Question

Old Southwest Canning Co. has determined that any one of four machines can be used in its chili-canning operation. The cost and revenues of the machines are estimated below, and all machines have a 7-year life. If the minimum attractive rate of return is 10% per year, determine the incremental rate of return of the last comparison on the basis of a rate of return analysis. (As of %)

Machine	First Cost, $	Annual Revenue, $
1	−105,000	21,000
2	−123,000	41,000
3	−312,000	78,000
4	−348,000	58,000

Answer 1

Taking in pairs we can find the incremental cash flows between the projects and thereafter determining the incremental IRR.

Incremental Cash flow = Difference in cash flows of project

For IRR, using the following formula or the excel in-built function of IRR.

Project 1 and Project 2
Rate of return	10%
Year	0	1	2	3	4	5	6	7	IRR
Project 1	-105000	21000	21000	21000	21000	21000	21000	21000	9%
Project 2	-123000	41000	41000	41000	41000	41000	41000	41000	27%
Incremental Cash flows (Project 2 - Project 1)	-18000	20000	20000	20000	20000	20000	20000	20000	111%

Here, incremental IRR > required rate of return and hence it is advisable to SWITCH from project 1 to Project 2.

Project 2 and Project 3
Rate of return	10%
Year	0	1	2	3	4	5	6	7	IRR
Project 2	-123000	41000	41000	41000	41000	41000	41000	41000	27%
Project 3	-312000	78000	78000	78000	78000	78000	78000	78000	16%
Incremental Cash flows (Project 3 - Project 2)	-189000	37000	37000	37000	37000	37000	37000	37000	9%

Here, incremental IRR < required rate of return and hence it is NOT advisable to SWITCH from project 2 to Project 3.

Project 3 and Project 4
Rate of return	10%
Year	0	1	2	3	4	5	6	7	IRR
Project 3	-312000	78000	78000	78000	78000	78000	78000	78000	16%
Project 4	-348000	58000	58000	58000	58000	58000	58000	58000	4%
Incremental Cash flows (Project 4 - Project 3)	-36000	-20000	-20000	-20000	-20000	-20000	-20000	-20000	#NUM!

Here, incremental cash flows are negative and hence no incremental IRR.