rate of return analysis - engineering economics

Applied Software Project Management

Engineering EconomicsEngineering Economics

Rate-of-Return Analysis Rate-of-Return Analysis

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Applied Software Project ManagementEVALUATIING BUSIINESS AND EVALUATIING BUSIINESS AND ENGIINEERIING ASSETSENGIINEERIING ASSETS

Present-Worth Analysis Annual Equivalence Analysis Rate-of-Return Analysis

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Road MapRoad Map

Chapter 6 Rate-of-Return Analysis Rate of Return Methods for Finding Rate of Return Internal-Rate-of-Return Criterion Incremental Analysis for Comparing Mutually

Exclusive Alternatives

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Return on InvestmentReturn on Investment

Definition 1- Rate of return is the interest earned on the unpaid balance of amortized loan

Example: Suppose that a bank lends $10,000, which is repaid in installments of $4,021 at the end of each year for three years. How would you determine the interest rate that the bank charges on this transaction?

10,000 = 4,021(P/A,i,3)

i = 10%

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Year Unpaid balance at

beginning of the year

Return on unpaid balance (10%)

Payment received

Unpaid balance at End of the

year

0 -10,000

1 -10,000 -1,000 4,021 -6,979

2 -6,979 -698 4,021

3

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When the last payment is made, the outstanding principal is eventually reduced to zero. If we calculate the PW of the loan transaction at its rate of return (10%). we see that

PW(10%) = -$10.000 + $4,021(P/A. 10%, 3) = 0

i.e. the bank can break even at a 10% rate of interest

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Definition 2- Rate of return is the break-even interest rate i* at which the present worth of the project is zero or

PW(i*) = PWcashinflow – PWcashoutflow

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nn

i

A

i

A

i

AiPW

)1(...

)1()1(*)(

*1*1

0*0


Return on Invested Capital Return on Invested Capital

Investment project can be views as analogous to bank loan

A project’s return is referred to as internal rate of return (IRR), or the Yield promised by an investment project over its useful life

Definition 3: The internal rate of return is the interest rate charges on the unrecovered project balance of the investment such that, when the project terminates, the unrecovered project balance is zero.

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Return on Invested Capital Return on Invested Capital

Suppose a company invest 10,000 in a computer with a three-year useful life and equivalent annual labor savings 4,021. Here, we may view the investment firm as the lender and the project as the borrower. The cashflow transaction between them would be identical to the amortized loan described above:

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Year Beginning project balance

Return on invested

capital (10%)

Cash generated from project

Project balance at End of the year

0 -10,000 0 0 -10,000

1 -10,000 -1,000

2

3


Road MapRoad Map



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Simple versus Non-simple Investments Simple versus Non-simple Investments

An investment project can be classified by counting the number of sign changes in its net cash flow sequence.

A change from either "-" to "+" or "+" to "-" is counted as one sign change (a zero cash flow is ignored)

A simple (or conventional) investment: is an investment in which the initial cash flows are negative and only one sign change occurs in the net cash flow series.

If the initial flows are positive and only one sign change occurs in the subsequent net cash flows, the flows are referred to as simple-borrowing cash flows.

A non-simple (or nonconventional) investment: is an investment in which more than one sign change occurs in the cash flow series.

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Investment ClassificationInvestment Classification

Year Project A Project B Project C

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

1 -500 3,900 -4,50

2 800 -5,030 -450

3 1,500 2,145 -450

4 2,000


Given: Cash flow sequences provided in the foregoing table.Find: Classify the sequences as either simple or non-simple investments.


Computational Methods Computational Methods


There are several ways to determine rate of return. Three most practical methods:

– direct-solution method,– trial-and-error method, and– Excel method.


Finding i* by DirectFinding i* by Direct

Compute the rate of return for each project:

Using future worth or present worth


n Project 1 Project 2

0 -1,000 -2,000

1 0 1,300

2 0 1,500

3 0

4 1,500



Project 1:

FW(i*) = -1,000(F/P,i*,4) + 1,500 = 0

-1,000*(1+i)4 + 1,500 = 0

(1+i)4 = 1.5

i = (1.5)1/4 – 1 = 10.67%

Project 2:

FW(i) = -2000(F/P,i,2) + 1,300(F/P,i,1) + 1,500 = 0




Project 2:

FW(i) = -2000(1 + i)2 + 1,300(1 + i) + 1,500 = 0



Finding i* by Trial and ErrorFinding i* by Trial and Error

The first step in the trial-and-error method is to make an estimated guess at the value of i*. For a simple investment, we use the guessed interest rate to compute the present worth of net cash flows and observe whether the result is positive, negative, or zero:

Case 1: PW(i) < 0. Since we are aiming for a value of i that makes PW(i) = 0, we must raise the present worth of the cash flow. To do this, we lower the interest rate and repeat the process.

Case 2: PW(i) > 0. We raise the interest rate in order to lower PW(i). The process is continued until PW(i) is approximately equal to zero

Whenever we reach the point where PW(i) is bounded by one negative value and one positive value. we use linear interpolation to approximate i*.




Agdist Corporation distributes agricultural equipment. The board of directors is considering a proposal to establish a facility to manufacture an electronically controlled "intelligent" crop sprayer invented by a professor at a local university. This crop-sprayer project would require an investment of $10 million in assets and would produce an annual after-tax net benefit of $1.8 million over a service life of eight years. All costs and benefits are included in these figures. When the project terminates, the net proceeds from the sale of the assets would be $1 million. Compute the rate of return of this project




Given: Find: i*


0 1 2 …………………………………... 7 8

1.8m

2.8m

10m


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Relationship to the PW Analysis Relationship to the PW Analysis

PW analysis is dependent on the rate of interest used for the PW computation. A different rate may change a project from being considered acceptable to being considered unacceptable, or it may change the ranking of several projects.

For the simple project:

– Interest rates below i*: project accepted, as PW > 0;

– Interest rates above i*: it should be rejected. For the simple project: there are regions of (+) and (-)

– not clear which i* to use to make an accept-or-reject decision

– i* value fails to provide an appropriate measure of profitability for an investment project



Decision Rule for Simple InvestmentsDecision Rule for Simple Investments

Evaluating a Single Project:– If IRR > MARR, accept the project.– If IRK = MARR. remain indifferent.– If IRR < MARR, reject the project

Evaluating Mutually Exclusive Projects:– apply the incremental analysis approach


Applied Software Project Managementlnvestment Decisionlnvestment Decisionfor a Simple Investmentfor a Simple Investment

Merco, lnc., a machinery builder Invest: 1,250,000 increased fabricated-steel production: 2,000 tons/year: average sales price per ton of fabricated steel: $2,566.50 labor rate: $10.50/hour tons of steel produced in a year: 15,000 cost of steel per ton (2.205 Ib): $1,950: number of workers on layout, hole making, sawing, and material

handling: 17; additional maintenance cost: $128,500/year direct-labor cost of fabricating1 lb at 10 cents $226,000 in corporate income taxes



Cost to produce 1 ton of steel– Total Cost = raw material cost + labor cost– Total cost = $1,950 + 0.1*2205 = 2,170.5

Profit per ton = price per ton – cost per ton– Profit per ton = 2,566.5 - 2,170.5 = 396

Total projected profit per year = 2,000 * 396 = 792,000 Benefits:

– Additional labor saving of using a new system:17 * 10.5 * 40 * 50 = 294,000

– After-tax salvage value: 80,000 Other costs:

– Additional Maintenance cost: $128,500/year– Corporate Tax: 226,000/year



Project investment cost: 1,250,000 projected annual net savings:

792,000 + 294,000 - 128,500 – 226,000 = 731,500

1. What is the projected IRR on this investment?

2. If Merco's MARR is known to be 18%, is this investment justifiable?

Solution:

1. IRR?a. Simple or non-simple

b. PW(i)

2. How to justify the project?


Applied Software Project ManagementDecision Rule for Nonsimple Decision Rule for Nonsimple InvestmentsInvestments

Simple project: IRR provides unambiguous criterion for measuring profitability

When multi rate occurs: none of them is an accurate portray of project’s acceptability or profitability

External Rate of return allows us to calculate a single true rate of return


Applied Software Project ManagementInvestment DecisionInvestment Decisionfor a Non-simple Projectfor a Non-simple Project

By outbidding its competitors, Trane Image Processing (TIP), a defense contractor, has received a contract worth $7,300,000 to build navy flight simulators for U.S. Navy pilot training over two years. For some defense contracts, the U.S. government makes an advance payment when the contract is signed. but in this case, the government will make two progressive payments: $4,300,000 at the end of the first year and the $3,000,000 balance at the end of the second year. The expected cash outflows required in order to produce these simulators are estimated to be $1,000,000 now, $2,000,000 during the first year, and $4,320,000 during the second year. The expected net cash flows from this project are summarized as follows:


Applied Software Project ManagementInvestment DecisionInvestment Decisionfor a Non-simple Projectfor a Non-simple Project

Cash flow table

a) Compute the values of the i*'s for this project.

b) Make an accept-or-reject decision, based on the results of part (a). Assume that the contractor's MARR is 15%.


Year Cash Inflow Cash Outflow Net Cash Flow

0 1,000,000

1 4,300,000 2,000,000

2 3,000,000 4,320,000


TutorialTutorial

Do end chapter problems: 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.11, 7.12


rate of return analysis - engineering economics

Documents

additional

sign change

unrecovered

return analysis

cash flow

pw analysis

unpaid balance

chapter 6