**Bethesda Mining Company**

To be able to analyze the project, we need to calculate the project’s NPV, IRR, MIRR, Payback Period, and Profitability Index.

Since net working capital is built up ahead of sales, the initial cash flow depends in part on this cashoutflow. So, we will begin by calculating sales. Each year, the company will sell 600,000 tons undercontract, and the rest on the spot market. The total sales revenue is the price per ton under contracttimes 600,000 tons, plus the spot market sales times the spot market price. The sales per year will be:

Year1 / 2 / 3 / 4

Contract / 20,400,000 / $20,400,000 / $20,400,000 / $20,400,000

Spot / $2,000,000 / $5,000,000 / $8,400,000 / $5,600,000

Total / $22,400,000 / $25,400,000 / $28,800,000 / $26,000,000

The current after-tax value of the land is an opportunity cost. The initial outlay for net workingcapital is the percentage required net working capital times Year 1 sales, or:

Initial net working capital = .05($22,400,000) = $1,120,000

So, the cash flow today is:

Equipment –$30,000,000

Land –5,000,000

NWC –1,120,000

Total –$36,120,000

Now we can calculate the OCF each year. The OCF is:

Year1 / 2 / 3 / 4 / 5 / 6

Annual

Revenue / $22,400,000 / $25,400,000 / $28,800,000 / $26,000,000

Less: Variable

Costs / $8,450,000 / $9,425,000 / $10,530,000 / $9,620,000

Less: Fixed

Costs / $2,500,000 / $2,500,000 / $2,500,000 / $2,500,000 / $4,000,000 / $6,000,000

Less: Depreciation / $4,290,000 / $7,350,000 / $5,250,000 / $3,750,000

EBIT / $7,160,000 / $6,125,000 / $10,520,000 / $10,130,000 / ($4,000,000) / ($6,000,000)

Tax @ 34% / $2,434,400 / $2,082,500 / $3,576,800 / $3,444,200 / ($1,360,000) / ($2,040,000)

Net Income / $4,725,600 / $4,042,500 / $6,943,200 / $6,685,800 / ($2,640,000) / ($3,960,000)

Add: Depreciation / $4,290,000 / $7,350,000 / $5,250,000 / $3,750,000

OCF / $9,015,600 / $11,392,500 / $12,193,200 / $10,435,800 / ($2,640,000) / ($3,960,000)

Years 5 and 6 are of particular interest. Year 5 has an expense of $4 million to reclaim the land, and

it is the only expense for the year. Taxes that year are a credit, an assumption given in the case. In

Year 6, the charitable donation of the land is an expense, again resulting in a tax credit. The land

does have an opportunity cost, but no information on the after-tax salvage value of the land is

provided. The implicit assumption in this calculation is that the after-tax salvage value of the land in

Year 6 is equal to the $6 million charitable expense.

Next, we need to calculate the net working capital cash flow each year. NWC is 5 percent of next

year’s sales, so the NWC requirement each year is:

Year0 / 1 / 2 / 3 / 4 / 5 / 6

Beginning WC / $1,120,000 / $1,270,000 / $1,440,000 / $1,300,000

Ending WC / $1,270,000 / $1,440,000 / $1,300,000 / $0

NWC CF / ($150,000) / ($170,000) / $140,000 / $1,300,000

The last cash flow we need to account for is the salvage value. The fact that the company is keeping

the equipment for another project is irrelevant. The after-tax salvage value of the equipment should

be used as the cost of equipment for the new project. In other words, the equipment could be sold

after this project. Keeping the equipment is an opportunity cost associated with that project. The

book value of the equipment is the original cost, minus the accumulated depreciation, or:

Book value of equipment = $30,000,000 – 4,290,000 – 7,350000 – 5,2502,000 – 3,750,000

Book value of equipment = $9,360,000

Since the market value of the equipment is $18 million, the equipment is sold at a gain to book

value, so the sale will incur the taxes of:

Taxes on sale of equipment = ($18,000,000 – 9,360,000)(.34) = $2,937,600

And the after-tax salvage value of the equipment is:

After-tax salvage value = $18,000,000 – 2,937,600

After-tax salvage value = $15,062,400

So, the net cash flows each year, including the operating cash flow, net working capital, and after-tax

salvage value, are:

Year0 / 1 / 2 / 3 / 4 / 5 / 6

Capital

Spending / ($30,000,000) / $0 / $0 / $0 / $15,062,400 / $0 / $0

Opportunity

Cost / ($5,000,000)

NWC / ($1,120,000) / ($150,000) / ($170,000) / $140,000 / $1,300,000

OCF / $9,015,600 / $11,392,500 / $12,193,200 / $10,435,800 / ($2,640,000) / ($3,960,000)

Total Project

Cash Flow / ($36,120,000) / $8,865,600 / $11,222,500 / $12,333,200 / $26,798,200 / ($2,640,000) / ($3,960,000)

So, the capital budgeting analysis for the project is:

Payback period = 3 + $3,698,700/$26,798,200

Payback period = 3.14 years

Profitability index =

Profitability index = 1.08

The equation for IRR is:

I have calculated the IRR using Trial & Error as noted on the attached excel sheet, the IRR = 15.6%.

MIRR = 13.39%

Year0 / 1 / 2 / 3 / 4 / 5 / 6

OCF / ($36,120,000) / $8,865,600 / $11,222,500 / $12,333,200 / $26,798,200 / ($2,640,000) / ($3,960,000)

PV Factor

@ 12% / 1 / 0.8929 / 0.7972 / 0.7118 / 0.6355 / 0.5674 / 0.5066

PV / ($36,120,000) / $7,915,714 / $8,946,508 / $8,778,528 / $17,030,741 / ($1,498,007) / ($2,006,259)

NPV / $3,047,225

From the above, the project should be undertaken since it has a positive Net Present Value, an IRR and MIRR that are higher than the required rate of return, a payback period that is less than 4 years, and finally a Profitability Index that is higher than 1.

Please see the attached excel sheet for all calculations.