Please solve with details A firm is considering which of two machines to install
ID: 1106116 • Letter: P
Question
Please solve with details
A firm is considering which of two machines to install to reduce costs. Both machines have useful life of 5 years and no salvage value. Machine A costs 826 QAR and can be expected to result in 200 QAR savings annually. Machine B costs 1,450 QAR and will provide cost savings of 300 QAR the first year but will increase 50 QAR annually, making the second-year savings 350 QAR, the third-year savings 400 QAR and so forth. 1. Develop the cash flow series (Incremental Cash Flow Table). 2. Set up the present worth relation for the incremental ROR. 3. If the company's MARR is 10% per year, determine which machine should be selected based on incremental present worth ROR analysis? 4. Find the exact ROR.Explanation / Answer
a) The incremental cash flow is shown below
Cash flows
End of year
A
B
B-A
0
-826
-1450
-624
1
200
300
100
2
200
350
150
3
200
400
200
4
200
450
250
5
200
500
300
b) For finding the ROR, we need to show that PW = 0
-624 + 100(P/A, i%, 5) + 50(P/G, i%, 5) = 0
c) The rate of return can be found by checking for a range of interest rate by trial and error
Take i = 10%
PW(10%) = -624 + 100(P/A, 10%, 5) + 50(P/G, 10%, 5) = -624 + 100*3.7908 + 50*6.8618 = 98.17
Take i = 15%
PW(10%) = -624 + 100(P/A, 15%, 5) + 50(P/G, 15%, 5) = -624 + 100*3.3522 + 50*5.7751 = -0.025
Note that when i% = 10, PW is positive while when interest rate is 15%, PW is almost zero. Hence PW is positive for 10% < i% < 15% and since MARR is 10%, increment gives a positive present worth. Hence B should be accepted.
d) Interpolation gives ROR
= (Lower interest rate) + (higher interest rate - lower interest rate)*(PV at lower interest rate / PV of lower interest rate - PV of higher interest rate)
= 10% + (15% - 10%)*(98.17/(98.17 + 0.025)) = 14.99%.
Cash flows
End of year
A
B
B-A
0
-826
-1450
-624
1
200
300
100
2
200
350
150
3
200
400
200
4
200
450
250
5
200
500
300