note

We will now extend the concept of INCREMENTAL ANALYSIS , already introduced in Chapter 7, to the analysis of MULTIPLE ALTERNATIVES .

We will define MUTUALLY EXCLUSIVE ALTERNATIVES a group of alternatives out of which ONLY ONE may be implemented. The object of the incremental analysis is to select THE BEST ONE from the stand point of NPW, therefore not necessarily the most “attractive” one, this is because the attractive ROI is decided by the specific criteria preferred by the investor.

As seen in Chapter 7, the comparison of two mutually exclusive alternatives is done by computing the ∆IRR, which is the interest rate at which the Net Present Value NPW of the ∆investment to go from the less expensive alternate to the more expensive alternate: the ∆IRR is the IRR of the incremental investment

HIGHER COST ALTERNATIVE = LOWER COST ALTERNATIVE +

+INCREMENTAL INVESTMENT

The higher is the ∆IRR, the more attractive is the higher cost alternative

In the Figure above:

· Alternative A yields a higher NPW for i ≤ ∆IRR (A-B)

· Alternative B yields a higher NPW for ∆IRR (A-B) ≤ i ≤ ∆IRR (B-C)

· Alternative C yields a higher NPW for ∆IRR (B-C) ≤ i ≤ IRR (C)

· For i ≥ IRR (C) all Alternatives would yield a negative NPW

Example 8.1 – Your Company must decide which new piece of machinery to purchase from one of three potential suppliers; the machinery will remain in service for 12 years, and thereafter will be sold on the used market. You are requested to do an economic analysis to help the Manager decide.

The three submitted bids are:

Deluxe Option Regular Option Economy Option

Price 220,000 125,000 75,000

Benefits/yr 79,000 43,000 28,000

O&M/yr 38,000 13,000 8,000

Salvage 16,000 6,900 3,000

Produce an Excel spreadsheet:

Based on your analysis, you can advise your manager as follows:

· For i ≤ 6% choose the Deluxe Option

· For 6% ≤ i ≤ 17% choose the Regular Option

· For 17% ≤ i ≤ 25% choose the Economy Option

· For i ≥25% do not purchase any equipment

However, your manager is not completely satisfied with this analysis, and he/she asks you to analyze the “ profitability ” of each Alternative. To do so, you turn to your Excel spreadsheet:

So, you now advise:

· The Alternative Deluxe is profitable only for i ≤ 2%

· The Alternative Regular is profitable only for i ≤ 6%

· The Alternative Economy is profitable only for i ≤ 7.5%

· Choosing to invest on Deluxe over Regular is never profitable

· Choosing to invest on Regular over Economy is profitable only for i ≤ 3%

Your manager will have to choose which decision criteria is more important: maximizing the worth of the investment, or maximizing its profitability

Example 8.2 – As the Operation Manager (OM) of your Company, you have been asked by your Chief Executive Officer (CEO) to analyze the opportunity of opening a new branch in one of the following locations proposed by the Marketing Dept. : Houston, Milan, Tokyo, Moskow. The Company intends to keep the branch for a period of 10 years and then sell it (divest).

You collect the necessary data:

Then use an Excel Spreadsheet to do the analysis:

An then you analyze the graphs:

Your conclusions are:

· For i ≤ 6% the Milan Location is better than any other as far as the NPW, but the Houston Location is better as far as ROI

· For i ≥ 6% the Houston Location is better than any other as far as the NPW, but for i ≥ 14% the ROI becomes negative

· The Moskow Location is not advisable in any case, because it yields the lowest NPW and its ROI becomes negative for i ≥ 5.5%

Example 8.3 – A Power Plant needs to replace a pressure vessel with a new one which is expected to last for approximately 75 years. Three alternatives are available:

Brass Stainless steel Titanium

Cost 100,000 175,000 300,000

Life (yrs) 4 10 25

The expected life of the Power Plant is 75 years, it exceeds the useful life of all the alternatives and can be considered ∞ for compound interest calculations therefore we will make the usual assumption of identical replacements and compare the EUAC of the three alternatives.

Using an Excel spreadsheet and the equivalence (A/, i, n) = PMT (i, n,-1,0) :

Remember, these are EUAC, i.e. they are costs so the lower the better, therefore:

· For i ≤ 6.4% take the Titanium alternative

· For 6.4% ≤ i ≥ 15.4% take the Stainless-Steel Alternative

· For i ≥ 15.4% take the Brass Alternative

Note: since we are considering only costs, considerations of ROI are not applicable