Question

10.24 An automaker is considering installing a three-dimensional (3-D) computerized car-styling system at a cost of $230,000 (including hardware and software). With the 3-D computer modeling system, designers will have the ability to view their design from many angles and to fully account for the space required for the engine and passengers. The digital information used to create the computer model can be revised in consultation with engineers, and the data can be used to run milling machines that make physical models quickly and precisely. The automaker expects to decrease the turnaround time for designing a new automobile model (from configuration to final design) by 22%. The expected savings in dollars is $250,000 per year. The training and operating maintenance cost for the new system is expected to be $50,000 per year. The system has a five-year useful life and can be depreciated according to the five-year MACRS class. The system will have an estimated salvage value of $5,000. The automaker's marginal tax rate is 25%. Determine the annual cash flows for this investment. What is the return on investment for the project?

Answer 1

The depreciation expense for each year is shown in the table below : -

Year	Depreciation rate	Depreciation expense per year
1	20%	0.20 x $230000 = $46000
2	32%	0.32 x $230000 = $73600
3	19.20%	0.1920 x $230000 = $44160
4	11.52%	0.1152 x $230000 = $26496
5	11.52%	0.1152 x $230000 = $26496
6	5.76%	0.0576 x $230000 = $13248

The after tax cash flows is calculated as shown in the table below

Year	Expected savings ($)	Training and operating maintenance costs($)	Depreciation expense ($)	Taxable income	Taxes @ 25%	After tax cash flow
1	250000	50000	46000	250000-50000-46000 =154000	154000 x 0.25 = 38500	154000 - 38500 = 115500
2	250000	50000	73600	250000-50000-73600 = 126400	126400 x 0.25 = 31600	126400 - 31600 = 94800
3	250000	50000	44160	250000-50000-44160 = 155840	155840 x 0.25 = 38960	155840 - 38960 =  116880
4	250000	50000	26496	250000-50000-26496 = 173504	173504 x 0.25 = 43376	173504 - 43376 =  130128
5	250000 + 5000 ( salvage)	50000	26496	255000-50000-26496 = 178504	178504 x 0.25 = 44626	178504 - 44626 =  133878

The results are summarized in the table below : -

Year	Expected savings ($)	Training and operating maintenance costs($)	Depreciation expense	Taxable income	Taxes @ 25%	After tax cash flow
1	250000	50000	46000	154000	38500	115500
2	250000	50000	73600	126400	31600	94800
3	250000	50000	44160	155840	38960	116880
4	250000	50000	26496	173504	43376	130128
5	255000	50000	26496	178504	44626	133878
						∑After tax cash flow = 591186

Average after tax cash flow = After tax cash flow Number of years

$ 591186 Average after tax cash flow =

Average after tax cash flow = $ 118,237.2

Average after tax cash flow Return on investment = - -x 100 Initial investment

$ 118,237.2 Return on investment = $230,000 X 100

Return on investment for the project = 51.41 %