Question

5) 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 $8,660,000 $8,240,000

2 $9,000,000 $8,660,000 $8,240,000

3 $9,000,000 $8,660,000 $8,240,000

4 $9,000,000 $8,660,000 $8,240,000

5 $9,000,000 $8,660,000 $8,240,000

6 $9,000,000 $8,660,000 $8,240,000

7 $9,000,000 $8,660,000 $8,240,000

8 $9,000,000 $8,660,000 $8,240,000

Answer 1

The amounts mentioned is cost therefore, it must be negative. Refer the attached picture below.

Here system A has the lowest initial investment therefore, consider it as the base alternative the determine the incremental cash flow that is system B minus system A.

We can determine the incremental internal rate of return through trial and error method. Ler us assume rate = 7%

At a rate of 7% the NPW is positive thus increase the rate. Assume rate = 8%

Now apply linear interpolation to determine the incremental rate of return

Here the incremental rate of return of B -A is less than marr. Thus, reject B and select system A.

Now refer the last column of the above table. The NPW can be determined as follows

Consider rate = 11%

Solving for NPW we get

Now consider rate = 10%

Now apply linear interpolation

Accept system C and reject System A.

I have solved it using Excel as well as manually please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me please help. Thank you.