chapter 7 - rate of return analysis click here for streaming audio to accompany presentation...

Chapter 7 - Rate of Return Analysis

Click here for Streaming Audio To Accompany Presentation (optional)

EGR 403 Capital Allocation Theory

Dr. Phillip R. RosenkrantzIndustrial & Manufacturing Engineering Department

Cal Poly Pomona

http://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asx



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 Worth– Ch. 7, 8 - Rate of Return (incremental analysis)– Ch. 9 - Benefit Cost Ratio & other techniques

• Refining the analysis– Ch. 10, 11 - Depreciation & Taxes– Ch. 12 - Replacement Analysis


Three Major Methods of Economic Analysis

• PW - Present Worth

• AW - Annual Worth

• IRR - Internal Rate of ReturnIf P = A(P/A, i, n)Then (P/A, i, n) = P/ASolve for (P/A, i, n) and look up interest in Compound Interest Tables


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 Payment1 5000.00 818.99 500.00 1318.992 4181.01 900.89 418.10 1318.993 3280.13 990.97 328.01 1318.994 2289.15 1090.07 228.92 1318.995 1199.08 1199.08 119.91 1318.996 0.00 0.00


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 = 0

PW Benefit = PW Cost


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 rateFrom Compound Interest Tables


Calculating IRR - Example 7-2

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 = 0100 + 75(A/G, i, 4) - 700(A/P, i, 4) = 0


Calculating IRR - Example 7-2 (cont’d)• 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%


Calculating IRR - Example 7-3• 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 indicated at the point where the NPW curve = 0.

Yr CF0 - 1001 + 202 + 203 + 304 + 405 + 40


Calculating IRR - Example 7-3 (Cont’d)

• We can use linear interpolation to find estimate the 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).


Calculating IRR - Example 7-3 (Cont’d)

-1002030204040

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 of investments very easily


Calculating IRR for a Bond - Example 7-4a

Bond Costs and Benefits:Purchase price = $1000Dividends = $40 every six monthsSold after one year for $950

Calculation of Periodic interest rate & IRR:m = 2 compounding periods/year1000 = 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%)


Example 7-4a EXCEL Solution

Period Buy/sell Dividend Total0 -1000 -10001 40 402 950 40 990

1.52% periodic3.04% nominal3.06% effective

• Use IRR function to find periodic IRR (i)• Find nominal using r = i * m• Use EFFECT function to find effective interest rate


Rate Of Return (ROR) Analysis

• Most frequently used measure of merit in industry.

• More accurately called Internal Rate of Return (IRR).


Calculating ROR• Where two mutually exclusive alternatives will

provide the same benefit, ROR is performed using an incremental rate of return (ROR) on the difference between the alternatives.

• You cannot simply choose the higher IRR alternative.

Choose lower-cost alternative

ROR MARR

Choose higher-cost alternative

ROR MARR

DecisionTwo-alternative situation


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 by financial analysts in the company and provided to those who evaluate projects

• It is the same as the interest rate used for Present Worth and Annual Worth analysis.


ROR on Alternatives With Equivalent Benefits

YearCash flow - alternative A (Leaseco)

Cash flow - alternative

B (Saleco)

Cash flow - alternative

B - A

0 -$1,000.00 -$2,783.00 -$1,783.001 $200.00 $1,200.00 $1,000.002 $200.00 $1,200.00 $1,000.003 $1,200.00 $1,200.00 $0.004 $1,200.00 $1,200.00 $0.005 $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


Example 7-5 (Cont’d)

• 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 Cost” alternative from the cash flows of the “Higher First Cost” alternative to obtain the “Incremental Cash Flow” or • Compute the IRR on the incremental cash flow. This is the ROR.• For this problem the ROR is 8.01% which is MARR, therefore choose the lower cost alternative.


Example 7-5 (Cont’d)

• Q. Why did we do this?

• A. Both alternatives were acceptable compared only to the MARR. Since either alternative will work, the question is whether we want to spend the additional $1783 to go from the lower cost to the higher cost alternative. The benefit for doing so is the savings of two years of $1000 lease payments. Essentially we are getting an 8.01% return on that $1783 investment. The company can get 10% ROR on its money elsewhere, so reject the increment. That is, spend $1000 now on Leaseco and invest the other $1783 for a higher return.


Analysis Period• Just as in PW and AW analysis the analysis period must

be considered:– Useful life of the alternative equals the analysis period.

– Alternatives have useful lives different from the analysis period.

– The analysis period is infinite, n =

7-10

For an example of that uses a common multiple of the alternate service lives, see Example 7-10. EXCEL would be useful here because of the irregularity of the cash flows.

chapter 7 - rate of return analysis click here for streaming audio to accompany presentation...

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