Question

Belan, Inc. is considering a new project. The project will generate sales of $1.8 million, $2.5 million, $2.4 million, and $1.9 million over the next four years, respectively. The fixed assets required for the project will cost $2.75 million and are eligible for 100 percent bonus depreciation. At the end of the project, the fixed assets can be sold for $175,000. Variable costs will be 25 percent of sales and fixed costs will be $500,000 per year. The project will require NWC equal to 15 percent of sales that must be accumulated in the year prior to sales. The required return on the project is 13 percent and the tax rate is 21 percent.

What is the NPV of the project? What is the IRR of the project?

Answer 1

Fixed Asset Cost : $2.75 million

Fixed asset is eligible for 100% bonus depreciation so tax benefit in year 1 for the company = 21% of $2.75 million = $577,500

NWC has to accumulated in the year prior to sales, therefore NWC for sales in first year will have be brought in as initial investment. Every year NWC has be increased or decreased based on requirement of next year from the profit of the year

Year	1	2	3	4
Sales ($)	1,800,000	2,500,000	2,400,000	1,900,000
Fixed Cost ($)	500,000	500,000	500,000	500,000
Variable Cost ($) @25%	450,000	625,000	600,000	475,000
NWC ($) @15%	270,000	375,000	360,000	285,000
Profit($) = Sales -fixed cost -variable cost	850,000	1,375,000	1,300,000	925,000
Tax@21% ($)	178,500	288,750	273,000	194,250
Net Profit = Profit - Tax@21% ($)	671,500	1,086,250	1,027,000	730,750

Initial Cash out flow = Fixed Asset cost + NWC for sales of year 1 = $2.75 million + 15% of $1.8 million = $3.02 million

Cash inflow in year1 = Net Profit + Tax benefit due to bonus depreciation - Additional NWC required for sales in years 2 = 671,500 + 577,500 - (375,000-270,000) = $1,144,000

Cash inflow in year 2 = Net Profit - Additional NWC required for sales in years 3 = 1,086,250 - (360,000 - 375,000) = $1,101,250

Cash inflow in year 3 = Net Profit - Additional NWC required for sales in years 4 = 1,027,000 - (285,000 - 360,000) = $1,102,000

Cash inflow in year 4 =  Net Profit + NWC = 730,750 + 285,000 = $1,015,750

NPV = Initial cashflow + Present value of cashflow of year 1 + Present value of cashflow of year 2 .........

Required rate of return given: 13%

Initial Cashflow = - $3,020,000

PV of cashflow of year 1 = cashflow of year 1 / (1+required rate of return)^1 = 1,144,000 / 1.13 = $1,012,389

PV of cashflow of year 2 = cashflow of year 2 / (1+required rate of return)^2 = 1,101,250 / 1.13^2 = $862,440

PV of cashflow of year 3 = cashflow of year 3 / (1+required rate of return)^3 = 1,102,000 / 1.13^3 = $763,741

PV of cashflow of year 4 = cashflow of year 4 / (1+required rate of return)^4 = 1,015,750 / 1.13^4 = $622,978

NPV = $241,578

IRR is internal rate of return at which NPV of the project is zero

Assuming IRR = X

Using NPV equation used above for the NPV calculation and equating the NPV to 0, X can be calculated

0 = Initial cashflow + ( cashflow of year 1 / (1+X)^1 ) + ( cashflow of year 1 / (1+X)^2 ) + ( cashflow of year 1 / (1+X)^3 ) + ( cashflow of year 1 / (1+X)^4 )

0 = - 3,020,000 + ( 1,144,000 / (1+X)^1 ) + ( 1,101,250 / (1+X)^2 ) + ( 1,102,000 / (1+X)^3 ) + ( 1,015,750 / (1+X)^4 )

On solving above equation using scientific calculator, we get

X = 0.1687

There IRR is 16.87%