Question

A project requires an initial investment of $20,000,000. The life of the project is 3 years. The $20,000,000 investment will be depreciated using the three-year modified accelerated cost recovery system (MACRS) class (see the table below). The firm estimates that, in the first year, the revenues and total production costs will be $60,000,000 and $45,000,000, respectively, in nominal terms. After that the sales and production costs are expected to increase at the inflation rate of 4 percent per year over the life of the project. In addition, it has a before-tax salvage value (or resale value) at the end of the project of $9,000,000. The mine will require a net working capital (NWC) investment of 7 percent of sales. The NWC will be built up in the year prior to the sales (e.g., the net working capital requirement for year 0 is 7% of sales in year 1 and the additional net working capital cash flow for year 1 is 7% of the difference in sales between year 2 and year 1). All net working capital cash flows are fully recoverable when the project ends. The tax rate is 25 percent. The project only depreciates the $20,000,000 initial cost. The salvage value is excluded from depreciation. a) Find the operating cash flow (OCF) of this project for each year. b) If the real discount rate (or required rate of return) of the project is 14 percent, what is its net present value (NPV)? Year MACRS Depreciation Allowances for 3-year Recovery Period Class 1 33.33% 2 44.44% 3 14.82% 4 7.41%

Answer 1

Year	1	2	3
cost of machine	20000000	20000000	20000000
MACRS rate	33.33%	44.44%	14.82%
Annual depreciation	6666000	8888000	2964000
Accumulated depreciaton	18518000
Book value of equipment at the end of year 3	20000000-18518000	1482000
gain on on sale of equipment	9000000-1482000-	7518000
tax on gain on sale of equipment	7518000*25%	1879500
after tax sale proceeds	9000000-1879500	7120500
Year	0	1	2	3
sales		60000000	62400000	64896000
required working capital-7% of next year sales	-4200000	-4368000	-4542720	0
Investment in working capital	-4200000	-168000	-174720	4542720
Year	0	1	2	3
cost of equipment	-20000000
annual revenue = revenue in year 1*(1+inflation rate)^n		60000000	62400000	64896000
annual cost = cost in year 1*(1+inflation rate)^n		45000000	46800000	48672000
annual depreciation		6666000	8888000	2964000
operating profit		8334000	6712000	13260000
less tax-25%		2083500	1678000	3315000
after tax profit		6250500	5034000	9945000
add depreciation		6666000	8888000	2964000
after tax sale proceeds				7120500
Investment in working capital	-4200000	-168000	-174720	4542720
net operating cash flow	-4200000	12748500	13747280	24572220
present value factor at 14% =1/(1+r)^n r =14%	1	0.877192982	0.769467528	0.674971516
present value of net operating cash flow = net operating cash flow*present value factor	-24200000	11182894.74	10578085.56	16585548.59
Net present value =sum of present value of net operating cash flow	14146528.89