Question

The cash flows for four mutually exclusive alternatives are provided in the table below. If the useful life is 10 years for each alternative, find the best alternative using incremental rate of return analysis. MARR = 10%

P Q R S

Initial Cost 19,000 16,000 11,000 8,500

EUAB 3,500 3,100 2,200 1,350

A. Alt. S B. Alt. P C. Alt. Q D. Alt. R

Answer 1

The cash flows for four mutually exclusive alternatives are provided in the table below. If the useful life is 10 years for each alternative, find the best alternative using incremental rate of return analysis. MARR = 10%

	P	Q	R	S
Initial Cost	19,000	16,000	11,000	8,500
EUAB	3,500	3,100	2,200	1,350

Using Incremental Cash Flow Analysis calculate the IRR.

1. IRR of the incremental cash flow between R and S

	R	S	ICF of R – S
Initial Cost	-11,000	-8,500	-2500
EUAB	2,200	1,350	850

Using trial and error method

NPW of the ICF of R – S at MARR of 10%

NPW = -2500 + 850 (P/A, 10%, 10)

NPW = -2500 + 850 (6.1446) = 2723

Increasing MARR to get negative NPW

NPW at 20 %

NPW = -2500 + 850 (P/A, 20%, 10)

NPW = -2500 + 850 (4.1925) = 1067

Increasing MARR to get negative NPW

NPW at 30 %

NPW = -2500 + 850 (P/A, 30%, 10)

NPW = -2500 + 850 (3.0915) = 128

Increasing MARR to get negative NPW

NPW at 35 %

NPW = -2500 + 850 (P/A, 35%, 10)

NPW = -2500 + 850 (2.7150) = -192

Using interpolation IRR = 30% + 128 – 0 / [128 – (-192)]*5% = 32%

IRR of R – S > MARR – Select R, Reject S

2. IRR of the incremental cash flow between Q and R

	Q	R	ICF of Q- R
Initial Cost	-16,000	-11,000	-5000
EUAB	3,100	2,200	900

Using trial and error method

NPW of Q – R at MARR of 10 %

NPW = -5000 + 900 (P/A, 10%, 10)

NPW = -5000 + 900 (6.1446) = 530

Increasing MARR 15% to get negative NPW

NPW at 15%

NPW = -5000 + 900 (P/A, 15%, 10)

NPW = -5000 + 900 (5.0188) = -483

Using interpolation IRR = 10% + 530 – 0 / [530 – (-483)]*5% = 12.60%

IRR of Q – R > MARR – Select Q, Reject R

3. IRR of the incremental cash flow between P and Q

	P	Q	ICF of P – Q
Initial Cost	-19,000	-16,000	-3000
EUAB	3,500	3,100	400

Using trial and error method, calculate NPW of ICF of P – Q at MARR of 10%

NPW = -3000 + 400 (P/A, 10%, 10)

NPW = -3000 + 400 (6.1446) = -542

Decrease the MARR to get positive NPW

NPW at 5%

NPW = -3000 + 400 (P/A, 5%, 10)

NPW = -3000 + 400 (7.7217) = 89

Using interpolation IRR = 5% + 89 – 0 / [89 – (-542)]*5% = 5.70%

IRR of P – Q < MARR – Select Q, Reject P

Final Decision

Select C. Alt. Q