Question

) Annual costs of 3 different systems are provided below. If the MARR is 8%, which system is the least costly of the three? Use incremental investment analysis and show all steps.

Year	System A	System B	System C
0	$0	$2,000,000	$4,000,000
1	$9,000,000	$3,800,000	$1,900,000
2	$9,000,000	$3,800,000	$1,900,000
3	$9,000,000	$3,800,000	$1,900,000
4	$9,000,000	$3,800,000	$1,900,000
5	$9,000,000	$3,800,000	$1,900,000
6	$9,000,000	$3,800,000	$1,900,000
7	$9,000,000	$3,800,000	$1,900,000
8	$9,000,000	$3,800,000	$1,900,000

Answer 1

MARR = 8%

We need to perform incremental IRR analysis

In order to calculate incremental IRR, first, we arrange the options in the increasing value of their initial cost

We need to find incremental cash flow between lowest and second lowest option first, then use the formula of IRR in excel on the incremental cash flow, if incremental IRR is greater than MARR then select the second lowest option if it is less than the MARR then select the lowest option.

Keep repeating the above until the last option is evaluated

Using excel

	System Costs			Incremental IRR Analysis
Year	A	B	C	B-A	C-B
0	0	-2000000	-4000000	-2000000	-2000000
1	-9000000	-3800000	-1900000	5200000	1900000
2	-9000000	-3800000	-1900000	5200000	1900000
3	-9000000	-3800000	-1900000	5200000	1900000
4	-9000000	-3800000	-1900000	5200000	1900000
5	-9000000	-3800000	-1900000	5200000	1900000
6	-9000000	-3800000	-1900000	5200000	1900000
7	-9000000	-3800000	-1900000	5200000	1900000
8	-9000000	-3800000	-1900000	5200000	1900000
Incremental IRR				259.99%	94.54%

We compare first A and B, since A has the lowest cost, and the second lowest option is B, incremental IRR > MARR so we select B, and reject A

Now we find incremental cash flow between C & B, we find incremental IRR>MARR, so we select C and reject B

Option C should be selected as per Incremental IRR analysis