RATE OF RETURN ANALYSIS (Chap7)

8/13/2019 RATE OF RETURN ANALYSIS (Chap7)

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Chapter 7 - Rate of

Return AnalysisClick here for Streaming Audio To

Accompany Presentation (optional)

EGR 403 Capital Allocation Theory

Dr. Phillip R. Rosenkrantz

Industrial & Manufacturing Engineering Department

Cal Poly Pomona
http://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asx


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EGR 403 - Cal Poly Pomona - SA9 2

EGR 403 - The Big Picture Framework:Accounting& Breakeven Analysis

Time-value of money concepts - Ch. 3, 4

Analysis methods

Ch. 5 - Present Worth

Ch. 6 - Annual WorthCh. 7, 8 - Rate of Return (incremental analysis)

Ch. 9 - Benefit Cost Ratio & other techniques

Refining the analysisCh. 10, 11 - Depreciation & Taxes

Ch. 12 - Replacement Analysis


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Three Major Methods of

Economic Analysis PW - Present Worth

AW - Annual Worth

IRR - Internal Rate of Return

If P = A(P/A, i, n)

Then (P/A, i, n) = P/A

Solve for (P/A, i, n) and look up

interest in Compound Interest Tables


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Internal Rate of Return (IRR)

The interest rate paid on the unpaid balance of a

loan such that the payment schedule makes the

unpaid loan balance equal to zero when the final

payment is made. Ex: P = $5000, i = 10%, n = 5

Year Principal Prin. Paid Int Paid Payment

1 5000.00 818.99 500.00 1318.99

2 4181.01 900.89 418.10 1318.99

3 3280.13 990.97 328.01 1318.994 2289.15 1090.07 228.92 1318.99

5 1199.08 1199.08 119.91 1318.99

6 0.00 0.00


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Calculating Rate of Return

The IRR is the interest rate at which the

benefits equal the costs. IRR = i*

PW Benefit - PW Cost = 0

PW Benefit/PW Cost = 1

NPW = 0

EUAB - EUAC = 0PW Benefit = PW Cost


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Calculating IRR - Example 7-1

PWB/PWC = 1 2000(P/A, i, 5)/8200 = 1

(P/A, i, 5) = 8200/2000 =

4.1

From Table, IRR =7%

3.9938%

4.1007%

4.2126%

(P/A,i,5)Interest rate

From Compound Interest Tables


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Sometimes we have more than one factor in our equation.

When that happens we cannot solve for just one factor.

If we use: EUAB - EUAC = 0

100 + 75(A/G, i, 4) - 700(A/P, i, 4) = 0


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Calculating IRR - Example 7-2 (contd) No direct method for calculating. Use trial and error

and iterate to get answer.

Try i = 5%:

100 + 75(A/G, 5%, 4) - 700(A/P, 5%, 4) = + 11

+ 11 is too high. The interest rate was too low Try i = 8%

100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = - 6

- 6 is too low. The interest rate was too high

Try i = 7%

100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = 0

Therefore IRR = 7%


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Example 7-3 shows a series of cash flows that does not match any

of our known patterns. We must use trial and error. Using NPW = 0, suppose we start with i = 10% . NPW = + 10.16,

which is too high.

Using i = 15%, NPW = - 4.02. IRR is between 10% & 15%

The iterations may be graphed and the true IRR will be indicatedat the point where the NPW curve = 0.

Yr CF

0 - 100

1 + 20

2 + 203 + 30

4 + 40

5 + 40


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Calculating IRR - Example 7-3 (Contd)

We can use linear interpolation to find estimatethe point where the curve crosses 0.

IRR = i* = 10% + (15%-10%)[10.16/(10.16 +

4.02)] = 13.5% This is a linear interpolation of a non-linear

function so the answer is slightly inaccurate,

but good enough for decision making here(after all, the guesswork in our future cash

flows introduces uncertainty in the analysis).


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Calculating IRR - Example 7-3 (Contd)

-100

20

30

2040

40

13.47%

To get an exact answer, we can use the IRR function in EXCEL

Select the IRR function from the fx icon.

Block the column on the spreadsheet that has the cash flows for

all years.

The function returns the IRR.

=IRR(A1:A6)

The IRR function in

EXCEL allows you to

evaluate the return ofinvestments very easily


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Calculating IRR for a Bond- Example 7-4a

Bond Costs and Benefits:Purchase price = $1000

Dividends = $40 every six months

Sold after one year for $950

Calculation of Periodic interest rate & IRR:m = 2 compounding periods/year

1000 = 40(P/A, i, 2) + 950(P/F, i, 2)

By trial and error and interpolation i* 1.5%

IRR Nominal rate = 2 x 0.015 = 0.03 (3%)

IRR Effective rate = (1 + 0.015)2- 1 = 0.0302 (3.02%)


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Example 7-4a EXCEL Solution

Period Buy/sell Dividend Total0 -1000 -1000

1 40 40

2 950 40 990

1.52% periodic3.04% nominal

3.06% effective

Use IRR function to find periodic IRR (i) Find nominal using r = i * m

Use EFFECT function to find effective interest rate


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Rate Of Return (ROR) Analysis

Most frequently used measure of merit in

industry.

More accurately called Internal Rate ofReturn (IRR).


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Calculating ROR

Where two mutually exclusive alternatives will

provide the same benefit, ROR is performed using anincremental rate of return(ROR)on the difference

between the alternatives.

You cannot simply choose the higher IRR alternative.

Choose lower-cost

alternative

DROR < MARR

Choose higher-cost

alternative

DROR MARR

DecisionTwo-alternative

situation


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The Minimum Attractive Rate of

Return (MARR) The MARR is a minimum return the

company will accept on the money it invests

The MARR is usually calculated byfinancial analysts in the company and

provided to those who evaluate projects

It is the same as the interest rate used forPresent Worth and Annual Worth analysis.


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ROR on Alternatives With Equivalent Benefits

Year

Cash flow -

alternative

A (Leaseco)

Cash flow -

alternative

B (Saleco)

Cash flow -

alternative

B - A

0 -$1,000.00 -$2,783.00 -$1,783.00

1 $200.00 $1,200.00 $1,000.00

2 $200.00 $1,200.00 $1,000.00

3 $1,200.00 $1,200.00 $0.00

4 $1,200.00 $1,200.00 $0.00

5 $1,200.00 $1,200.00 $0.00

IRR/period 48.72% 32.60% 8.01%

Example 7-5: Consider the lease vs. buy situation. MARR = 10%

Leasco: Lease for five years for 3 annual payments of $1000 each

Saleco: Purchase up front for $2783

Both alternatives have a $1200/year benefit for 5 years


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Example 7-5 (Contd)

Cannot simply pick the highest IRR if alternatives have

different investment costs

Must examine the incremental cash flows!!

Subtract the cash flows for the Lower First Costalternative from the cash flows of the Higher First Cost

alternative to obtain the Incremental Cash Flow or D.

Compute the IRR on the incremental cash flow. This is

the DROR. For this problem the DROR is 8.01% which is

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RATE OF RETURN ANALYSIS (Chap7)