Question

1. Three mutually exclusive projects are being considered. The cash flows for each and corresponding rate of return are list below. MARR = 8% can any project eliminated? Using functional notation to solve for the incremental rate of return.

	1	2	3
0	-20000	-25000	-29000
1	2000	2500	3000
2	5000	6200	7000
3	8000	9900	11000
4	11000	13600	15000
ROR	9%	8.7%	7.4%

2. Which project must you choose based on the information provided below using conventional payback period.

	1	2	3	4
Initial cost	50000	30000	60000	45000
Annual Revenues	6500	4200	7700	7400
Length of ownership	10	15	10	6

Answer 1

1.

	1	2	3
ROR	9%	8.70%	7.40%

From the above it can be seen that the project 3 has ROR that is less than the MARR. Hence project 3 can be eliminated if MARR is 8%.

So let’s consider project 1 & 2 for the evaluation and calculate the incremental rate of return of the incremental cash flow of 2 – 1

	1	2	Incremental cash flow between cash flows of 2 and cash flows of 1
0	-20000	-25000	-25000 – (-20000) = -5000
1	2000	2500	2500 – 2000 = 500
2	5000	6200	6200 – 5000 = 1200
3	8000	9900	9900 – 8000 = 1900
4	11000	13600	13600 – 11000 = 2600

Calculating ROR by using trial and error method

PW of the ICF at MARR of 8%

PW at 8% = -5000 + 500 (1+.08) ^-1 + 1200 (1+.08) ^-2 + 1900 (1+.08) ^-3 + 2600 (1+.08) ^-4 = -89

As the PW is negative decrease the rate of interest to get positive NPW. Let the interest rate is 7%.

PW at 7% = 5000 + 500 (1+.07) ^-1 + 1200 (1+.07) ^-2 + 1900 (1+.07) ^-3 + 2600 (1+.07) ^-4 = 50

Using interpolation

Rate of Return = 7 + [50 – 0 ÷ 50 – (-89)]*1% = 7.35%

ROR of 2 – 1 < MARR – Select Project 1

2. Which project must you choose based on the information provided below using conventional payback period.

	1	2	3	4
Initial cost	50000	30000	60000	45000
Annual Revenues	6500	4200	7700	7400
Length of ownership	10	15	10	6
Payback period	50000/6500 =7.69 years	30000/4200 = 7.14 years	60000/7700 = 7.79 years	45000/7400 = 6.08 years
	ACCEPTABLE	ACCEPTABLE	ACCEPTABLE	REJECTED

ACCEPT PROJECT 2 BECAUSE OF LOWEST PAYBACK PERIOD.

Note – Payback period = Initial cost/Annual revenues.