Question

A businessman has an opportunity to invest in one of three mutually exclusive alternatives. The first alternative has a first cost of $7000, a uniform annual benefit of $2000, and a salvage value of $500. The second has a first cost of $3500, a benefit of $900 the first year, and increasing by $100 per year thereafter. Its salvage value is $400. The third alternative has a first cost of $8000, a benefit of $2000 the first year, and increasing by 2% each year thereafter. Its salvage value is $500. Assume all alternatives have a 10 year life, and the company’s MARR is 10%.

A) Use incremental rate of return analysis to determine which alternative is best. State the rates as percentages, formatted to two decimal places (i.e., xx.xx%).You can do this manually or using Excel… in either case, be sure to show all your work!

B) Plot the results on a graph for values of i from 0 – 50%, and construct a choice table. Assuming a MARR of 10%, which alternative would you choose?

C) Are the results from part “a” and “b” consistent? Briefly discuss… (in 1-2 sentences).

(if using excel please post code)

Answer 1

HI,

Firstly let us calculate the IRR for all the 3 alterntives. They are computed as follows in the excel sheet. The IRR is calculated using the IRR formula in the excel.

From Above we can see that all the three alternatives have the IRR greater than the MARR of 10%. But the 3rd alternative has least IRR for higher investment amount. Hence this can be avoided.

When ROR analysis is applied for mutually exclusive projects; two steps need to be considered:
1) the rate of return on total individual project investment must be greater than or equal to the minimum rate of return, i*.
2) the ROR on incremental investment compared to the last satisfactory level of investment must be greater than or equal to the minimum ROR, i*.
The largest level of investment that satisfies both criteria is the economic choice.
Therefore, in mutually exclusive projects, a smaller ROR on a bigger investment often is economically better than a big ROR on a smaller investment. Therefore, it is often preferable to invest a large amount of money at a moderate rate of return rather than a small amount at a large return with the remainder having to be invested elsewhere at a specified minimum rate of return.

Based on above explanation the incremental ROR for Alternative A and B is as follows,

Based on the above explanations and workings the Alternative A is best suitable for the company.