Question

Potable (drinkable) water is in short supply in many countries. To address this need, two mutually exclusive systems to purify water are being considered for implementation in one country by Engineers without Borders. Doing nothing is not an option. Refer to the data below and state your key assumptions in working this problem. Use a MARR of 10%. Capital Investment Annual Revenues Annual Expenses Market Value at End of Life Useful Life $100,000 $48,000 $24,000 $18,000 5 years $150,000 $65,000 $35,000 10 years

Please do in Excel

Answer 1

Details given:
	Particulars	Option 1	Option 2
1	Capital Investment	100000	150000
2	Annual Revenue	48000	65000
3	Annual Expense	24000	35000
4	Market value at the end of life	18000	0
5	Useful life (years)	5	10

Assumptions:

No depreciation

Cash flow at the end of each period

Answer to Qn. No.4:

By trial and error method based on MARR of 10%, to arrive at an NPV of zero

Option 1:

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	NPV
Investment	-100000
Annual revenue		48000	48000	48000	48000	48000
Annual expense		-24000	-24000	-24000	-24000	-24000
Mkt. value						18000
Net cash outflow/inflow	-100000	24000	24000	24000	24000	42000	38000
PV @ IRR of 10%	-100000.00	21818.18	19834.71	18031.56	16392.32	26078.70	2155.47
PV @ IRR of 10.5%	-100000.00	21719.46	19655.62	17787.89	16097.64	25494.00	754.60
PV @ IRR of 11%	-100000.00	21621.62	19478.94	17548.59	15809.54	24924.96	-616.35
Hence, the IRR is between 10.5 and 11%
PV @ IRR of 10.75%	-100000.00	21670.43	19566.98	17667.70	15952.78	25207.55	65.43
PV @ IRR of 10.76%	-100000.00	21668.47	19563.45	17662.92	15947.02	25196.17	38.02
PV @ IRR of 10.77%	-100000.00	21666.52	19559.91	17658.13	15941.26	25184.80	10.62
PV @ IRR of 10.774%	-100000.00	21665.73	19558.50	17656.22	15938.96	25180.25	-0.34
PV @ IRR of 10.78%	-100000.00	21664.56	19556.38	17653.35	15935.50	25173.44	-16.77

Hence, IRR for option 1 is 10.774%

Option 2

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10	NPV
Capital Investment	-150000
Annual Revenue		65000	65000	65000	65000	65000	65000	65000	65000	65000	65000
Annual Expense		-35000	-35000	-35000	-35000	-35000	-35000	-35000	-35000	-35000	-35000
Net cash outflow/inflow	-150000	30000	30000	30000	30000	30000	30000	30000	30000	30000	30000
PV @ IRR of 10%	-150000.00	27272.73	24793.39	22539.44	20490.40	18627.64	16934.22	15394.74	13995.22	12722.93	11566.30	34337.01
PV @ IRR of 12%	-150000.00	26785.71	23915.82	21353.41	19065.54	17022.81	15198.93	13570.48	12116.50	10818.30	9659.20	19506.69
PV @ IRR of 15%	-150000.00	26086.96	22684.31	19725.49	17152.60	14915.30	12969.83	11278.11	9807.05	8527.87	7415.54	563.06
PV @ IRR of 16%	-150000.00	25862.07	22294.89	19219.73	16568.73	14283.39	12313.27	10614.89	9150.76	7888.59	6800.51	-5003.18
PV @ IRR of 15.5%	-150000.00	25974.03	22488.33	19470.42	16857.51	14595.24	12636.57	10940.76	9472.52	8201.31	7100.70	-2262.61
Hence, the IRR is between 15 and 15.5%
PV @ IRR of 15.2%	-150000.00	26041.67	22605.61	19622.93	17033.79	14786.28	12835.31	11141.76	9671.67	8395.55	7287.80	-577.63
PV @ IRR of 15.1%	-150000.00	26064.29	22644.91	19674.12	17093.07	14850.62	12902.36	11209.70	9739.10	8461.42	7351.37	-9.04
PV @ IRR of 15.098%	-150000.00	26064.74	22645.70	19675.14	17094.25	14851.91	12903.71	11211.06	9740.45	8462.75	7352.64	2.36

Hence, IRR for option2 is 15.098%

Since the IRR for option 2 is higher, option 2 shall be chosen.

Answer to Question no.5:

Using Average (discounted) payback method

Option 1

Net cash inflow per year	48000-24000	24000
PVAF of 10% for 5 years		3.791
Discounted cash inflow at MARR of 10%		90984
Market value at the end of 5 years		18000
PV of Market value at the end of 5th year	PVF=0.621	11178
Total discounted net cash inflow		102162
Initial investment		100000
Pay back period		0.9788
		i.e.0.98 years
		11 months 23 days

Option 2

Net cash inflow per year	48000-24000	24000
PVAF of 10% for 10 years		11.914
Discounted cash inflow at MARR of 10%		285936
Initial investment		150000
Payback period		1.9062
		i.e.1.91 years
		1 year 10 months and 28 days

Based on Discounted, Averaging PB method, Option 1 is better

Note: Since Market value at the end of the period is given for option 1, and MARR of 10% is also given, Discounted, Averaging method used for finding payback period