CHAPTER 7, Case #1
BETHESDA MINING
To analyze this project, we must calculate the incremental cash flows generated by the project. Since
net working capital is built up ahead of sales, the initial cash flow depends in part on this cash
outflow. So, we will begin by calculating sales. Each year, the company will sell 600,000 tons under
contract, and the rest on the spot market. The total sales revenue is the price per ton under contract
times 600,000 tons, plus the spot market sales times the spot market price. The sales per year will be:
Contract
Spot
Total
Year 1
$20,400,000
2,000,000
$22,400,000
Year 2
$20,400,000
5,000,000
$25,400,000
Year 3
$20,400,000
8,400,000
$28,800,000
Year 4
$20,400,000
5,600,000
$26,000,000
The current aftertax value of the land is an opportunity cost. The initial outlay for net working
capital 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
Land
NWC
Total
–$30,000,000
–5,000,000
–1,120,000
–$36,120,000
Now we can calculate the OCF each year. The OCF is:
Sales
Var. costs
Fixed costs
Dep.
EBT
Tax
Net income
+ Dep.
OCF
Year 1
Year 2
Year 3
Year 4
$22,400,000 $25,400,000 $28,800,000 $26,000,000
8,450,000
9,425,000 10,530,000
9,620,000
2,500,000
2,500,000
2,500,000
2,500,000
4,290,000
7,350,000
5,250,000
3,750,000
$7,160,000 $6,125,000 $10,520,000 $10,130,000
2,720,800
2,327,500
3,997,600
3,849,400
$4,439,200 $3,797,500 $6,522,400 $6,280,600
4,290,000
7,350,000
5,250,000
3,750,000
$8,729,200 $11,147,500 $11,772,400 $10,030,600
Year 5
$4,000,000
Year 6
$6,000,000
–$4,000,000 –$6,000,000
–1,520,000 –2,280,000
–$2,480,000 –$3,720,000
–$2,480,000 –$3,720,000
CHAPTER 7 CASE #1 C-21
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 aftertax salvage value of the land is
provided. The implicit assumption in this calculation is that the aftertax 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:
Beg. NWC
End NWC
NWC CF
Year 1
$1,120,000
1,270,000
–$150,000
Year 2
$1,270,000
1,440,000
–$170,000
Year 3
$1,440,000
1,300,000
$140,000
Year 4
$1,300,000
0
$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 aftertax 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)(.38) = $3,283,200
And the aftertax salvage value of the equipment is:
Aftertax salvage value = $18,000,000 – 3,283,200
Aftertax salvage value = $14,716,800
So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax
salvage value, are:
Time
0
1
2
3
4
5
6
Cash flow
–$36,120,000
8,579,200
10,977,500
11,912,400
26,047,400
–2,480,000
–3,720,000
C-22 CASE SOLUTIONS
So, the capital budgeting analysis for the project is:
Payback period = 3 + $4,650,900/$26,047,400
Payback period = 3.18 years
Profitability index = ($8,579,200/1.12 + $10,977,500/1.122 + $11,912,400/1.123 + $26,047,400/1.124
– $2,480,000/1.125 – $3,720,000/1.126) / $36,120,000
Profitability index = 1.0563
To calculate the AAR, we divide the average net income by the average book value. Since the cash
flows from the project extend for two years past the end of mining operation, we will include an
average book value of zero for the last two years. So, the AAR is:
AAR = [($4,439,200 + 3,797,500 + 6,522,400 + 6,280,600 – 2,480,000 – 3,720,000) / 6] /
[($25,710,000 + 18,360,000 + 13,110,000 + 9,360,000 + 0 + 0) / 6]
AAR = .1487 or 14.87%
The equation for IRR is:
0 = –$36,120,000 + $8,579,200/(1 + IRR) + $10,977,500/(1 + IRR)2 + $11,912,400/(1 + IRR)3
+ $26,047,400/(1 + IRR)4 – $2,480,000/(1 + IRR)5 – $3,720,000/(1 + IRR)6
Using a spreadsheet or financial calculator, the IRRs for the project are:
IRR = 14.41%, –61.75%
MIRR = 12.94%
NPV = –$36,120,000 + $8,579,200/1.12 + $10,977,500/1.122 + $11,912,400/1.123
+ $26,047,400/1.124 – $2,480,000/1.125 – $3,720,000/1.126
NPV = $2,031,914.04
In the final analysis, the company should accept the project since the NPV is positive.