Question

A small café is considering replacing one of its waitstaff with a ‘robot’ – a device that will take orders, deliver food and interact with customers in an entertaining way. The cost of the robot is $225,000. From the salary savings and the extra customers the robot is expected to attract, it is estimated that the net inflows from the idea will be: • Year 1: $95,100 • Year 2: $80,000 • Year 3: $60,000 • Year 4: $55,000 It is expected that novelty will lessen over time, and after four years the robot will be worthless and superseded with a newer model.

TASK 1: Using the formulas and examples from the Week 10 lecture, perform a cost benefit analysis by calculating the payback period (PBP), the return on investment (ROI), the Net Present Value (NPV) and the Internal Rate of Return (IRR). Assume the desired rate of return is 12%.

Answer 1

1)	PAYBACK PERIOD:
	Year	Cash flows	Cumulative Cash Flows
	0	$       -2,25,000	$             -2,25,000
	1	$            95,100	$             -1,29,900
	2	$            80,000	$                 -49,900
	3	$            60,000	$                  10,100
	4	$            55,000	$                  65,100
	Payback period = 2+49900/60000 =			2.83	Years
2)	RETURN ON INVESTMENT:
	= Average annual profit/Investment
	Average annual profit = (95100+80000+60000+55000-225000)/4 =					$      16,275
	[To get profit, depreciation is to be deducted from cash flow.
	So total depreciation, that is cost of the asset is deducted from the
	total of cash flows for the 4 years]
	ROI = 16275/225000 =			7.23%
3)	NPV:
	Year	Cash flows	PVIF at 12%	PV at 12%
	0	$       -2,25,000	1	$   -2,25,000
	1	$            95,100	0.89286	$        84,911
	2	$            80,000	0.79719	$        63,776
	3	$            60,000	0.71178	$        42,707
	4	$            55,000	0.63552	$        34,953
	NPV =			$           1,347
4)	IRR is that discount rate for which NPV = 0. It is to be found
	out by trial and error.
	Discounting with 13%.
	Year	Cash flows	PVIF at 13%	PV at 13%
	0	$       -2,25,000	1	$   -2,25,000
	1	$            95,100	0.88496	$        84,159
	2	$            80,000	0.78315	$        62,652
	3	$            60,000	0.69305	$        41,583
	4	$            55,000	0.61332	$        33,733
	NPV =			$         -2,873
	IRR [0 NPV] lies between 12% and 13%. By simple
	interpolation IRR = 12%+1%*1347/(1347+2873) =			12.32%