Question

Two mutually exclusive alternatives of A and B have both useful lives of 6 years. For Alternative A there is an initial cost of $7,200, and the annual benefits, which is $2,100 for the first year and it increases by $120 each year for the next 5 years. For Alternative B, there is an initial cost of $3000 and the annual benefits, which is $1200 for the first year, and it increases by $100 each year for the next 5 years, By following Rate of Return Analysis and defining incremental rate of return define which alternative should be chosen? MARR is 11% (Wherever Necessary, use interest rates of 8% and 10% for your trials)

Answer 1

MARR = 11%

Life = 6 years

Calculating the incremental IRR using trial and error method

Let the interest rate is 9%

Calculate the PW of the incremental cash flow at 9%.

Years	Alternative A	Alternative B	Incremental Cash Flow of A - B	PW Factor at i=9%	PW of ICF
0	-7200	-3000	-4200	1	-4200
1	2100	1200	900	0.917431193	825.688073
2	2220	1300	920	0.841679993	774.345594
3	2340	1400	940	0.77218348	725.852471
4	2460	1500	960	0.708425211	680.088203
5	2580	1600	980	0.649931386	636.932759
6	2700	1700	1000	0.596267327	596.267327
Net Present Worth at 9%					39.1744265

The NPW of the incremental cash flow is positive. Increase the rate of interest to get negative PW. Increase the rate of interest to 10% to get negative PW.

Calculate the PW of the incremental cash flow at 10%.

Years	Alternative A	Alternative B	Incremental Cash Flow of A - B	PW Factor at i=10%	PW of ICF
0	-7200	-3000	-4200	1	-4200
1	2100	1200	900	0.909090909	818.181818
2	2220	1300	920	0.826446281	760.330579
3	2340	1400	940	0.751314801	706.235913
4	2460	1500	960	0.683013455	655.692917
5	2580	1600	980	0.620921323	608.502897
6	2700	1700	1000	0.56447393	564.47393
Net Present Worth at 10%					-86.5819467

Using interpolation

IRR = 9% + [39 – 0 ÷ 39 – (-87)]*1% = 9.31

IRR of Incremental Cash Flow of A – B is less than MARR (11%), so select B (Lowest Cost Alternative)

Note – For the accuracy purpose instead of 8%, we have used the 9%.