Question

Green Lawn Care is analyzing the replacement of an aging compactor motor. The key parameters of the three motors under scrutiny (Small, Medium and Big) are provided below.
Parameters	Small	Medium	Big
1. Initial Cost ($)	300,000	425,000	510,000
2. Revenues ($)	200,000 annually	200,000 at EOY1 increasing by 1% annually thereafter	290,000 at EOY1 decreasing by 1% annually thereafter
3. Operating Costs ($)	100,000 at EOY1 decreasing by $2,000 annually thereafter.	110,000 at EOY1 increasing by $500 annually thereafter.	165,000 at EOY1 increasing by $2,500 annually thereafter
4. End-of-life salvage value ($)	10,000	-5,000	30,000
5. Useful life (years)	5	10	10
EOY = End-of-year Industry Standard = 4 years MARR = 10%

21. Medium’s External Rate of Return (ERR) (second decimal; no rounding) is a) 10.98%; b) 11.30%; c) 13.60%; d) 14.37%.

22. Big’s External Rate of Return (ERR) (second decimal; no rounding) is a) 10.15%; b) 11.30%; c) 12.46%; d) 12.83%.

23. The incremental External Rate of Return (ΔERR) between Small and Big (second decimal; no rounding) is
    a) 9.00%; b) 9.38%; c) 10.16%; d) 10.32%.

24. The incremental External Rate of Return (ΔERR) between Medium and Big (second decimal; no rounding) is
    a) 8.40%; b) 8.76%; c) 9.18%; d) 10.06%.

25. The best (valid) motor based on the External Rate of Return (ERR) method (use as many decimals as required) is
    a) Small; b) Medium; c) Big.

Answer 1

Medium
	Cost
Year	Cash Outflow	ERR	Net Discounted Cost
1	110000	0.1098	12078
2	110500	0.113	12486.5
3	111000	0.136	15096
4	111500	0.1437	16022.55
Salvage Value	5000	0.1437	718.5
			56401.55
	Revenue
Year	Cash Inflow	ERR	Net Discounted Revenue
1	200000	0.1098	21960
2	202000	0.113	22826
3	204020	0.136	27746.72
4	206060.2	0.1437	29610.85074
			102143.5707
	Net Incremental ERR		45742.02074

	Big
	Cost
Year	Cash Outflow	ERR	Net Discounted Cost
1	165000	0.1015	16747.5
2	167500	0.113	18927.5
3	170000	0.1246	21182
4	172500	0.1283	22131.75
Salvage Value	-30000	0.1283	-3849
			75139.75
	Revenue
Year	Cash Inflow	ERR	Net Discounted Revenue
1	290000	0.1015	29435
2	287100	0.113	32442.3
3	284229	0.1246	35414.9334
4	281387	0.1283	36101.9521
		0.1283	133394.1855
	Net Incremental ERR		58254.4355

Incremental ERR Small & Big
Year	Cash Flow Small	Cash Flow Big	Incremental Cash Flow	Incremental ERR	Incremental Cash Flow
1	200000	165000	35000	0.09	3150
2	200000	167500	32500	0.938	30485
3	200000	170000	30000	0.1016	3048
4	200000	172500	27500	0.1032	2838
			Incremental ERR Small & Big		39521

	Incremental ERR Medium & Big
Year	Cash Flow Big	Cash Flow Midium	Incremental Cash Flow	Incremental ERR	Incremental Cash Flow
1	165000	110000	55000	0.84	46200
2	167500	110500	57000	0.876	49932
3	170000	111000	59000	0.918	54162
4	172500	111500	61000	0.1006	6136.6
		Incremental ERR Small & Big			156430.6

Conclusion

The Best Method of is

Incremental ERR Medium & Big