## Multiple Alternatives and Incremental Analysis

As was in the case of other analysis methods discussed, very often the decision is to choose the best of two or more alternatives. At first glance, it seems logical that the alternative with the highest rate of return is preferred. This is true only in the specific case where the initial investment is the same for all available alternatives. In cases where the initial investment is not the same, the alternatives are

A: To invest in the lower initial investment case and invest the rest of the capital where the investor can get his MARR.

B: To invest in the program with the higher initial investment.

To solve this problem, we perform what is called ''incremental analysis". The procedure is Step 1:

Set up the cash flow of all alternatives in ascending order of initial investment. Step 2:

Discard all alternatives that have an ROR less than the MARR. This step can be ignored but performing it will save time on the rest of the steps.

Step 3:

Construct the cash flow of the difference of alternatives two by two, starting from the two with the lowest ROR. Always subtract the one with lowest initial investment from the one with the higher initial investment. A check on this step is that the cash flow at time zero of the differential should always be negative.

If the ROR of the differential is higher than the MARR, the alternative with the higher initial investment is preferred, otherwise the one with the lower initial investment is preferred. Next we compare the preferred alternative with the next alternative on the list in the same manner.

### Example 5.2

An investor is offered two investment opportunities. Proj ect A is an investment in frozen yogurt equipment that requires an initial investment of \$40,000 with a life of three years. Its annual operating costs and annual incomes are presented in table A. The equipment can be sold at the end of year 3 at a resale value of \$5,000.

Table A

Year 1 2 3

Income 25000 33000 45000

### Expense 15000 18000 20000

The second opportunity is purchase of printing equipment with an initial investment of \$200,000. Annual operating costs and annual incomes are presented in table B. The equipment can be sold at the end of year 5 at a resale value of \$20,000.

Table B

Income 110000 135000 170000 210000 230000

Expense 100000 110000 115000 120000 130000

If the MARR for this investor is 10%, which project should he invest in? Ignore tax and depreciation. Step 1:

Draw the cash flow diagram of the frozen yogurt project, and check it against the null alternative.

The net cash flow is

NPW = -40000+10000(P/F,i*,1)+15000(P/F,i*,2)+30000(P/F,i*,3) By trial and error, i* = 14.7% i* > 10%

Therefore, this alternative compared to the null alternative is acceptable Step 2:

Draw the cash flow diagram of the print shop proposal.

 L 2ÛOOO i L I 200000 1000 J ii Î000 t ] ÎÛOO 12 DOOO JOOO

The net cash flow diagram in this case is

 * T 90ÛI 1 )0 L i L 200000

Calculating ROR as we did in the case of project A we obtain ROR=11%.

At first look, we are inclined to state that we should choose project A, which means we invest \$40,000 in project A and invest the rest where we can get the required MARR of 10%.

But let us follow the rules and do the incremental analysis. We will see that our hunch is not correct.

Step 3:

We have to use the incremental cash flow diagram, i.e.,. B-A. In calculating ROR, we do not have to equalize the lives. That makes it easier. The incremental cash flow is

120000

90000

A. ^ 1

L

fc-

V

2 00000-40000= 160000

>

The ROR for this incremental cash flow is calculated as follows: NPW^-160000 ^OfP/i, ¿M) 4 lOOOOtP/F, i',2) + 25GM(P,'*; +90000(F.T, /*,4>

By trial and error, i* = 10.5. Therefore, ¿>10%; hence, project B is preferred.

This means it is better to invest all the available money (\$200,000) in project B at 10.5% rather than invest \$40,000 in project A and the rest at MARR of10%.

Another way of testing is to substitute the value of MARR for i* in the equation obtained for the NPW of the incremental analysis of the two proj ects. If the resulting NPW is positive, proj ect B is preferred.

An interested reader can follow the hunch and calculate the return of the combination of choosing project A and investing the difference between the initial payment of project A and B at the MARR and see that the initial hunch is not correct. The spreadsheet for Example 5.2 is shown below. The discrepancy is due to rounding to different decimal points.

 • 1 £ F I B H ■; 1 EllAfJc i.i t 10Ï I * Proitc.[ A: s Yiir 0 1 2 3 4 5 ^ IftCQIM c as.ooc ».00« 50,000 t Evpcnj 40.000 15.000 18,000 £0,000 Mo (40,00(11 10. WQ 15,004 30,000 * 1 » Fer Excel iw* «IRR! m G 7 tRRi 14 70Ï 11 For QitsîUo Pro 1 OVCS'Fei it Hi IRB= 14,701 i j Project B 1 ) Ytir 0 1 2 3 1 5 1 J Inç^mi 1 10,000 134,000 170.000 i 10,000 HO.WO Expend Kill.«« 100,000 ito.ooc 115,000 120,000 130.000 N.I IPOO.WC) 10,000 Î3.W0 55,000 90,000 iSUjOCC )i For EkîcI uJi =IRR(Cl 6..Mf t) Iffl: 11.001 11 For Guattro fro «¡^ i'. IF:R| 1!f■ H !Ç,) i* H 1S IRRi 11.00Ï H :t bcrim^rtil Projtii B ■ Projaït A SI 0 10,000 £5,000 30,000 tsojoco U For Eitdtiit MnntCSI .MS1 1 ir rft 10.4SÏ F or Uuutrî Pre u IRR( 1 QÎ.CÎ t H21 ) a»H 2* IRRc l0.«t