Chapter 10 ◼ Cash Flow Estimation 365
18. NPV. Using the operating cash flow information from Problem 16, find the NPV of the
project for Miglietti Restaurants if the manufacturing equipment can be sold for $140,000 at
the end of the ten-year project and the cost of capital for this project is 8%. Hint: Use a
spreadsheet.
ANSWER
Find the after-cash flow at disposal of the equipment:
19. Project cash flows and NPV. The managers of Classic Autos Incorporated plan to
manufacture classic Thunderbirds (1957 replicas). The necessary foundry equipment will
cost a total of $4,000,000 and will be depreciated using a five-year MACRS life. Projected
sales in annual units for the next five years are 300 per year. If sales price is $27,000 per car,
366 Brooks ◼ Financial Management: Core Concepts, 4e
variable costs are $18,000 per car, and fixed costs are $1,200,000 annually, what is the
annual operating cash flow if the tax rate is 30%? The equipment is sold for salvage for
$500,000 at the end of year five. What is the after-tax cash flow of the salvage? Net working
capital increases by $600,000 at the beginning of the project (year 0) and is reduced back to
its original level in the final year. What is the incremental cash flow of the project? Using a
discount rate of 12% for the project, determine whether the project be accepted or rejected
with the NPV decision model.
ANSWER
Annual depreciation of foundry equipment is:
Chapter 10 ◼ Cash Flow Estimation 367
Operating Cash Flows are:
In thousands (rounded)
Year 1 Year 2 Year 3 Year 4 Year 5
Sales Revenue $8,100 $8,100 $8,100 $8,100 $8,100
–COGS $5,400 $5,400 $5,400 $5,400 $5,400
Incremental Cash Flows for Project (Answer in Thousands, $000)
Account/Activity Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Investment –$4,000
368 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
Accept the project because NPV is positive $613,345 (with rounding to nearest thousand).
20. Project cash flows and NPV. The sales manager has a new estimate for the sale of the classic
Thunderbirds in Problem 19. The annual sales volume will be as follows:
Year one: 240
Year two: 280
Year three: 340
Year four: 360
Year five: 280.
Rework the cash flows for operating cash flows with these new sales estimates and find the
internal rate of return for the project using the incremental cash flows.
ANSWER
Operating Cash Flows are:
Chapter 10 ◼ Cash Flow Estimation 369
– Depreciation $ 800 $ 1,280 $ 768 $ 461 $ 461
EBIT $ 160 $ 40 $ 1,092 $ 1,579 $ 859
– Taxes $ 48 $ 12 $ 328 $ 474 $ 258
Net Income $ 112 $ 28 $ 764 $ 1,050 $ 601
And the incremental cash flows are:
Incremental Cash Flows for Project (Answer in Thousands, $000)
Account/Activity Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Investment –$4,000
NWC –$ 600 $ 600
The IRR is via calculator:
CF0 = – 4,600,000
370 Brooks ◼ Financial Management: Core Concepts, 4e
Solutions to Advanced Problems for Spreadsheet Application
1. Erosion costs.
2. Working capital impact on project.
Solutions to Mini-Case
BioCom, Inc.: Part 2, Evaluating a New Product Line
This case is designed to integrate the student’s understanding of incremental cash flows for
capital budgeting decisions and touches on all major topics: investment, operating cash flows,
working capital, and disposal cash flows. It also requires students to apply the NPV calculations
and decision rules covered in the previous chapter.
1. What is the total relevant initial investment for BioCom’s new product line? Would you
include the designs and prototypes? Would you include the change in net working capital?
Cost of new plant and equipment:
$24,000,000
Increase in net working capital
$ 480,000
$24,480,000
FIND OCF:
1 2 3 4 5 6
Revenue $10,000,000.00 $13,000,000.00 $17,000,000.00 $23,000,000.00 $18,000,000.00 $12,000,000.00
Variable $ 4,000,000.00 $ 5,200,000.00 $ 6,800,000.00 $ 9,200,000.00 $ 7,200,000.00 $ 4,800,000.00
Fixed $ 1,500,000.00 $ 1,500,000.00 $ 1,500,000.00 $ 1,500,000.00 $ 1,500,000.00 $ 1,500,000.00
S,G & A $ 1,250,000.00 $ 1,400,000.00 $ 1,750,000.00 $ 2,000,000.00 $ 2,000,000.00 $ 1,500,000.00
Depreciation 2,000,000.00$ 3,200,000.00$ 1,920,000.00$ 1,152,000.00$ 1,120,000.00$ 576,000.00$
EBIT 1,250,000.00$ 1,700,000.00$ 5,030,000.00$ 9,148,000.00$ 6,180,000.00$ 3,624,000.00$
Taxes 462,500.00$ 629,000.00$ 1,861,100.00$ 3,384,760.00$ 2,286,600.00$ 1,340,880.00$
Net Income 787,500.00$ 1,071,000.00$ 3,168,900.00$ 5,763,240.00$ 3,893,400.00$ 2,283,120.00$
Add Depreciation 2,000,000.00$ 3,200,000.00$ 1,920,000.00$ 1,152,000.00$ 1,120,000.00$ 576,000.00$
OCF 2,787,500.00$ 4,271,000.00$ 5,088,900.00$ 6,915,240.00$ 5,013,400.00$ 2,859,120.00$
Capital outlay
10,000,000.00$
0
1 2 3 4 5 6
Working Capital CHG 2,000,000.00$ 600,000.00$ 800,000.00$ 1,200,000.00$ (1,000,000.00)$ (1,200,000.00)$ (2,400,000.00)$
Incremental CF 0
1 2 3 4 5 6
Capital (10,000,000.00)$
Change in WC (2,000,000.00)$ (600,000.00)$ (800,000.00)$ (1,200,000.00)$ 1,000,000.00$ 1,200,000.00$ 2,400,000.00$
OCF 2,787,500.00$ 4,271,000.00$ 5,088,900.00$ 6,915,240.00$ 5,013,400.00$ 2,859,120.00$
Incremental CF (12,000,000.00)$ 2,187,500.00$ 3,471,000.00$ 3,888,900.00$ 7,915,240.00$ 6,213,400.00$ 5,259,120.00$
IRR 26.84%
NPV $5,524,065.25
372 Brooks ◼ Financial Management: Core Concepts, 4e
6. Compute the project’s net present value.
NPV
(24,480,00
0)
5,575,000
1.09
2
7,029,504
1.09
3
6,250,522
1.09
4
6,027,622
1.09
5
8,989,654
1.09
Cash flows
discounte
d at 9%
(24,480,00
0)
5,114,678.9
0
5,916,592.8
8
4,826,549.8
3
4,270,119.3
9
5,842,658.2
9
Summing the discounted cash flows, NPV➔
$1,490,599.29
7. Does your answer to Question 6 indicate that management should accept or reject the
product?
374 Brooks ◼ Financial Management: Core Concepts, 4e
NPV @ 9%
$ 4,419,790.77
Operating Cash Flows (sales growth rate = 0%)
Year
1
2
3
4
5
Revenue
$16,500,000
$16,500,000
$16,500,000
$16,500,000
$16,500,000
COGS
6,600,000
6,600,000
6,600,000
6,600,000
6,600,000
Fixed Costs
600,000
600,000
600,000
600,000
600,000
S,G, and A
825,000
825,000
825,000
825,000
825,000
Depreciation
4,800,000
7,680,000
4,608,000
2,764,800
2,764,800
EBIT
3,675,000
795,000
3,867,000
5,710,200
5,710,200
Taxes
1,249,500
270,300
1,314,780
1,941,468
1,941,468
Net Income
$2,425,500
$524,700
$2,552,220
$3,768,732
$3,768,732
Add back dep.
4,800,000
7,680,000
4,608,000
2,764,800
2,764,800
Less erosion costs
1,650,000
1,650,000
1,650,000
1,650,000
1,650,000
Operating cash flows
$5,575,500
$6,554,700
$5,510,220
$4,883,532
$4,883,532
Incremental cash flows
T0
T1
T2
T3
T4
T5
Capital
Spending
–24,000,000
Change in
NWC
–480,000
480,000
OCF
5,575,500
6,554,700
5,510,220
4,883,532
4,883,532
Disposal cash
flow
2,054,016
Incremental
Cash Flow
–24,480,000
5,575,500
6,554,700
5,510,220
4,883,532
7,417,548
NPV @ 9%
$(1,312,487.24)
© 2018 Pearson Education, Inc.
376 Brooks ◼ Financial Management: Core Concepts, 4e
Additional Problems with Solutions
1. Erosion cost. Volvo is looking to introduce a new “hybrid” car in the United States. Their
analysts estimate that they will sell 20,000 of these new cars per year. The unit cost per car
is $18,000, and they plan on selling the vehicle for $22,000. If the current sales of Volvo’s
sedan, which costs $15,000 to produce and sells for $20,000, go down from 25,000 units per
year to 18,000 units, is this a worthwhile move for Volvo? Calculate the amount of the
erosion cost and the incremental cash flow that will result if they go ahead with the launch.
ANSWER (Slides 10-36 to 10-37)
OLD SEDAN
2. Depreciation rates. R.K. Boats Inc. has just installed a new hydraulic lift system, which is
being categorized as a five-year class-life asset under MACRS. The total purchase cost plus
installation amounted to $750,000. RKB has always used straight-line depreciation in the
past, but their accountant is pushing the owner to use the MACRS rates this time around.
The owner seems to think that it really doesn’t matter because the total depreciation under
each method will still sum up to $750,000 and be spread over six years with the application
of the “half–year” convention. Do you agree with the owner? Please explain by making the
appropriate calculations. RKB’s hurdle rate is 10%, and its marginal tax rate is 30%.
ANSWER (Slides 10-38 to 10-39)
Under straight-line depreciation:
Chapter 10 ◼ Cash Flow Estimation 377
Using “half–year” convention the comparison of yearly depreciation under the two methods is as
follows:
Year
MACRS rate
MACRS
Dep.
St. Line
Dep
Diff.
Tax Gain
1
20%
150000
75,000
75,000
22500
2
32%
240000
150000
90,000
27000
3
19.20%
144000
150000
–6,000
–1800
4
11.52%
86400
150000
–63,600
–19080
5
11.52%
86400
150000
–63,600
–19080
6
5.76%
43200
75000
–31,800
–9540
Total
100%
750000
750000
0
0
NPV of tax
gain @10%
➔$11,152.07
So clearly, with the tax advantages coming in earlier, i.e., in the first two years, the time value of
money advantages makes it a positive NPV move.
3. Disposal Cash Flow. Reddy Laboratories had purchased some manufacturing equipment
five years ago for a total cost of $3,000,000, and has been depreciating it using the
MACRS – seven-year class-life rates. Currently, newer, more efficient equipment is available,
and Reddy has found a buyer who is willing to pay $500,000 for the old equipment. If the
firm, which has a marginal tax rate of 35%, disposes of the system to the buyer, how much
will the after-tax cash flows add up to?
ANSWER (Slides 10-40 to 10-41)
The seven-year MACRS rates are as follows:
378 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
Loss on sale = Selling Price – Book value = $500,000 – $669,300 = –$169,300
Tax credit = Tax rate × Loss = 0.35 × $169,300 = $59,255
After-tax cash inflow = Selling price + Tax credit
= $500,000 + $59,255 = $559,255
4. Operating cash flow (growing each year; MACRS). Balik Ventures is looking at a project with
the following forecasted sales: first-year sales quantity of 20,000 with an annual growth rate
of 4% over the next five years. The sales price per unit is $35.00 and will grow at 5% per
year. The production costs are expected to be 45% of the current year’s sales price. The
manufacturing equipment to aid this project will have a total cost (including installation) of
$2,200,000. It will be depreciated using MACRS and has a five-year MACRS life classification.
Fixed costs are $285,000 per year. The firm has a tax rate of 35%.What is the operating cash
flow for this project over these five years? Hint: Use a spreadsheet and round units to the
nearest whole number.
ANSWER (Slides 10-42 to 10-45)
Based on five-year MACRS rates, the annual depreciation expense is as follows:
Dep. Basis
➔
2,200,000
Year
Rate
Depreciation
1
0.2
440,000
2
0.32
704,000
3
0.192
422,400
4
0.1152
253,440
5
0.1152
253,440
6
0.0576
126,720
Chapter 10 ◼ Cash Flow Estimation 379
The operating cash flow over the 5-year period is calculated as follows:
Rate
Year 1
Year 2
Year 3
Year 4
Year 5
Unit sales
4%
30,000
31,200
32,448
33,746
35,096
Sales price
5%
$35.00
$36.75
$38.59
$40.52
$42.54
Revenues
$1,050,000
$1,146,600
$1,252,087
$1,367,279
$1,493,069
Prod. Costs
45%
$472,500
$515,970
$563,439
$615,276
$671,881
Fixed costs
$ 285,000
$ 285,000
$ 285,000
$ 285,000
$ 285,000
Depreciation
$440,000
$704,000
$422,400
$253,440
$253,440
EBIT
($147,500)
($358,370)
($18,752)
$213,564
$282,748
Taxes
35%
($51,625)
($125,430)
($6,563)
$74,747
$98,962
Net Income
($95,875)
($232,941)
($12,189)
$138,816
$183,786
Add Dep
$440,000
$704,000
$422,400
$253,440
$253,440
Op. Cash Flow
$344,125
$471,060
$410,211
$392,256
$437,226
5. Comprehensive Capital Budgeting. Let’s say that Balik Ventures has forecasted the operating
cash flows over the five year project life as shown in Problem 4 above. The project will entail
an investment of 10% of the first year’s forecasted production costs for working capital,
which will be recovered at the end of the five-year life. In addition, the equipment will be
sold for 20% of its initial cost when the project is terminated. If the firm uses a hurdle rate of
14% for similar risk projects, should they go ahead with this venture? Why or why not?
ANSWER (Slides 10-46 to 10-49)
In addition to the operating cash flow for years one through five, we need to calculate the initial
year and terminal year cash flow and add them in.
380 Brooks ◼ Financial Management: Core Concepts, 4e
© 2018 Pearson Education, Inc.
Selling Price = 20% of Cost = 0.2 × (2,200,000) = $440,000
Book Value = Year 6 MACRS Dep. Rate × Dep. Basis = 0.0576 × 2,200,000 = $126,720
Tax on Gain = 0.35 × ($440,000 – $126.720) = $109,648
After-tax Salvage Value = $440,000 – $109,648 = $330,352
Total Terminal Year Cash Flow (not including OCF) = 47, 250 + 330,352 = 377,602
Year Cash Flow
0 –$2,247,250
1 $344,125
2 $471,060
3 $410,211
4 $392,256
5 $437,226 + 377,602 = $814,828
NPV @10% = –$463,045.5
REJECT THE PROJECT!