Question

In: Economics

Annual costs of 3 different systems are provided below. If the MARR is 8%, which system...

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

If you use Excel to solve these problems, please provide details of the functions that you used.

Solutions

Expert Solution

MARR = 8%

We need to perform incremental IRR analysis

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

Showing formula in excel

System Costs Incremental IRR Analysis
Year A B C B-A C-B
0 0 -2000000 -4000000 =O30-N30 =P30-O30
1 -9000000 -3800000 -1900000 =O31-N31 =P31-O31
2 -9000000 -3800000 -1900000 =O32-N32 =P32-O32
3 -9000000 -3800000 -1900000 =O33-N33 =P33-O33
4 -9000000 -3800000 -1900000 =O34-N34 =P34-O34
5 -9000000 -3800000 -1900000 =O35-N35 =P35-O35
6 -9000000 -3800000 -1900000 =O36-N36 =P36-O36
7 -9000000 -3800000 -1900000 =O37-N37 =P37-O37
8 -9000000 -3800000 -1900000 =O38-N38 =P38-O38
Incremental IRR =IRR(Q30:Q38) =IRR(R30:R38)

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