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CHAPTER 8, CASE 2 C-1
CHAPTER 8A
EXPANSION AT EAST COAST YACHTS
The preliminary analysis of the project is a sunk cost and should be ignored. The cash flow to start the
project is the $55 million and will occur immediately. The $30 million outlay will occur in one year.
We need to be careful in depreciating the equipment. The $55 million expenditure will have
depreciation in Year 1, while the depreciation for the Year 1 expenditure will not begin being
depreciated until Year 2. The depreciation for next five years will be:
Year
Total
1
$55,000,000(.03750)
$ 2,062,500
2
$55,000,000(.07219) + $30,000,000(.03750)
$ 5,095,450
3
$55,000,000(.06677) + $30,000,000(.07219)
$ 5,838,050
4
$55,000,000(.06177) + $30,000,000(.06677)
$ 5,400,450
5
$55,000,000(.05713) + $30,000,000(.06177)
$ 4,995,250
Since the NWC is a percentage of sales, we need to determine the NWC cash flow each year.
Calculating the beginning and ending NWC requirement for each year, we can find the NWC cash
flows will be:
Year 1
Year 2
Year 3
Year 4
Year 5
Beginning
$1,440,000
$2,160,000
$2,800,000
$3,120,000
Ending
1,440,000
2,160,000
2,800,000
3,120,000
3,440,000
NWC cash flow
–$1,440,000
–$720,000
–$640,000
–$320,000
–$320,000
Now we can calculate the OCF for each year. Since the cash flows will grow at 3 percent after five
years, we only need to calculate the OCF for the next five years, so:
Year 1
Year 2
Year 3
Year 4
Year 5
Revenue
$18,000,000
$27,000,000
$35,000,000
$39,000,000
Variable costs
10,800,000
16,200,000
21,000,000
23,400,000
Fixed costs
2,500,000
2,500,000
2,500,000
2,500,000
Depreciation
2,062,500
5,095,450
5,838,050
5,400,450
4,995,250
EBT
–$2,062,500
–$395,450
$2,461,950
$6,099,550
$8,104,750
Tax
–825,000
–150,180
984,780
2,439,820
3,241,900
Net income
–$1,237,500
–$237,270
$1,477,170
$3,659,730
$4,862,850
OCF
$825,000
$4,858,180
$7,315,220
$9,060,180
$9,858,100
Next, we need to calculate the value of the perpetual cash flows. The total cash flow in Year 5 will be:
Year 5 cash flow = $9,858,100 – 320,000
Year 5 cash flow = $9,538,100
CHAPTER 8, CASE 2 C-2
The value of the perpetual cash flows beyond Year 5 at Year 5 is a growing perpetuity. So, the value
of the cash flows in Year 5 will be:
Year 0
Year 1
Year 2
Year 3
Year 4
Year5
OCF
$825,000
$4,858,180
$7,315,220
$9,060,180
$9,858,100
Capital spending
–$55,000,000
–30,000,000
Net working capital
–1,440,000
–720,000
–640,000
–320,000
–320,000
Terminal value
122,803,038
Total cash flows
–$55,000,000
–$30,615,000
$4,138,180
$6,675,220
$8,740,180
$132,341,888
So the NPV of the project is:
NPV = –$55,000,000 – $30,615,000/(1.11) + $4,138,180/(1.11)2 + $6,675,760/(1.11)3
The profitability index is:
PI = [–$30,615,000/(1.11) + $4,138,180/(1.11)2 + $6,675,760/(1.11)3 + $8,740,180/(1.11)4
The equation for the IRR is:
0 = –$55,000,000 – $30,615,000/(1 + IRR) + $4,138,180/(1 + IRR)2 + $6,675,760/(1 + IRR)3
Notice that we can’t use the Excel IRR function. The Excel function requires us to use all of cash
flows from the project, which is not possible with this project as the cash flows are perpetual. However,
we can use Solver or Goal Seek to find the IRR. Using the terminal cash flow value in Year 5
($137,866,788) as a cash flow in the IRR function is incorrect as the terminal cash flows have already
been discounted by the required return.
CHAPTER 8B
BETHESDA MINING
CHAPTER 8, CASE 2 C-3
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 500,000 tons under contract,
and the rest on the spot market. The total sales revenue is the price per ton under contract times 500,000
tons, plus the spot market sales times the spot market price. The sales per year will be:
Year 1
Year 2
Year 3
Year 4
Contract
$30,000,000
$30,000,000
$30,000,000
$30,000,000
Spot
12,000,000
14,880,000
15,840,000
10,560,000
Total
$42,000,000
$44,880,000
$45,840,000
$40,560,000
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($42,000,000) = $2,100,000
So, the cash flow today is:
Equipment
–$43,000,000
Land
–7,300,000
NWC
–2,100,000
Total
–$52,400,000
Now we can calculate the OCF each year. The OCF is:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Sales
$42,000,000
$44,880,000
$45,840,000
$40,560,000
Var. costs
15,750,000
17,010,000
17,430,000
15,120,000
Fixed costs
3,700,000
3,700,000
3,700,000
3,700,000
$3,900,000
Dep.
6,144,700
10,530,700
7,520,700
5,370,700
EBT
$16,405,300
$13,639,300
$17,189,300
$16,369,300
–$3,900,000
Tax
6,234,014
5,182,934
6,531,934
6,220,334
–1,482,000
–2,774,000
Net income
$10,171,286
$8,456,366
$10,657,366
$10,148,966
–$2,418,000
$2,774,000
+ Dep.
6,144,700
10,530,700
7,520,700
5,370,700
OCF
$16,315,986
$18,987,066
$18,178,066
$15,519,666
–$2,418,000
$2,774,000
Years 5 and 6 are of particular interest. Year 5 has an expense of $3.9 million to reclaim the land, and
it is the only expense for the year. In Year 6, the charitable donation of the land is a relevant cost.
However, the deduction is not an opportunity cost even though the company plans to donate the land.
The decision is already made when (or if) the project is accepted since the donation is required to
receive the necessary mining permits. However, the donation of does carry a charitable expense
deduction of $7.3 million, so the taxes that are saved by expensing this deduction are relevant.
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:
Year 1
Year 2
Year 3
Year 4
CHAPTER 8, CASE 2 C-4
Beg. NWC
$2,100,000
$2,244,000
$2,292,000
$2,028,000
End NWC
2,244,000
2,292,000
2,028,000
NWC CF
–$144,000
–$48,000
$264,000
$2,028,000
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
of the equipment is the original cost, minus the accumulated depreciation, or:
Book value of equipment = $43,000,000 – 6,144,700 – 10,530,700 – 7,520,700 – 5,370,700
Book value of equipment = $13,433,200
Since the market value of the equipment is $25.8 million, the equipment is sold at a gain to book value,
so the sale will incur the taxes of:
Taxes on sale of equipment = ($25,800,000 – 13,433,200)(.38)
So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax salvage
value, are:
Time
Cash flow
0
–$52,400,000
1
16,171,986
2
18,939,066
3
18,442,066
4
38,648,282
5
–2,418,000
6
2,774,000
So, the capital budgeting analysis for the project is:
Payback period = 2 + $17,288,948/$18,442,066
Payback period = 2.94 years
Profitability index = ($16,171,986/1.12 + $18,939,066/1.122 + $18,442,066/1.123
The equation for IRR is:
0 = –$52,400,000 + $16,171,986/(1 + IRR) + $18,939,066/(1 + IRR)2 + $18,442,066/(1 + IRR)3
CHAPTER 8, CASE 2 C-5
+ $38,648,282/(1 + IRR)4 – $2,418,000/(1 + IRR)5 + $2,774,000/(1 + IRR)6
Using a spreadsheet or financial calculator, the IRR for the project is:
IRR = 23.00%
Note, the sign changes of the cash flows indicate up to 3 IRRs. Another IRR is about –188 percent.
The third IRR is less than negative 200 percent, greater than 200 percent, or not a real number.
NPV = –$52,400,000 + $16,171,986/1.12 + $18,939,066/1.122 + $18,442,066/1.123
+ $38,648,282/1.124 – $2,418,000/1.125 + $2,774,000/1.126
NPV = $14,859,117.49
