Question

Dixon Weed Seeds Inc. is considering expanding. An outlay of ​$173 million is required for equipment for the​ expansion, and additional net working capital of ​$16 million is required to support the expansion. The equipment is expected to have a productive life of 9 ​years, and will be depreciated over 9 years to ​$25.31 million. It is expected to be sold at the end of its life for ​$20.76 million. Revenues minus expenses are expected to be ​$37.368 million per year for the life of the equipment. The​ corporation's marginal tax rate is 26​% and the cost of capital for this investment is 9​%. Compute the NPV of​ Dixon's proposed expansion. ​ (In $millions with 3​ decimals.)

Answer 1

The project has initial capital outlay of $173 million and additional net working capital requirement of $16 million. Both of these are initial investments in the project.

The project life is for 9 years. At the end of the 9^th year, the equipment would be depreciated to $25.31 million. We are concerned with how this depreciation takes place as depreciation expense is not a cash expense and is not considered in capital budgeting decisions.
Although the equipment's depreciated vlue is $25.31, it is expected to be sold at $20.76, which will result in loss on sale of equipment. This loss would provide a tax shield, which needs to be considered while calculating the cash flow.
Hence we first consider revenue minus expenses, loss on sale of equpiment and add them to arrive at profit before tax. We deduct tax from this to arrive at profit after tax. And then we add the salvage value of the equipment to arrive at the net cash flow for the concerned year. This way, we have considered cash flow from operations, cash flow from selling of equipment and the tax effect on it.

Then we discount each year's cash flow to today's date. Summing all of them gives us the NPV of the project.

Following table illustrates the cash flows

Year	0	1	2	3	4	5	6	7	8	9
Capital outlay	$ (173.000)
Working capital	$   (16.000)
Depreciated value										$ 25.310
Salvage value										$ 20.760
Gain / (loss) on sale of equipment										$ (4.550)
Revenue minus expenses		$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368
Profit before tax		$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 32.818
Tax @ 26%		$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (8.533)
Profit after tax		$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 24.285
Net cash flow	$ (189.000)	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 45.045
PV of cash flow	$ (189.000)	$ 25.369	$ 23.274	$ 21.353	$ 19.590	$ 17.972	$ 16.488	$ 15.127	$ 13.878	$ 20.740
NPV	$   (15.209)

From the calculations above we see that the NPV of the project is -$15.209 million

Edit 1 -

In that case, we need to change 2 two assumptions
Current assumption 1 - Capital outlay occurs now, and the asset goes operational at the beginning of year 1. If we change this to assume that the capital outlay happens now and the equipment starts producing goods right away. This means capital outlay and first year's operating cash flows occur in the same year. There is no clarity about this assumption in the question and it was safe to assume that the equipment takes one year to be production-ready and production begins at the beginning of year 1.

Current assumption 2 - As the question does not talk about what happens to the investment in working capital. Generally, when nothing is mentioned, it is safe to assume that this investment in working capital will be written down. The reason being, the seller will not be able to sell the last piece on the shelf. As there was no mention in the question about these assumptions, more logical assumptions were made.
We change this to assume that when the equipment is sold off, investment in working capital is also liquidated. The following table shows the calculations with changed assumptions and NPV of the project is calculated as $19.810

Year	0	1	2	3	4	5	6	7	8	9
Capital outlay	$ (173.000)
Working capital	$   (16.000)
Depreciated value										$ 25.310
Salvage value										$ 20.760
Gain / (loss) on sale of equipment										$ (4.550)
Revenue minus expenses	$      37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368
Profit before tax	$      37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 37.368	$ 32.818
Tax @ 26%	$      (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (9.716)	$ (8.533)
Profit after tax	$      27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 24.285
Proceeds from selling equipment										$ 20.760
Proceeds from liquidating working capital										$ 16.000
Net cash flow	$ (161.348)	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 27.652	$ 61.045
PV of cash flow	$ (161.348)	$ 25.369	$ 23.274	$ 21.353	$ 19.590	$ 17.972	$ 16.488	$ 15.127	$ 13.878	$ 28.107
NPV	$      19.810