ Year 2 50,000 190,000 100,000 325,000Year 3 80,000 220,000 100,000 325,000Year 4 84,000 224,000 100,000 325,000

Project AAcct.

IncomeNet Cash

FlowAcct.

IncomeNet Cash

Flow

Project B

Project A Project BCost $560,000 $900,000Expected Life 4 Years 4 YearsExpected Residual Value $0 $0

Investment Analysis

The Net Present Value Method

To determine net present value (NPV) we . . .Determine the net initial investment in the projectCalculate the sum of the present values of the future

cash flowsSubtract the amount of the net initial investment from

the sum of the present value of the future cash flows to obtain the net present value of the project

The interest rate (discount rate) used in determining net present value is the company’s minimum desired rate of return

Let’s use 15% as the discount rate to calculate the net present value for Projects A and B

Project A

NPV @ 15%

Year Net Cash Flow PV Factor Present Value

1 $150,000 .870 $130,500

2 $190,000 .756 $143,640

3 $220,000 .658 $144,760

4 $224,000 .572 $128,128

Total $547,028

Investment $560,000

Net Present Value ($12,972)

Project B

NPV @ 15%

Year Annual Cash Flow PV Factor Present Value

1-4 $325,000 2.855 $927,875

Investment $900,000 $900,000

Net Present Value $27,875

General decision rule . . .If the Net Present Value is . . . Then the Project is . . .

Positive . . . Acceptable, since it promises a

return greater than the minimum desired rate of return.

Zero . . . Acceptable, since it promises a

return equal to the minimum desired rate of return.

Negative . . . Not acceptable, since it

promises a return less than the mininmum desired rate of return.

The Net Present Value Method

Net Present Value Method

The net present value of one project cannot be directly compared to the net present

value of another project (for ranking) unless the investments are equal.

Ranking Capital Investment Opportunities Using NPV

Present Value Index =

Sum of PV of cash inflowsInitial Investment

Project A = = 0.977$547,028$560,000

Project B = = 1.031$927,875$900,000

Project B yields a higher return than Project A.

Internal Rate of Return (IRR) Method• The internal rate of return is the true rate of

return promised by an investment project over its useful life.

• It is computed by finding the discount rate that will cause the net present value of a project to be zero.

• A trial and error process must be used to find the internal rate of return.

• It works better if a project’s cash flows are identical every year.

• Let’s calculate the IRR for Projects A and B

Project A

NPV @ 12%

Year Net Cash Flow PV Factor Present Value

1 $150,000 .893 $133,950

2 $190,000 .797 $151,430

3 $220,000 .712 $156,640

4 $224,000 .636 $142,464

Total $584,484

Investment $560,000

Net Present Value $24,484

Project B

NPV @ 20%

Year Annual Cash Flow PV Factor Present Value

1-4 $325,000 2.589 $841,425

Investment $900,000 $900,000

Net Present Value ($58,575)

Internal Rate of Return MethodGeneral decision rule . . .

If the Internal Rate of Return is . . . Then the Project is . . .

Equal to or greater than the minimum desired rate of return . . . Acceptable.

Less than the minimum desired rate of return . . . Rejected.

When using the internal rate of return, the cost of capital acts as a hurdle rate

that a project must clear for acceptance.

Internal Rate of Return Method

The higher the internal rate of return, the

more desirable the project.

When using the internal rate of return method to rank competing investment

projects, the preference rule is:

Internal Rate of Return Method - Example

• Decker Company can purchase a new machine at a cost of $72,100 that will save $20,000 per year in cash operating costs.

• The machine has a 7-year life.• What is the Internal Rate of Return?

The Payback Method

The payback period is the length of time (in years) that it takes for a project to recover its initial cost out of the cash

receipts that it generates.Let’s calculate the payback period for

Projects A and B

Project A

Payback Period

Year Net Cash Flow Cumulative Cash Flow

1 $150,000 $150,000

2 $190,000 $340,000

3 $220,000 $560,000

4 $224,000

Initial Investment: $560,000

Project B

Payback Period

Year Net Cash Flow Cumulative Cash Flow

1 $325,000 $325,000

2 $325,000 $650,000

3 $325,000 $975,000

4 $325,000

Initial Investment: $900,000

The Payback Method – Another Example• Myers Company wants to install an espresso bar in place of several coffee

vending machines in one of its stores. The company estimates that incremental annual revenues and expenses associated with the espresso bar would be:

Sales $100,000 Less variable expenses 30,000 Contribution margin 70,000 Less fixed expenses: Insurance $ 9,000 Salaries 26,000 Depreciation 15,000 50,000 Net operating income $ 20,000

• Equipment for the espresso bar would cost $150,000 (salvage value is 0) and have a 10-year life. The old vending machines would be thrown away since they have no salvage value. The company requires a payback period of 5 years or less on all investments.

Let’s calculate the Payback Period

Average Rate of Return Method• Does not focus on cash flows -- rather it

focuses on accounting income.• The following formula is used to calculate

the simple rate of return:

• Let’s calculate the Average Rate of Return for Projects A and B.

Average rateof return =

Average annual incomeAverage investment

The Average Rate of Return Method – Another Example

• Myers Company wants to install an espresso bar in place of several coffee vending machines in one of its stores. The company estimates that incremental annual revenues and expenses associated with the espresso bar would be:

Sales $100,000 Less variable expenses 30,000 Contribution margin 70,000 Less fixed expenses: Insurance $ 9,000 Salaries 26,000 Depreciation 15,000 50,000 Net operating income $ 20,000

• Equipment for the espresso bar would cost $150,000 (salvage value is 0) and have a 10-year life. The old vending machines would be thrown away since they have no salvage value. The company requires an average rate of return of 25% or more on all investments.

Let’s calculate the Average Rate of Return