Evaluating a Single Project

7/24/2019 Evaluating a Single Project

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Engr. Charity Hope Gayatin

EVALUATING a

SINGLE PROJECT


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Learning Unit Objectives

The objective of this chapter on EVALUATING a SINGLEPROJECT is to discuss and critique contemporary methods fordetermining project profitability. Proposed capital projects canbe evaluated in several ways.

1. Determining the Minimum Attractive Rate of Return (MARR)2. The Present Worth Method

3. The Future Worth Method

4. The Annual Worth Method

5. The Internal Rate of Return Method6. The External Rate of Return Method

7. The Payback (Payout) Period Method (generally notappropriate as a primary decision rule)


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To be attractive, a capital project must provide a return thatexceeds a minimum level established by the organization.

This minimum level is reflected in a firms Minimum AttractiveRate of Return (MARR).

Minimum Attractive Rate of Return (MARR)


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Many elements contribute to determining the MARR.

Amount, source, and cost of money available

Number and purpose of good projects available

Perceived risk of investment opportunities

Type of organization

Minimum Attractive Rate of Return (MARR)


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The most-used method is the present worth method.

The present worth (PW) is found by discounting all cash inflowsand outflows to the present time at an interest rate that isgenerally the MARR.

A positive PW for an investment project means that the projectis acceptable (it satisfies the MARR).

Present Worth Method


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Consider a project that has an initial investment of $50,000 andthat returns $18,000 per year for the next four years. If theMARR is 12%, is this a good investment?


Present worth example


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A piece of new equipment has been proposed by engineers toincrease the productivity of a certain manual welding operation.The investment cost is $25,000, and the equipment will have amarket value of $5,000 at the end of a study period of five years.Increased productivity attributable to the equipment will amountto $8,000 pear year after extra operating costs have beensubtracted from the revenue generated by the additionalproduction. A cash-flow diagram for this investment opportunityis given below. If the firmsMARR is 20% per year, is this proposala sound one? Use the PW method.

Present Worth MethodEvaluation of New Equipment Purchase Using PW

$25,000

$8,000 $8,000

$5,000

$8,000$8,000$8,000

1 2 3 4 5


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Assumptions of the present worth method.

1. It is assumed we know the future with certainty.

2. It is assumed we can borrow or lend money at the sameinterest rate.



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Capitalized worth is the present worth of all revenues orexpenses over an infinite length of time.

If only expenses are considered this is sometimes referred to ascapitalized cost.

The capitalized worth method is especially useful in problemsinvolving endowments and public projects with indefinite lives.

As n becomes very large, (P/A) = 1/i. So, CW = A (1/i).


Capitalized worth is a special variation of presentworth.


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Suppose that a firm wishes to endow a laboratory at auniversity. The endowment principal will earn interest thataverages 8% per year, which will be sufficient to cover allexpenditures incurred in the establishment and maintenance ofthe laboratory for an indefinitely long period of time. Cashrequirements of the laboratory are estimated to be $100,000now, $30,000 per year indefinitely, and $20,000 at the end of

every 4th year for equipment replacement.

What amount of endowment principal is required to establishthe laboratory and then earn enough interest to support theremaining cash requirements of this laboratory for a long time?


Capitalized worth example


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Future Worth (FW) Method is an alternative to the PW Method.

Looking at FW is appropriate since the primary objective is tomaximize the future wealth of owners of the firm.

FW is based on the equivalent worth of all cash inflows andoutflows at the end of the study period at an interest rate thatis generally the MARR.

Decisions made using FW and PW will be the same.

A positive FW for an investment project means that the project

is acceptable (it satisfies the MARR).

Future Worth Method


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A $45,000 investment in a new conveyor system is projected toimprove throughput and increasing revenue by $14,000 peryear for five years. The conveyor will have an estimated marketvalue of $4,000 at the end of five years. Using FW and a MARRof 12%, is this a good investment?

Future Worth Method

Future worth example


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A piece of new equipment has been proposed by engineers toincrease the productivity of a certain manual welding operation.The investment cost is $25,000, and the equipment will have amarket value of $5,000 at the end of a study period of five years.Increased productivity attributable to the equipment will amount

to $8,000 pear year after extra operating costs have beensubtracted from the revenue generated by the additionalproduction. A cash-flow diagram for this investment opportunityis given below. If the firmsMARR is 20% per year, is this proposala sound one? Use the FW method.

Future Worth Method

$25,000

$8,000 $8,000

$5,000

$8,000$8,000$8,000

1 2 3 4 5

Evaluation of New Equipment Purchase Using FW


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Annual Worth (AW)

Annual Worth (AW) is another way to assess projects.

Annual worth is an equal periodic series of dollar amounts thatis equivalent to the cash inflows and outflows, at an interestrate that is generally the MARR.

The AW of a project is annual equivalent revenue (R) orsavings minus annual equivalent expenses (E), less its annualcapital recovery (CR) amount.

AW (i%) = R E CR (i%)


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Capital Recovery

Capital Recovery reflects the capital cost of the asset.

CR is the annual equivalent cost of the capital invested.

The CR covers the following items.

Loss in value of the asset.

Interest on invested capital (at the MARR).

The CR distributes the initial cost (I) and the salvage value (S)

across the life of the asset.

CR (i%) = I (A/P, i%, N) S (A/F, i%, N)

Equivalent Uniform annual Cost (EUAC) = CR + E

Annual Worth (AW)


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A project requires an initial investment of $45,000, has asalvage value of $12,000 after six years, incurs annual expenses

of $6,000, and provides an annual revenue of $18,000. Usinga MARR of 10%, determine the AW of this project.

Annual worth example

Annual Worth (AW)


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A corporate jet costs $1,350,000 and will incur $200,000 peryear in fixed cost (maintenance, ) and $277 per hour variable

cost (fuel, ). The jet will be operated 1200 hours per year for 5years and then sold for $650,000. The jet revenues $1,000 perhour. The MARR is 15% per year.

(a) Determine the Capital Recovery (CR) value of the jet.

(b) Determine the Annual Worth (AW) of the jet.(c) Determine the Equivalent Uniform Annual Cost (EUAC) of

the jet.

Annual worth example

Annual Worth (AW)


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Internal Rate of Return

The internal rate of return (IRR) method is the most widely usedrate of return method for performing engineering economicanalysis.

It is also called the investorsmethod, the discounted cash flow

method, and the profitability index.

If the IRR for a project is greater than the MARR, then theproject is acceptable.


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How the IRR works

The IRR is the interest rate that equates the equivalent worth ofan alternatives cash inflows (revenue, R) to the equivalentworth of cash outflows (expenses, E).

The IRR is sometimes referred to as the breakeven interest rate.

The IRR is the interest i'% at which



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The method of solving for the i'% that equates revenues andexpenses normally involves trial-and-error calculations, or solvingnumerically using mathematical software.

The use of spreadsheet software can greatly assist in solving forthe IRR. Excel uses the IRR(range, guess) or RATE (nper, pmt, pv)functions.

Solving for the IRR is a bit more complicated than PW,FW, or AW



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It is computationally difficult without proper tools.

In rare instances multiple rates of return can be found.

The IRR method must be carefully applied and interpreted whencomparing two more mutually exclusive alternatives (e.g., do notdirectly compare internal rates of return).

Challenges in applying the IRR method.



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ABC, Inc. is considering the purchase of an equipment. Thecapital investment requirement is $345,000 and the estimatedmarket value of the system after a 6 year study period is

$115,000. Annual revenues attributable to the new system willbe $120,00, whereas additional annual expenses will be$22,000. You have been asked by management to determinethe IRR of this project and to make a recommendation. ThecorporationsMARR is 20% per year. Solve first by using linearinterpolation and then by using a spreadsheet.

Internal Rate of Return example



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A piece of new equipment has been proposed by engineers toincrease the productivity of a certain manual weldingoperation. The investment cost is $25,000 and the equipment

will have a market value of $5,000 at the end of its expectedlife of 5 years. Increased productivity attributable to theequipment will amount to $8,000 per year after extraoperating costs have been subtracted from the value of theadditional production. Is the investment a good one? TheMARR is 20% per year.

Internal Rate of Return example



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Reinvesting Revenuethe External Rate of Return (ERR)

The IRR assumes revenues generated are reinvested at the IRRwhich may not be an accurate situation.

The ERR takes into account the interest rate, , external to aproject at which net cash flows generated (or required) by aproject over its life can be reinvested (or borrowed). This isusually the MARR.

If the ERR happens to equal the projects IRR, then using theERR and IRR produce identical results.

External Rate of Return


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The ERR procedure

Discount all the net cash outflows to time 0 at % percompounding period.

Compound all the net cash inflows to period N at at %.

Solve for the ERR, the interest rate that establishes equivalencebetween the two quantities.



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where

Rk = excess of receipts over expenses in period k,Ek = excess of expenses over receipts in period k,

N = project life or number of periods, and = external reinvestment rate per period.

ERR is the i% at which



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Year 0 1 2 3 4

Cash Flow -$15,000 -$7,000 $10,000 $10,000 $10,000

For the cash flows given below, find the ERR when the externalreinvestment rate is = 12% (equal to the MARR).

Expenses

Revenue

Solving, we find

Applying the ERR method



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The payback period method is simple, but possibly misleading.

The simple payback period is the number of years required forcash inflows to just equal cash outflows.

It is a measure of liquidity rather than a measure of profitability.

Payback Period Method


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The payback period is the smallest value of (N) for whichthe relationship below is satisfied.

For discounted payback future cash flows are discounted back

to the present, so the relationship to satisfy becomes

How to Calculate Payback



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It doesntreflect any cash flows occurring after , or '.

It doesnt indicate anything about project desirability exceptthe speed with which the initial investment is recovered.

Recommendation: use the payback period only assupplemental information in conjunction with one or more of

the other methods in this chapter.


Problems with the Payback Period Method.


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End of

Year

Net Cash

Flow

Cumulative

PW at 0%

Cumulative

PW at 6%

0 -$42,000 -$42,000 -$42,000

1 $12,000 -$30,000 -$30,679

2 $11,000 -$19,000 -$20,889

3 $10,000 -$9,000 -$12,493

4 $10,000 $1,000 -$4,572

5 $9,000 $2,153

Finding the Simpleand DiscountedPayback Period for aSet of Cash Flows.

The cumulative cashflows in the tablewere calculated usingthe formulas forsimple and

discounted payback.

From the calculations= 4 years and ' = 5years.


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Evaluating a Single Project