Question

With the growing popularity of casual surf print clothing, two recent MBA graduates decided to broaden this casual surf concept to encompass a “surf lifestyle for the home.” With limited capital, they decided to focus on surf print table and floor lamps to accent people’s homes. They projected unit sales of these lamps to be 7,900 in the first year, with growth of 7 percent each year for the next five years. Production of these lamps will require $44,000 in net working capital to start. The net working capital will be recovered at the end of the project. Total fixed costs are $104,000 per year, variable production costs are $24 per unit, and the units are priced at $52 each. The equipment needed to begin production will cost $184,000. The equipment will be depreciated using the straight-line method over a five-year life and is not expected to have a salvage value. The effective tax rate is 35 percent and the required rate of return is 25 percent. What is the NPV of this project?

Answer 1

Net present value is difference between initial cost and present value of cash inflows.

discount factors are used to find present value of cash inflows.

Here, we will first find net income after tax for 5 years.

	1	2	3	4	5
sales units	7900	8,453[7900+7%]	9,044.71 [8453+7%]	9677.8397 [9044.71+7%]	10,355.288479[9677.8397+7%]
price per unit	$52	$52	$52	$52	$52
sale revenue	$410,800[7900*$52]	$439,556[8453*$52]	$470324.92[9044.71*$52]	$503,247.6644[9677.8397*$52]	$538,475[10355.288479*$52]
Less: variable costs	$189,600[7900*$24]	$202,872[8453*$24]	$217,073.04[9045*$24]	$232,268.1528[9677.8397*$24]	$248,526.923[10355.288479*$24]
Less: fixed costs	$104,000	$104,000	$104,000	$104,000	$104,000
Less: depreciation cost	$36,800	$36,800	$36,800	$36,800	$36,800
Net income before tax	$80,400[410,800-189600-104000-36800]	$95,884[439556-202872-104000-36800]	$112,451.88[470324.92-217073.04-104000-36800]	$130,179.5116[503247.664-232268.152-104000-36800]	$149,148.077[538,475-248,526.923-104000-36800]
Tax at 35%	$28,140[80400*35%]	$33,559[95884*35%]	$39,358.158[112451.88*35%]	$45,562.82906[130179.51156*35%]	$52,201.82695[149,148.077*35%]
Net income after tax	$52,260[80400-28140]	$62,325[95884-33559]	$73,093.72[112444.92-39355.722]	$84616.68254[130179.5116-45562.82906]	$96,946.25[149148.077-52201.82695]
Add: non cash depreciation expense	$36,800	$36,800	$36,800	$36,800	$36,800
Net cash inflows	$89,060[$52,260+36800]	$99,124.60[62325+36800]	$109,893.72[73093.72+36800]	$121,416.68254[84616.68254+36800]	$133,746.25[96946.25+36800]

variable costs changes with change in number of units

fixed costs remains constant at all levels of sale.

depreciation cost = cost-salvage/useful life

=$184,000/5

=$36,800

depreciation is non cash expense it does not result in cash outflow. so it will be added back however it save tax so it is necessary to give its effect while calculating net income.

Net present value

Year	Present value of cash flows	PV factor 25%	present value of cash inflows
0	($184,000)	1	($184,000)
0	($44,000)	1	($44,000)
1	$89,060	0.8[1/1.25]1	$71,248[$89060*0.8]
2	$99,124.60	0.64[1/1.25]2	$63,439.74[$99124.60*0.64]
3	$109,83.72	0.512[1/1.25]3	$56,265.59 [$10983.72*0.512]
4	$121,416.68	0.4096[1/1.25]4	$49,732.27 [$121416.68*0.4096]
5	$133,746.25	0.32768[1/1.25]5	$43,825.97 [$133,746.25*.32768]
5	$44,000(working capital received back)	0.32768	$14,418
Net present value			$70,929.57 [71248+63439.74+56265.59+49732.27+43825.97+14418-184000-44000]