Download Chapter 10 Cash Flow Estimation

Chapter 10 Cash Flow Estimation LEARNING OBJECTIVES (Slide 10-­‐2) 1. Understand the importance of cash flow and the distinction between cash flow and
profits.
2. Identify incremental cash flow.
3. Calculate depreciation and cost recovery.
4. Understand the cash flow associated with the disposal of depreciable assets.
5. Estimate incremental cash flow for capital budgeting decisions.
IN A NUTSHELL… In this chapter, the author examines how cash flow differs from profits. Since cash flow
is the lifeline of business, it is very important to understand how to measure and forecast
the various sources of cash flow that arise from the investment and disposal of assets.
Accordingly, topics such as identifying and estimating incremental cash flow, calculating
depreciation and cost recovery, and adjusting for salvage and terminal values are covered
as part of the steps necessary prior to making capital budgeting decisions.
LECTURE OUTLINE 10.1 The Importance of Cash Flow (Slides 10-­‐3 to 10-­‐4) Cash flow measures the actual inflow and outflow of cash, while profits represent merely
an accounting measure of periodic performance.
Figures 10.1 and 10.2 (shown below), help clarify the difference between net income and
operating cash flow (OCF) of a firm.
It is important to remind students that a firm can spend its operating cash flow but not its
net income.
Some firms have net losses (due to high depreciation write-offs) and yet can pay
dividends from cash balances, while others show profits and may not have the cash
available.
335 ©2013 Pearson Education, Inc. Publishing as Prentice Hall 336 Brooks n Financial Management: Core Concepts, 2e Thus, cash flow is broader than net income as shown below.
FIGURE 10.1
FIGURE 10.2
Figure 10.2 is a modified income statement in that it only considers the cash flow arising
from operations. Accordingly, interest expense (which is a financing cash flow) is not
included, and depreciation (which had been deducted in Figure 10.1, mainly for tax
purposes ) is added back. Thus,
OCF = EBIT –Taxes +Depreciation=Net Income + Interest +Depreciation
$4,603 =$5,046 – $1,555 + $1,112 = $3313+$178+$1,112
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 337 10.2 Estimating Cash Flow for Projects: Incremental Cash Flow (Slides 10-­‐5 to 10-­‐13) When a firm is considering either expanding a current line of business, starting a new
venture, or replacing an existing asset with a newer one, the changes in revenue and costs
that occur will have an incremental effect on its operating cash flow.
It is the timing and magnitude of these incremental cash flows that have to be carefully
estimated and evaluated as part of any capital budgeting analysis.
There are 7 important issues that have to be kept track of during a comprehensive cash
flow estimation process. These issues include: sunk costs, opportunity cost, erosion,
synergy gains, working capital, capital expenditures, and depreciation or cost recovery of
assets.
10.2 (A) Sunk costs: are expenses that have already been incurred, or that will be
incurred, regardless of the decision to accept or reject a project. For example, a marketing
research study exploring business possibilities in a region would be a sunk cost, since its
expenditure has been done prior to undertaking the project and will have to be paid
whether or not the project is taken on. These costs although part of the income statement,
should not be considered as part of the relevant cash flows when evaluating a capital
budgeting proposal.
10.2 (B) Opportunity costs: include costs that may not be directly observable or obvious,
but result from benefits being lost as a result of taking on a project. For example, if a firm
decides to use an idle piece of equipment as part of a new business, the value of the
equipment that could be realized by either selling or leasing it would be a relevant
opportunity cost.
10.2 (C) Erosion costs: arise when a new product or service competes with revenue
generated by a current product or service offered by a firm. For example, if a store offers
two types of photo-copying services, a newer, more expensive choice and an older
economical one, some of the revenues from the older repeat customers will be lost and
should therefore be accounted for in the incremental cash flows.
Example 1: Erosion costs Frosty Desserts currently sell 100,000 of its Strawberry-Shortcake Delight each year for
$3.50 per serving. Its cost per serving is $1.75. Its chef has come up with a newer, richer
concoction, “Extra-Creamy Strawberry Wonder,” which costs $2.00 per serving, will
retail for $4.50 and should bring in 130,000 customers. It is estimated that after the
launch the sales for the original variety will drop by 15%. Estimate the erosion cost
associated with this venture.
To calculate the erosion cost we must consider the amount of lost contribution margin
(Selling price – unit cost) from SSD’s drop in sales.
Erosion cost = (Unit sales of SSD before launch –Unit sales after launch)
X (Selling Price – Unit Cost)
èErosion cost = (100,000 – 85,000) × ($3.50-$1.75) = $26,250
©2013 Pearson Education, Inc. Publishing as Prentice Hall 338 Brooks n Financial Management: Core Concepts, 2e Margin contributed by ESW = ($4.50-$2.00) × 130,000= $325,000
Margin prior to new launch = 100,000 × ($3.50 – $1.75) = $175,000
Margin after launch = ($3.50 – $1.75) × 85,000 + $325,000 = $473,750
Net change in margin = $473, 750 – $175,000 = $298,750
Erosion cost = ESW’s contribution margin – net change in margin
= $325,000 – $298,750 = $26,250
10.2 (D) Synergy gains: refer to the impulse purchases or sales increases for other
existing products related to the introduction of a new product. For example, if a gas
station with a convenience store attached, adds a line of fresh donuts and bagels, the sales
of coffee and milk, would result in synergy gains.
10.2 (E) Working capital: investment refers to the additional cash flows arising from
changes in current assets such as inventory and receivables (uses) and current liabilities
such as accounts payables (sources) that occur as a result of a new project.
Generally, at the end of the project, these additional cash flows are recovered and must be
accordingly shown as cash inflows.
Even though the net cash outflows—due to increase in net working capital at the start—
may equal the net cash inflow arising from the liquidation of the assets at the end, the
time value of money effects make these costs relevant.
10.3 Capital Spending and Depreciation (Slides 10-­‐14 to 10-­‐22) When a firm spends capital to acquire a productive (depreciable) asset, it is allowed to
expense a portion of the cost of the asset each year, as a process of cost recovery via the
reduced taxes that result from the write-off.
The portion written off in the income statement, each year, is called the depreciation
expense; and the accumulated total kept track of in the Balance sheet is known as
Accumulated Depreciation.
Thus, the book value of an asset equals its original cost less its accumulated depreciation.
The two reasons we need to deal with depreciation when doing capital budgeting
problems are:
(1) the tax flow implications from the operating cash flow and
(2) the gain or loss at disposal of a capital asset.
Firms have a choice of using either straight line depreciation rates, or modified
accelerated cost recovery system (MACRS) rates for allocating the annual depreciation
expense, arising from an asset acquisition.
10.3 (A) Straight-­‐line depreciation: rates are easy to apply since the annual depreciation
expense is calculated by dividing the initial cost plus installation minus the expected
residual value (at termination) equally over the expected productive life of the asset. The
annual depreciation expenses are the same for each year.
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 339 10.3 (B) Modified Accelerated Cost Recovery System: rates are established by the
federal government, since 1981, as a way to allow for firms to accelerate the depreciation
write-off in early years of the asset’s life.
These rates (shown below in Table 10.4) are set up based on various asset categories
(class-lives), as shown in Table 10.3 in the text.
Each column relating to an asset life has one additional year of depreciation than the
class-life states, e.g. a 3-year class life asset is depreciated over 4 years. This is because
the government assumes that the asset is put into use for only half a year at the start (halfyear convention), and thereby allowed ½ depreciation, with the last year (Year 4) being
allowed the balance required to reach 100% (which amounts to ½ the prior year’s
percentage. The depreciation rates in each column add up to 100%, i.e. no need to deduct
residual value, with higher rates being allowed in earlier years and less in later years.
With higher depreciation rates allowed in earlier years, the tax savings are higher due to
the time value of money.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 340 Brooks n Financial Management: Core Concepts, 2e Example 2: MACRS depreciation The Grand Junction Furniture Company has just bought some specialty tools to be used
in the manufacture of high-end furniture. The cost of the equipment is $400,000 with an
additional $30,000 for installation. If the company has a marginal tax rate of 30%,
compare its annual tax savings that would be realized from using MACRS depreciation
rates.
According to Table 10.3, specialty tools falls under a 3-year class asset with rates in
Years 1-4 of 33.33%, 44.45%, 14.81%, and 7.41% respectively.
Depreciable basis = Cost + Installation = $400,000 + $30,000 = $430,000
The annual depreciation expenses (i.e. annual rate × Dep. Basis)are shown below:
Total
MACRS
rate
Dep. Exp
33.33%
$ 143,319
44.45%
$ 191,135
14.81%
$ 63,683
7.41%
$ 31,863
100.00%
$ 430,000
Two other specific depreciation-related issues, that affect capital budgeting analysis,
include:
1. Dealing with assets which are sold off prior to being fully depreciated, would be true
if we were replacing an asset with a newer model and salvaging some value from the
old one prior to it being fully depreciated.
2. Selling a fully depreciated asset i.e. zero book value.
10.4 Cash Flow and the Disposal of Capital Equipment (Slides 10-­‐23 to 10-­‐26) When a depreciable asset is sold, the cash inflow that results can be higher than, equal to,
or lower than the actual selling price of the asset, depending on whether it was sold above
(taxable gain), at (zero-gain) or below (tax credit) book value.
If the sale results in a taxable gain, then the cash inflow is reduced by the amount of the
taxes (Tax rate × (Selling Price –Book Value).
If the selling price is exactly equal to book value the cash inflow equals the sale price.
If the asset is sold below its book value, a loss results, and can be written off taxes for the
year, resulting effectively in an addition to cash inflows equal to (Book Value-Selling
Price) × Tax rate.
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 341 Thus, the cash flow resulting from after-tax salvage value of a depreciable asset is
calculated as follows:
After-tax Salvage Value = Selling Price – Tax rate × (Selling price – Book Value)
Or Selling Price + Tax rate × (Book Value – Selling Price)
Example 3: Tax effects from disposal cash flow Let’s say that the manager of the Grand Junction Furniture Company decides to dispose
of the specialty tools, acquired 2 years ago at a cost of $430,000 (including installation),
to another firm for $125,000. How much of an after-tax cash flow will result, assuming
that the tools were being depreciated based on the 3-year MACRS rates and the
company’s marginal tax rate is 35%
Depreciable basis = $430,000
Year 1 depreciation rate
= 33.33%
Year 2 depreciation rate
= 44.45%
Total depreciation taken so far = $430,000 × (33.33% + 44.45%) = $334, 454
Book Value
= Depreciable basis – Accumulated depreciation
Book Value
= $430,000 – $334,454 = $95,546
Selling price = $125,000 > Book Value è Taxable gain on the sale è Taxable gain
= $125,000-$95,546=$29,454
After-tax Salvage Value
= Selling Price – (Tax rate × Taxable gain )
=$125,000 – .35 × ($29,454)
=$125,000-$10,308.9=$114,691.1
After-tax Salvage Value
= $114,691.1
Note: If Selling Price > BV è Cash Inflow = Selling Price less tax
If Selling Price < BVè Cash Inflow = Selling Price + tax credit
If Selling Price = BVè Cash Inflow = Selling Price
10.5 Projected Cash Flow for a New Product(Slides 10-­‐27 to 10-­‐34) A comprehensive capital budgeting analysis requires the estimation of initial and future
incremental cash flows that are likely to result over the productive life of the project,
followed by the application of one or more of the evaluation techniques that were covered
in Chapter 9.
In particular, the following 4 steps are typically involved:
1. Determination of the initial capital investment for the project
Purchase cost + Installation + Initial Increase in net working capital – After-tax
salvage value from disposal of old asset (if any)
2. Estimation of the annual operating cash flows (incremental) generated by the project,
ignoring sunk costs and including erosion costs and side-effects. (Figure 10.3-10.5 in
the text)
OCF = EBIT – Taxes + Depreciation
©2013 Pearson Education, Inc. Publishing as Prentice Hall 342 Brooks n Financial Management: Core Concepts, 2e In the terminal year, besides the usual OCF we have to account for any salvage value
that is received, which requires the calculation of Book value and taxes (or tax
credits) on sale of the asset. (Table 10.7 in the text)
Terminal Year Cash flow = OCF + After-tax Salvage Value
3. Determination of the change in net working capital which is usually an increase
(outflow) at the beginning and a reduction (inflow) at the end.
(Table 10.7 in the text)
4. Evaluation of the proposed project using an appropriate discount or hurdle rate and
either the NPV or IRR approach. (See Figure 10.6 shown below.)
Questions 1. How is cash flow different from profit or net income?
Cash flow refers to the amount of cash received or spent in a specific period while
profit or net income is an accounting measure of performance during a specific period
of time. Cash flow can be spent; profits may not be available for spending.
2. Why is depreciation expense added back to the net income of a company to find
the operating cash flow?
Depreciation expense is a non cash flow item in the income statement. It represents a
portion of the original cost (cash outflow) of a capital asset that occurred in a previous
period. The expense reduces taxable income and thus taxes so it is included in the
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 343 income statement but must be added back to net income to find the operating cash
flow.
3. Why are owners of a business only interested only in incremental cash flow for a
project and not the total cash flow of a project?
Only the incremental cash flow of a project adds value to the company as a whole and
therefore value to the owners. When a project has revenue that is the result of lost
revenue from another project owners do not see an increase in total revenue.
4. Why are sunk cost excluded from the incremental cash flow of a project? Does
this mean that they were wasted expenses? Why or why not?
Sunk costs are costs that would be spent regardless of the decision to accept or reject a
project so they are not part of the cash flow that will be used to make the decision on
a project. They are not wasted expenses as they may have been used to gather vital
information for the decision. For example, a market study to determine the potential
market of a new product may be critical in determining future sales and thus is
important is estimating future cash flow. However, the cost of the study is a sunk cost.
5. Give an example of an erosion cost. Explain why this cost is part of the
incremental cash flow of a project. Is there a case when a new product should get
credit for additional revenue of another already existing product?
Erosion cost is the lost profit of an existing product when a new product takes part of
current sales of the existing product from a company’s current clients. For example,
introducing bottled water by a beverage company may reduce its sale of carbonated
beverages thus the lost profits from the carbonated beverages must be covered by the
bottle water and therefore these erosion costs are part of the bottled water’s cash flow.
However, if a competitor is also introducing bottled water and the beverage sales will
be lost to a competitor if the company does not also introduce its bottled water into
the market; these lost sales from the carbonated beverages are not part of the
incremental costs of the bottled water.
6. Give an example of an opportunity cost and explain how you would estimate the
cost as it applies to a particular project.
An opportunity cost is a foregone benefit due to the selection of a project. An example
of an opportunity cost is the potential lost revenue from selling land that is used in a
plant expansion when there was a market for the vacant land. The opportunity cost is
this case is the fair market value of the land, the amount that the company could have
received if it had chosen to sell the land instead of expanding the plant.
7. Why must a company typically invest in working capital when starting a new
project? Why is this investment in working capital recovered at the completion
of the project?
Working capital is necessary for making a project go. For example, if you are
introducing a new product to the market such as a soft drink, you must bottle the drink
for customers and this bottling process requires an investment in inventories such as
bottles, labels, and caps. Increasing the working capital inventories at the start of a
project is required but once the project is stopped (the product discontinued), there is
no longer a need to keep these inventories and so they are reduced to zero. Reducing
the inventories to zero is viewed as the recovered capital at the end of the project as it
is a reduction in an asset account.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 344 Brooks n Financial Management: Core Concepts, 2e 8. How does depreciation spread the capital expenditure of a project over the life of
the capital asset? Why is using MACRS usually beneficial to a company versus
using straight-line depreciation?
The original cost of new equipment or other large assets is not expensed on the
income statement when it is purchased. However, each period a portion of this cash
outlay is “expensed” to the income statement via depreciation. Over the life of the
asset, these periodic depreciation expenses will add up to the original cost of the asset
and thus spread this expense over the life of the asset. MACRS allows a greater
percentage of the cost to be depreciated in the early years compared to straight-line
depreciation. Because these expenses reduce taxes, the higher the expense the lower
the taxes and the lower the cash outflow. Due to the time-value-of-money the earlier
these expenses are recorded the sooner the tax reduction is received so MACRS is
beneficial to the company based on the timing of the tax payments.
9. Why is there typically a tax gain or tax loss at the disposal of capital assets?
There is typically a tax gain or tax loss at the disposal of capital assets because it is
rare that the cash flow from the disposal is exactly equal to the current book value of
the asset. The book value is the original cost minus the accumulated depreciation.
10. All six decision models from Chapter 9 rely on the appropriate timing and
amount of cash flow. What are the potential errors a manager can make if this
information is not accurate?
If we use inappropriate amounts or an inappropriate timing of cash flow we can end
up with one of two potential errors. We could reject good projects or we could accept
bad projects. Both of these errors reduce the value of the company to the owners
Prepping for Exams 1. a.
2. c.
3. d.
4. b.
5. a.
6. d.
7. a.
8. c.
9. c.
10. b.
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 345 Problems 1. Erosion costs. Fat Tire Bicycle Company currently sells 40,000 bicycles per year.
The current bike is a standard balloon tire bike, selling for $90 with a production and
shipping cost of $35. The company is thinking of introducing an off-road bike with a
projected selling price of $410 and a production and shipping cost of $360. The
projected annual sales for the off-road bike are 12,000. The company will lose sales
in fat-tire bikes of 8,000 units per year if it introduces the new bike, however. What is
the erosion cost from the new bike? Should Fat Tire start producing the off-road bike?
ANSWER Erosion Cost = ($90 – $35) × 8,000 = $440,000
Net Annual Cash Flow with standard bike: ($90 – $35) × 40,000 = $2,200,000
Net Annual Cash Flow with standard and off-road bikes:
($90 – $35) × (40,000 – 8,000) = $1,760,000
($410 – $360) × 12,000 = $600,000
Net Annual CF = $1,760,000 + $600,000 = $2,360,000
Increase of $160,000 per year so add new off-road bike to production.
2. Erosion costs. Heavenly Cookie Company has the following annual sales and costs
for its current product line:
Heavenly is thinking of adding Mississippi Mud brownies to the product line. The
ultra-rich brownies would sell for $0.99 a piece and cost $0.81 to produce. The
forecasted brownie volume is 250,000 per year. Introduction of brownies, however,
will reduce cookie sales by 250,000 with the following drop in sales per cookie:
130,000 in chocolate chip, 60,000 in snickerdoodle, 40,000 in peanut butter, 10,000
in lemon drop, and 10,000 in cream-filled. What is the erosion cost of introducing the
brownies? What is the net change in annual margin if Mississippi Mud brownies are
added to the product line?
ANSWER Erosion Cost for Chocolate Chip
Erosion Cost for Snicker Doodle
Erosion Cost for Peanut Butter
Erosion Cost for Lemon Drop
Erosion Cost for Cream Filled
= ($0.49 – $0.19) × 130,000 = $39,000
= ($0.49 – $0.17) × 60,000 = $19,200
= ($0.49 – $0.15) × 40,000 = $13,600
= ($0.49 – $0.22) × 10,000 = $2,700
= ($0.59 – $0.31) × 10,000 = $2,800
©2013 Pearson Education, Inc. Publishing as Prentice Hall 346 Brooks n Financial Management: Core Concepts, 2e Total erosion cost:
$39,000 + $19,200 + $13,600 + $2,700 + $2,800 = $77,300
Brownie Margin:
($0.99 – $0.81) × 250,000 = $45,000
Net Change in annual margin dollars is $45,000 – $77,300 = –$32,300 so do not add
brownies to the product mix.
3. Opportunity costs. Revolution Records will build a new recording studio on a vacant
lot next to the operations center. The land was purchased five years ago for $450,000.
Today the value of the land has appreciated to $780,000. Revolutionary Records did
not consider the value of the land (it had already spent the money to acquire the land
long before this project was considered). The NPV of the recording studio was
$600,000. Should Revolution Records consider the land as part of the cash flow of the
recording studio? If yes, what value should be used, $450,000 or $780,000? How will
the value affect the project?
ANSWER The land needs to be included as part of the cash flow for the studio project because there
is an opportunity cost here. If Revolution Records does not want to keep the land it can
sell it for $780,000. So this current market value of $780,000 is the opportunity cost that
the studio must cover.
If the NPV without considering this cost is $600,000 for the studio then Revolution
Records should just sell the land and have $780,000 as cash income (unless there are
taxes that would reduce the net cash flow below $600,000).
4. Opportunity cost. Richards Tree Farm Inc. has branched into gardening over the
years, and is now considering adding patio furniture to its product lineup. Currently,
the area where the patio furniture is to be displayed is a vacant slab of concrete
attached to the indoor shop. The company originally paid $8,500 to put in the slab of
concrete three years ago. It would now cost $12,000 to put in the same slab of
concrete. Should Richards consider the concrete slab when expanding its outdoor
garden shop to include patio furniture? If yes, which value should it use?
ANSWER The slab is a sunk cost unless there is another use for the slab that could provide cash
flow to Richards Tree Farm. The additional cash flow that the slab could provide is the
opportunity cost, not the current replacement cost or the original cost.
5. Working capital cash flow. Cool Water Inc. sells bottled water. The firm keeps in
inventory plastic bottles at 10% of the monthly projected sales. These plastic bottles
cost $0.005 each. The monthly sales for the coming year are as follows:
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 347 Show the anticipated cost of plastic bottles each month for these projected sales, the
beginning inventory volume and ending inventory volume each month, and the
monthly increase or decrease in cash flow for inventory given that an increase is a use
of cash and a decrease is a source of cash.
ANSWER COGS = Monthly Sales × $0.005
Beginning Inventory Balance = Current Month’s Sales Projection × 10%
Ending Inventory Balance = Next Month’s Sales Projection × 10%
Increase in Working Capital Cash = Ending Inventory – Beginning Inventory × $0.005
Month
Exp. Sales
(units)
Ant. COGS
Beg. Inv.
Bal
End. Inv.
Bal.
W. Cap.
Increase
January
2,000,000
$10,000
200,000
220,000
$100.00
February
2,200,000
$11,000
220,000
270,000
$250.00
March
2,700,000
$13,500
270,000
300,000
$150.00
April
3,000,000
$15,000
300,000
360,000
$300.00
May
3,600,000
$18,000
360,000
550,000
$950.00
June
5,500,000
$27,500
550,000
700,000
$750.00
July
7,000,000
$35,000
700,000
900,000
$1,000.00
August
9,000,000
$45,000
900,000
600,000
($1,500.00)
September
6,000,000
$30,000
600,000
400,000
($1,000.00)
October
4,000,000
$20,000
400,000
250,000
($750.00)
November
2,500,000
$12,500
250,000
130,000
($600.00)
December
1,300,000
$6,500
130,000
220,000
$450.00
TOTAL
$244,000
$100.00
6. Working capital cash flow. Tires for Less is a franchise of tire stores throughout the
greater Northwest. It has projected the following unit sales per tire and costs of tires
for the coming year:
©2013 Pearson Education, Inc. Publishing as Prentice Hall 348 Brooks n Financial Management: Core Concepts, 2e The company policy is to have the next month’s anticipated sales for each tire type in
the warehouse. Shipments are made to the various stores throughout the Northwest
from the central warehouse. Show the anticipated cost of tires each month for these
projected sales by tire type, the beginning inventory volume and ending inventory
volume each month for each tire, and the monthly increase or decrease in cash flows
for inventory given that an increase is a use of cash and a decrease is a source of cash.
Find the total cost of goods sold and change in monthly working capital cash flows
for all tires. What do you notice about the working capital change when you combine
all four tires?
ANSWER (Please note that there is an error in the data table…the amounts shown are actually
units sold per type of tire, not dollars)
COGS = Tire’s Monthly Volume × Tires Cost
Beginning Inventory Balance = Current Month’s Sales Projection
Ending Inventory Balance = Next Month’s Sales Projection
Increase in Working Capital Cash = Ending Inventory – Beginning Inventory × cost of
tire
SNOW TIRES
Month
Anticipated
COGS
Beginning
Inventory
Balance
Ending
Inventory
Balance
©2013 Pearson Education, Inc. Publishing as Prentice Hall Working Capital
Increase
Chapter 10 n Cash Flow Estimation 349 January
$1,848,000
44,000
38,000
–$252,000
February
$1,596,000
38,000
14,000
–$1,008,000
March
$588,000
14,000
2,000
–$504,000
April
$84,000
2,000
0
–$84,000
May
$0
0
0
$0
June
$0
0
0
$0
July
$0
0
0
$0
August
$0
0
0
$0
September
$0
0
0
$0
October
$0
0
16,000
$672,000
November
$672,000
16,000
82,000
$2,772,000
December
$3,444,000
82,000
48,000
–$1,428,000
TOTAL
$8,232,000
$168,000
Rain Tire Working Capital and COGS
Anticipated
COGS
Beginning
Inventory
Balance
Ending
Inventory
Balance
Working
Capital
Increase
January
$620,000
20,000
36,000
$496,000
February
$1,116,000
36,000
46,000
$310,000
March
$1,426,000
46,000
22,000
–$744,000
April
$682,000
22,000
40,000
$558,000
May
$1,240,000
40,000
20,000
–$620,000
June
$620,000
20,000
2,000
–$558,000
July
$62,000
2,000
2,000
$0
August
$62,000
2,000
2,000
$0
September
$62,000
2,000
14,000
$372,000
October
$434,000
14,000
18,000
$124,000
November
$558,000
18,000
20,000
$62,000
December
$620,000
20,000
22,000
$62,000
Month
TOTAL
$7,502,000
$62,000
All-Terrain Tire Working Capital and COGS
Month
January
Anticipated
COGS
Beginning
Inventory
Balance
Ending
Inventory
Balance
Working Capital
Increase
$192,000
4,000
5,000
$48,000
©2013 Pearson Education, Inc. Publishing as Prentice Hall 350 Brooks n Financial Management: Core Concepts, 2e February
$240,000
5,000
7,000
$96,000
March
$336,000
7,000
8,000
$48,000
April
$384,000
8,000
12,000
$192,000
May
$576,000
12,000
30,000
$864,000
June
$1,440,000
30,000
39,000
$432,000
July
$1,872,000
39,000
22,000
–$816,000
August
$1,056,000
22,000
8,000
–$672,000
September
$384,000
8,000
2,000
–$288,000
October
$96,000
2,000
1,000
–$48,000
November
$48,000
1,000
3,000
$96,000
December
$144,000
3,000
5,000
$96,000
TOTAL
$6,768,000
$48,000
All-Purpose Tire Working Capital and COGS
Anticipated
COGS
Beginning
Inventory
Balance
Ending
Inventory
Balance
Working Capital
Increase
January
$2,220,000
60,000
54,000
–$222,000
February
$1,998,000
54,000
50,000
–$148,000
March
$1,850,000
50,000
60,000
$370,000
April
$2,220,000
60,000
65,000
$185,000
May
$2,405,000
65,000
68,000
$111,000
June
$2,516,000
68,000
75,000
$259,000
July
$2,775,000
75,000
80,000
$185,000
August
$2,960,000
80,000
70,000
–$370,000
September
$2,590,000
70,000
70,000
$0
October
$2,590,000
70,000
65,000
–$185,000
November
$2,405,000
65,000
60,000
–$185,000
December
$2,220,000
60,000
60,000
$0
TOTAL
$28,749,000
Month
$0
All Tires Working Capital and COGS
COGS
Beginning
Inventory
Balance
Ending
Inventory
Balance
Working Capital
Increase
January
$4,880,000
128,000
133,000
$70,000
February
$4,950,000
133,000
117,000
–$750,000
Anticipated
Month
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 351 March
$4,200,000
117,000
92,000
–$830,000
April
$3,370,000
92,000
117,000
$851,000
May
$4,221,000
117,000
118,000
$355,000
June
$4,576,000
118,000
116,000
$133,000
July
$4,709,000
116,000
104,000
–$631,000
August
$4,078,000
104,000
80,000
–$1,042,000
September
$3,036,000
80,000
86,000
$84,000
October
$3,120,000
86,000
100,000
$563,000
November
$3,683,000
100,000
165,000
$2,745,000
December
$6,428,000
165,000
135,000
–$1,270,000
TOTAL
$51,251000
$278,000
When you look across all the tires you see that the swings from month to month in
inventory are reduced as some of the large swings in one type of tire are offset by the
opposite swings of the other tires. This is one type of diversification effect from products
that have seasonal sales variation when their individual sales variations across the seasons
are offsetting.
7. Depreciation expense. Brock Florist Company buys a new delivery truck for
$29,000. It is classified as a light-duty truck.
a. Calculate the depreciation schedule using a five-year life, straight-line
depreciation, and the half-year convention for the first and last years.
b. Calculate the depreciation schedule using a five year life and MACRS
depreciation.
c. Compare the depreciation schedules from parts (a) and (b) before and after taxes
with a 30% tax rate. What do you notice about the difference between these two
methods?
ANSWER a. Annual depreciation is cost of truck divided by five; $29,000/ 5 = $5,800
And for the first and last year we have $5,800 / 2 = $2,900.
b. Depreciation schedule using MACRS;
Year One Depreciation = $29,000 × 0.2000 = $5,800
Year Two Depreciation = $29,000 × 0.3200 = $9,280
Year Three Depreciation = $29,000 × 0.1920 = $5,568
Year Four Depreciation = $29,000 × 0.1152 = $3,340.80
Year Five Depreciation = $29,000 × 0.1152 = $3,340.80
Year Six Depreciation = $29,000 × 0.0576 = $1,670.40
©2013 Pearson Education, Inc. Publishing as Prentice Hall 352 Brooks n Financial Management: Core Concepts, 2e c. Comparing the two depreciation schedules before and after taxes (at 30%):
Year
Straight Line
MACRS
∆ Before Tax
∆ After Tax
One
$2,900
$5,800
$2,900
$870
Two
$5,800
$9,280
$3,480
$1,044
Three
$5,800
$5,568
–$232
–$69.60
Four
$5,800
$3,340.80
–$2,459.20
–$737.76
Five
$5,800
$3,340.80
–$2,459.20
–$737.76
Six
$2,900
$1,670.40
–$1,229.60
–$368.88
Total
$29,000
$29,000
$0
$0
The difference is that the MACRS moves up the tax shield to the early years of
depreciation yet the total tax shield is the same under both depreciation schedules.
8. Depreciation expense. Richards Tree Farm, Inc. has just purchased a new aerial tree
trimmer for $91,000. Calculate the depreciation schedule using the property class
category of a single-purpose agricultural and horticultural structure (from Table 10.3)
for both straight line depreciation and MACRS. Use the half-year convention for both
methods. Compare the depreciation schedules before and after taxes using a 40% tax
rate. What do you notice about the difference between these two methods?
ANSWER Annual straight line depreciation is cost of tree-trimmer divided by 7; $91,000/ 7 =
$13,000 the first year would be $6,500 and the eighth year $6,500 (half year convention)
and the other years $13,000.
Depreciation schedule using MACRS;
Year One Depreciation
= $91,000 × 0.1429 = $13,003.90
Year Two Depreciation
= $91,000 × 0.2449 = $22,285.90
Year Three Depreciation = $91,000 × 0.1749 = $15,915.90
Year Four Depreciation
= $91,000 × 0.1249 = $11,365.90
Year Five Depreciation
= $91,000 × 0.0893 = $8,126.30
Year Six Depreciation = $91,000 × 0.0893 = $8,126.30
Year Seven Depreciation = $91,000 × 0.0893 = $8,126.30
Year Eight Depreciation = $91,000 × 0.0445 = $4,049.50
Comparing the two depreciation schedules before and after taxes (at 40%):
Year
Straight Line
MACRS
∆ Before Tax ∆ After Tax
One
$6,500
$13,003.90
$6,503.90
$2,601.56
Two
$13,000
$22,285.90
$9,285.90
$3,714.36
Three
$13,000
$15,915.90
$2,915.90
$1,166.36
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 353 Four
$13,000
$11,365.90
–$1,634.10
–$653.64
Five
$13,000
$8,126.30
–$4,873.70
–$1,949.48
Six
$13,000
$8,126.30
–$4,873.70
–$1,949.48
Seven
$13,000
$8,126.30
–$4,873.70
–$1,949.48
Eight
$6,500
$4,049.50
–$2,450.50
–$980.20
Total
$91,000
$91,000
$0
$0
The difference is that the MACRS moves up the tax shield to the early years of
depreciation yet the total tax shield is the same under both depreciation schedules.
9. Cost recovery. Brock Florist Company sold their delivery truck in problem (see
Problem 7) after three years of service. If MACRS was used for the depreciation
schedule, what is the after tax cash flow from the sale of the truck (continue to use
30% tax rate) if
a. the sales price was $15,000?
b. the sales price was $10,000?
c. the sales price was $5,000?
ANSWER The accumulated depreciation after three years using MACRS is $29,000 × (0.20 + 0.32
+ 0.192) = $20,648. The basis in the truck is therefore $29,000 – $20,648 = $8,352.
a. If the sales price is $15,000 then the truck had a gain on sale of $15,000 – $8,352
= $6,648 and the tax liability is $6,648 × 0.30 = $1,994.40. The after tax cash
flow is $15,000 – $1,994.40 = $13,005.60
b. If the sales price is $10,000 then the truck had a gain on sale of $10,000 – $8,352
= $1,648 and the tax liability is $1,648 × 0.30 = $494.40. The after tax cash flow
is $10,000 – $494.40 = $9,505.60
c. If the sales price is $5,000 then the truck had a loss on sale of $5,000 – $8,352 =
$3,352 and the tax credit is $3,352 × 0.30 = $1,005.90. The after tax cash flow is
$5,000 + $1,005.90 = $6,005.90
10. Cost recovery. Jake Richards sold the tree trimmer (see Problem 8) after four years of
service. If MACRS was used for the depreciation schedule, what is the after-tax cash
flow from the sale of the trimmer (continue to use a 40% tax rate) if
a. the sales price was $35,000?
b. the sales price was $28,428.40?
c. the sales price was $21,000?
©2013 Pearson Education, Inc. Publishing as Prentice Hall 354 Brooks n Financial Management: Core Concepts, 2e ANSWER The accumulated depreciation after four years using MACRS is $91,000 × (0.1429 +
0.2449 + 0.1749+ 0.1249) = $62,571.60. The basis in the trimmer is therefore $91,000 –
$62,571.60 = $28,428.40.
a. If the sales price is $35,000 then the trimmer had a gain on sale of $35,000 –
$28,428.40 = $6,571.60 and the tax liability is $6,571.60 × 0.40 = $2,628.64. The
after tax cash flow is $35,000 – $2,628.64 = $32,371.36
b. If the sales price is $28,428.40 then the truck had neither a gain nor loss on sale.
There is no tax liability or tax credit on disposal so the after tax cash flow is
$28,428.40
c. If the sales price is $21,000 then the truck had a loss on sale of $21,000 –
$28,428.40 = $7,428.40 and the tax credit is $7,428.40 × 0.40 = $2,971.36. The
after tax cash flow is $21,000 + $2,971.36 = $23,971.36
11. Operating cash flow. Grady Precision Measurement Tools has forecasted the
following sales and costs for a new GPS system: annual sales of 48,000 units at $18 a
unit, production costs at 37% of sales price, annual fixed costs for production at
$180,000, and depreciation expense (straight-line) of $240,000 per year. The
company tax rate is 35%. What is the annual operating cash flow of the new GPS
system?
ANSWER Revenue (48,000 × $18)
$864,000
COGS (48,000 × $18 × 0.37)
319,680
Fixed Costs
180,000
Depreciation
240,000
EBIT
$124,320
Taxes ($124,320 × 0.35)
43,512
Net Income
$ 80,808
Add Back Depreciation
240,000
Operating Cash Flow (per year) $320,808
12. Operating cash flow. Huffman Systems has forecasted the following sales for home
alarm systems to be 63,000 units per year at $38.50 per unit. The cost to produce each
unit is expected to be about 42% of the sales price. The new product will have an
additional $494,000 fixed costs each year, and the manufacturing equipment will
have an initial cost of $2,400,000 and will be depreciated over eight years (straightline). The company tax rate is 40%. What is the annual operating cash flow for the
alarm systems if the projected sales and price per unit are constant over the next eight
years?
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 355 ANSWER Revenue (63,000 × $38.50) $2,425,500
COGS (63,000 × $38.50 × 0.42)1,018,710
Fixed Costs
494,000
Depreciation ($2,400,000 / 8) 300,000
EBIT
$ 612,790
Taxes ($612,790 × 0.40)
245,116
Net Income
$ 367,674
Add Back Depreciation
300,000
Operating Cash Flow (per year)$ 667,674
13. NPV. Using the operating cash flow information in Problem 11, determine whether
Grady Precision Measurement Tools should add the GPS system to its set of products.
The initial investment is $1,440,000 and is depreciated over six years (straight-line)
and will be sold at the end of five years for $380,000. The cost of capital is 10% and
the tax rate is still 35%.
ANSWER Find the after-tax cash flow at disposal of the equipment:
Book Value (Basis at end of five years)
Original Cost $1,440,000
Depreciation expense per year is $1,440,000 / 6 = $240,000
Accumulated depreciation is 5 × $240,000 = $1,200,000
Basis = $1,440,000 – $1,200,000 = $240,000
Gain on Disposal = $380,000 – $240,000 = $140,000
Tax on Disposal = $140,000 × 0.35 = $49,000
After-tax cash flow at disposal = $380,000 – $49,000 = $331,000
1
5
(1.10)
1
NPV = −$1,440,000 + $320,808×
+ $331,000×
5
(1.10)
(1.10)
1−
NPV = -$1,440,000 + $320,808 × 3.7908 + $331,000 × 0.6209
NPV = -$1,440,000 + $1,216,114.72 + $205,524.96 = -$18,360.32
Reject the project.
14. NPV. Using the operating cash flow information in Problem 12, determine whether
Huffman Systems add the home alarm system to their set of products. The
manufacturing equipment will be sold off at the end of eight years for $210,000 and
the cost of capital for this project is 14%.
ANSWER Find the after-tax cash flow at disposal of the equipment:
©2013 Pearson Education, Inc. Publishing as Prentice Hall 356 Brooks n Financial Management: Core Concepts, 2e Book Value (Basis at end of five years)
Original Cost $2,400,000
Depreciation expense per year is $2,400,000 / 8 = $300,000
Accumulated depreciation is 8 × $300,000 = $2,400,000
Basis = $2,400,000 – $2,400,000 = $0
Gain on Disposal = $210,000 – $0 = $210,000
Tax on Disposal = $210,000 × 0.40 = $84,000
After-tax cash flow at disposal = $210,000 – $84,000 = $126,000
1
8
(1.14)
1
NPV = −$2,400,000 + $667,674×
+ $126,000×
8
( 0.14)
(1.14)
1−
NPV = -$2,400,000 + $667,674 × 4.6389 + $126,000 × 0.3506
NPV = -$2,400,000 + $3,097,248.81 + $44,170.44 = $741,419.25
Accept the project.
15. Operating cash flow (growing each year; MACRS). Mathews Mining Company is
looking at a project that has the following forecasted sales: first-year sales are 6,800
units and will grow at 15% over the next four years (a five-year project). The price of
the product will start at $124 per unit and increase each year at 5%. The production
costs are expected to be 62% of the current year’s sales price. The manufacturing
equipment to aid this project will have a total cost (including installation) of
$1,400,000. It will be depreciated using MACRS and has a seven-year MACRS life
classification. Fixed costs will be $50,000 per year. Mathews Mining has a tax rate of
30%.What is the operating cash flow for this project over these five years? Hint: Use
a spreadsheet.
ANSWER Set up in a spreadsheet
Year
1
2
3
4
5
6,800
6,800 ×
1.15
6,800 ×
1.152
6,800 ×
1.153
6,800 ×
1.154
$124
$124 × 1.05
$124 ×
1.052
$124 ×
1.053
$124 ×
1.054
Revenue
$843,200
$1,018,164
$1,229,433
$1,484,540
$1,792,583
COGS
$522,784
$631,262
$762,248
$920,415
$1,111,401
Fixed Costs
$50,000
$50,000
$50,000
$50,000
$50,000
Depreciation
$200,060
$342,860
$244,860
$174,860
$125,020
EBIT
$70,356
-$5,958
$172,325
$339,265
$506,162
Taxes (30%)
$21,107
-$1,787
$51,698
$101,780
$151,849
Unit Sales
Price per unit
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 357 Net Income
$49,249
-$4,171
$120,627
$237,485
$354,313
Add Back
Depreciation
$200,060
$342,860
$244,860
$174,860
$125,020
OCF
$249,309
$338,689
$365,487
$412,345
$479,333
Revenue is Unit Sales × Price per Unit
COGS is Revenue × 0.62
Depreciation is as follows:
Year one $1,400,000 × 0.1429
Year two $1,400,000 × 0.2449
Year three $1,400,000 × 0.1749
Year four $1,400,000 × 0.1249
Year five $1,400,000 × 0.0893
= $200,060
= $342,860
= $244,860
= $174,860
= $125,020
Taxes are EBIT × 0.30
Net Income is EBIT – Taxes
OCF is Net Income + Depreciation
16. Operating cash flow (growing each year; MACRS). Miglietti Restaurants is looking
at a project with the following forecasted sales: first-year sales quantity of 31,000
with an annual growth rate of 3.5% over the next ten years. The sales price per unit is
$42.00 and will grow at 2.25% per year. The production costs are expected to be 55%
of the current year’s sales price. The manufacturing equipment to aid this project will
have a total cost (including installation) of $2,400,000. It will be depreciated using
MACRS and has a seven-year MACRS life classification. Fixed costs are $335,000
per year. Miglietti Restaurants has a tax rate of 30%.What is the operating cash flow
for this project over these ten years? Hint: Use a spreadsheet.
ANSWER Set up in a spreadsheet
Year
1
2
3
4
5
31,000
31,000 ×
1.035
31,000 ×
1.0352
31,000 ×
1.0353
31,000 ×
1.0354
$42
$42 × 1.0225
$42 × 1.02252
$42 × 1.02253
$42 × 1.02254
$1,302,000
$1,377,890
$1,458,204
$1,543,187
$1,633,138
COGS
$716,100
$757,840
$802,012
$848,753
$898,232
Fixed Costs
$335,000
$335,000
$335,000
$335,000
$335,000
Depreciation
$342,960
$587,760
$419,760
$299,760
$214,320
EBIT
–$92,060
–$302,710
–$98,568
$59,674
$185,586
Taxes (30%)
–$27,618
–$90,813
–$29,570
$17,902
$55,676
Net Income
–$64,442
–$211,897
–$68,998
$41,772
$129,910
Add Back
Depreciation
$342,960
$587,760
$419,760
$299,760
$214,320
Unit Sales
Price per unit
Revenue
©2013 Pearson Education, Inc. Publishing as Prentice Hall 358 Brooks n Financial Management: Core Concepts, 2e OCF
$375,863
$350,762
6
7
8
9
10
31,000 ×
1.0355
31,000 ×
1.0356
31,000 ×
1.0357
31,000 ×
1.0358
31,000 ×
1.0359
$42 × 1.02255
$42 × 1.02256
$42 × 1.02257
$42 × 1.02258
$42 × 1.02259
$1,728,341
$1,829,081
$1,935,682
$2,048,508
$2,167,910
COGS
$950,588
$1,005,995
$1,064,625
$1,126,679
$1,192,350
Fixed Costs
$335,000
$335,000
$335,000
$335,000
$335,000
Depreciation
$214,320
$214,320
$106,800
$0
$0
EBIT
$228,433
$273,766
$429,257
$586,829
$640,560
Taxes (30%)
$68,530
$82,130
$128,777
$176,049
$192,168
Net Income
$159,903
$191,636
$300,480
$410,780
$448,392
Add Back
Depreciation
$214,320
$214,320
$106,800
$0
$0
OCF
$374,223
$405,956
$407,280
$410,780
$448,392
Year
Unit Sales
Price per unit
Revenue
$278,518
$341,532
$344,230
Revenue is Unit Sales × Price per Unit
COGS is Revenue × 0.55
Depreciation is as follows:
Year one $2,400,000 × 0.1429 = $342,960
Year two $2,400,000 × 0.2449 = $587,760
Year three $2,400,000 × 0.1749 = $419,760
Year four $2,400,000 × 0.1249 = $299,760
Year five $2,400,000 × 0.0893 = $214,320
Year six $2,400,000 × 0.0893 = $214,320
Year seven $2,400,000 × 0.0893 = $214,320
Year eight $2,400,000 × 0.0445 = $106,800
Taxes are EBIT × 0.30
Net Income is EBIT – Taxes
OCF is Net Income + Depreciation
17. NPV. Using the operating cash flow information from Problem 15, find the NPV of
the project for Mathews Mining if the manufacturing equipment can be sold for
$80,000 at the end of the five-year project and the cost of capital for this project is
12%. Hint: Use a spreadsheet.
ANSWER Find the after-tax cash flow at disposal of the equipment:
Book Value (Basis at end of five years)
Original Cost $1,400,000
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 359 Depreciation is as follows:
Year one $1,400,000 × 0.1429 = $200,060
Year two $1,400,000 × 0.2449 = $342,860
Year three $1,400,000 × 0.1749
= $244,860
Year four $1,400,000 × 0.1249 = $174,860
Year five $1,400,000 × 0.0893 = $125,020
Accumulated depreciation = $1,087,660
Basis = $1,400,000 – $1,087,660 = $312,340
Loss on Disposal = $80,000 – $312,340 = -$232,340
Tax Credit on Disposal = $232,340 × 0.30 = $69,702
After-tax cash flow at disposal = $80,000 + $69,702 = $149,702
NPV = -$1,400,000 + $249,309 / (1.12) + $338,689 / (1.12)2 + $365,487 / (1.12)3 +
$412,345 / (1.12)4 + (479,333 + 149,702) / (1.12)5 = -$28,271.4
Reject the project.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 360 Brooks n Financial Management: Core Concepts, 2e 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:
Book Value (Basis at end of five years)
Original Cost $2,400,000
Depreciation is as follows:
Year one $2,400,000 × 0.1429 = $342,960
Year two $2,400,000 × 0.2449 = $587,760
Year three $2,400,000 × 0.1749
Year four $2,400,000 × 0.1249 = $299,760
Year five $2,400,000 × 0.0893 = $214,320
Year six $2,400,000 × 0.0893 = $214,320
Year seven $2,400,000 × 0.0893
Year eight $2,400,000 × 0.0445
Accumulated depreciation = $2,400,000
= $419,760
= $214,320
= $106,800
Basis = $2,400,000 – $2,400,000 = $0
Gain on Disposal = $140,000 – $0 = $140,000
Tax Credit on Disposal = $140,000 × 0.30 = $42,000
After-tax cash flow at disposal = $140,000 – $42,000 = $98,000
NPV = -$2,400,000 + 278,518 / (1.08) + 375,863 / (1.08)2 + $350,762 / (1.08)3 +
$341,532 / (1.08)4 + $344,230 / (1.08)5 + $374,223 / (1.08)6 + $405,956 /
(1.08)7 + $407,280 / (1.08)8 + $410,780 / (1.08)9 + ($448,392 + $98,000) /
(1.08)10 = $95,202.13
Accept the project.
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, 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?
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 361 ANSWER Annual depreciation of foundry equipment is:
Year One, $4,000,000 × 0.20 = $800,000
Year Two, $4,000,000 × 0.32 = $1,280,000
Year Three, $4,000,000 × 0.192 = $768,000
Year Four, $4,000,000 × 0.1152 = $460,800
Year Five, $4,000,000 × 0.1152 = $460,800
Operating Cash Flows are:
Annual Sales, 300 × $27,000 = $8,100,000
Annual COGS, 300 × $18,000 = $5,400,000
In thousands (rounded)
Year 1
Year 2
Year 3
Year 4
Sales Revenue
$8,100
$8,100
$8,100
$8,100
-COGS
$5,400
$5,400
$5,400
$5,400
-Fixed Costs
$1,200
$1,200
$1,200
$1,200
- Depreciation
$800
$1,280
$ 768
$ 461
EBIT
$ 700
$ 220
$ 732
$1,039
-Taxes (30%)
$ 210
$ 66
$ 220
$ 312
Net Income
$ 490
$ 154
$ 512
$ 727
+Depreciation
$ 800
$1,280
$ 768
$ 461
Operating Cash Flows $1,290
$1,434
$1,280
$1,188
Year 5
$8,100
$5,400
$1,200
$ 461
$1,039
$ 312
$ 727
$ 461
$1,188
The equipment is sold for salvage for $500,000 at the end of year five. It has a book value
of $4,000,000 – $800,000 – $1,280,000 – $768,000 – $460,800 – $460,800 =
$230,400
Gain on Sale is $500,000 – $230,400 = $269,600
Tax on Gain is $269,600 × 0.30 = $80,880
And after-tax cash flow on disposal is $500,000 – $80,880 = $419,120.
Incremental Cash Flows for Project (Answer in Thousands, $000)
Account/Activity
Investment
ΔNWC
OCF
Salvage Value
Total Cash Flows
(Incremental)
Year 0
-$4,000
-$ 600
Year 1 Year 2 Year 3
Year 4
Year 5
$ 600
$1,290 $1,434 $1,280
$1,188
$1,188
$ 419
-$4,600
$1,290 $1,434 $1,280
$1,188
$2,207
NPV @ 12% = -$4,600 + $1,290/1.12 + $1,434/1.122 + $1,280/1.123 + $1,188/1.124 +
$2,207/1.125 = -$4,600 + 1,152 + 1,143 + $911 + $755 + $1,252 = $613.345
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:
©2013 Pearson Education, Inc. Publishing as Prentice Hall 362 Brooks n Financial Management: Core Concepts, 2e Year 1: 240
Year 2: 280
Year 3: 340
Year 4: 360
Year 5: 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:
Annual Sales, Year 1
Year 2
Year 3
Year 4
Year 5
Annual COGS, Year 1
Year 2
Year 3
Year 4
Year 5
Sales Revenue
- COGS
- Fixed Costs
- Depreciation
EBIT
- Taxes
Net Income
+ Depreciation
Operating Cash Flows
Year 1
$6,480
$4,320
$1,200
$ 800
$ 160
$ 48
$ 112
$ 800
$ 912
= 240 × $27,000 = $6,480,000
= 280 × $27,000 = $7,560,000
= 340 × $27,000 = $9,180,000
= 360 × $27,000 = $9,720,000
= 280 × $27,000 = $7,560,000
= 240 × $18,000 = $4,320,000
= 280 × $18,000 = $5,040,000
= 340 × $18,000 = $6,120,000
= 360 × $18,000 = $6,480,000
= 280 × $18,000 = $5,040,000
Operating Cash Flows
In thousands (rounded)
Year 2
Year 3
Year 4
$7,560 $ 9,180 $ 9,720
$ 5,040 $ 6,120 $ 6,480
$ 1,200 $ 1,200 $ 1,200
$ 1,280
$ 768
$ 461
$ 40 $ 1,092 $ 1,579
$ 12
$ 328
$ 474
$ 28
$ 764 $ 1,050
$ 1,280
$ 768
$ 461
$ 1,308 $ 1,532 $ 1,511
Year 5
$ 7,560
$ 5,040
$ 1,200
$ 461
$ 859
$ 258
$ 601
$ 461
$ 1,062
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
-$4,000
ΔNWC
-$ 600
$ 600
OCF
$ 912 $1,308 $1,532 $1,511 $1,062
Salvage Value
$ 419
Total Cash Flows
-$4,600
$ 912 $1,308 $1,532 $1,511 $2,081
(Incremental)
The IRR is via calculator:
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 363 CF0 = – 4,600,000
C01 = $912,000
C02 = $1,308,000
C03 = $1,532,000
C04 = $1,511,000
C05 = $2,081,000 and Solving for IRR = 15.7115% and if the hurdle rate is still 12%,
accept the project.
Solutions to Advanced Problems for Spreadsheet Application 1. Erosion costs.
1
2
3
4
5
6
7
8
9
Eroded Revenue $ 136,893.75 $ 6,637.50 $ (159,442.50) $ (337,587.50) $ (441,970.00) $ (498,845.00) $ (514,900.00) $ (490,525.00) $ (493,075.00)
Reduced Costs $ 62,537.50 $ 3,024.00 $ (72,297.50) $ (153,527.00) $ (199,038.00) $ (224,313.00) $ (231,160.00) $ (220,435.00) $ (221,180.00)
Eroded CF
$ 74,356.25 $ 3,613.50 $ (87,145.00) $ (184,060.50) $ (242,932.00) $ (274,532.00) $ (283,740.00) $ (270,090.00) $ (271,895.00)
2. Working capital impact on project.
FIND OCF:
Revenue
Variable
Fixed
S,G & A
Depreciation
EBIT
Taxes
Net Income
Add Depreciation
OCF
1
$10,000,000.00
$ 4,000,000.00
$ 1,500,000.00
$ 1,250,000.00
$ 2,000,000.00
$ 1,250,000.00
$ 462,500.00
$ 787,500.00
$ 2,000,000.00
$ 2,787,500.00
2
$13,000,000.00
$ 5,200,000.00
$ 1,500,000.00
$ 1,400,000.00
$ 3,200,000.00
$ 1,700,000.00
$ 629,000.00
$ 1,071,000.00
$ 3,200,000.00
$ 4,271,000.00
3
$17,000,000.00
$ 6,800,000.00
$ 1,500,000.00
$ 1,750,000.00
$ 1,920,000.00
$ 5,030,000.00
$ 1,861,100.00
$ 3,168,900.00
$ 1,920,000.00
$ 5,088,900.00
4
$23,000,000.00
$ 9,200,000.00
$ 1,500,000.00
$ 2,000,000.00
$ 1,152,000.00
$ 9,148,000.00
$ 3,384,760.00
$ 5,763,240.00
$ 1,152,000.00
$ 6,915,240.00
5
$18,000,000.00
$ 7,200,000.00
$ 1,500,000.00
$ 2,000,000.00
$ 1,120,000.00
$ 6,180,000.00
$ 2,286,600.00
$ 3,893,400.00
$ 1,120,000.00
$ 5,013,400.00
6
$12,000,000.00
$ 4,800,000.00
$ 1,500,000.00
$ 1,500,000.00
$ 576,000.00
$ 3,624,000.00
$ 1,340,880.00
$ 2,283,120.00
$ 576,000.00
$ 2,859,120.00
Capital outlay
$
10,000,000.00
Working Capital CHG $
Incremental CF
Capital
Change in WC
OCF
Incremental CF
IRR
NPV
0
2,000,000.00 $
1
600,000.00 $
2
3
4
5
6
800,000.00 $ 1,200,000.00 $ (1,000,000.00) $ (1,200,000.00) $ (2,400,000.00)
0
1
2
3
4
5
6
$ (10,000,000.00)
$ (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
$ 2,787,500.00 $ 4,271,000.00 $ 5,088,900.00 $ 6,915,240.00 $ 5,013,400.00 $ 2,859,120.00
$ (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
26.84%
$5,524,065.25
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.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 364 Brooks n Financial Management: Core Concepts, 2e 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
The cost of designs and prototypes is a sunk cost and should not be
included.
2. What is the cash flow resulting from disposal of the equipment at the end of the
project?
Disposal price
$2,400,000
Book Value $24,000,000.9424(24,000,000)
1,382,400
Gain on disposal
1,017,600
Tax 34%
345,984
Cash flow from disposal (disposal price –
tax)
$2,054,016
3. Compute a schedule of depreciation for the plant and equipment.
Depreciation Schedule
year
1
2
3
4
5
6
rate
20%
32%
19.20%
11.52%
11.52%
0.0576
4,800,00
0
7,680,00
0
4,608,00
0
2,764,80
0
2,764,80
0
1,382,40
0
depreciatio
n
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 365 4. Compute a schedule of operating cash flows for BioCom’s new product.
Operating Cash Flows
Year
1
Revenue
2
$16,500,000 $17,490,000
COGS
3
4
5
$18,539,400
$19,651,764
$20,830,870
6,600,000
6,996,000
7,415,760
7,860,706
Fixed Costs
600,000
600,000
600,000
600,000
600,000
S,G, and A
825,000
699,600
926,970
982,588
1,041,543
Depreciation
4,800,000
7,680,000
4,608,000
2,764,800
2,764,800
EBIT
3,675,000
1,514,400
4,988,670
7,443,670
8,092,178
Taxes
1,249,500
Net Income
514,896
$2,425,500
$999,504
1,696,148
$3,292,522
8,332,348
2,530,848
$4,912,822
2,751,341
$5,340,838
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
$7,029,504
$6,250,522
$6,027,622
$6,455,638
5. Compute a schedule of incremental cash flows for BioCom’s new product.
Incremental cash
flows
T0
Capital Spending
Change in NWC
OCF
Disposal cash flow
Incremental Cash
Flow
T1
T2
T3
T4
T5
-24,000,000
-480,000
480,000
5,575,500
7,029,504 6,250,522
6,027,622
6,455,638
2,054,016
-24,480,000
5,575,500
7,029,504 6,250,522
6,027,622
8,989,654
6. Compute the project’s net present value.
NPV
(24,480,00
0)
5,575,000
1.09
7,029,504
1.092
6,250,522
1.093
6,027,622
1.094
8,989,654
1.095
Cash
flows
discounted
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,
NPVè
$1,490,599.29
7. Does your answer to Question 6 indicate that management should accept or
reject the product?
The net present value is positive, so the project should be accepted.
8. Challenge question. A spreadsheet is recommended for this question.
a. Recompute your answers to Questions 4 through 7 assuming sales grow at 12%
per year.
b. Recompute your answers to Questions 4 through 7 assuming sales grow at 0% per
year.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 366 Brooks n Financial Management: Core Concepts, 2e c. Comment on the sensitivity of the NPV to the rate of growth in sales.
Spreadsheet solution is on next page.
Operating Cash Flows (with sales growth rate = 12% per year)
Year
1
2
3
4
5
$16,500,00
0
$18,480,00
0
$20,697,60
0
$23,181,3
12
$25,963,069
6,600,000
7,392,000
8,279,040
9,272,525
10,385,228
Fixed Costs
600,000
600,000
600,000
600,000
600,000
S,G, and A
825,000
924,000
1,034,880
1,159,066
1,298,153
Depreciation
4,800,000
7,680,000
4,608,000
2,764,800
2,764,800
EBIT
3,675,000
1,884,000
6,175,680
9,384,922
10,914,888
Taxes
1,249,500
640,560
2,099,731
3,190,873
3,711,062
$2,425,500
$1,243,440
$4,075,949
$6,194,04
8
$7,203,826
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
$5,575,500
$7,273,440
$7,033,949
$7,308,84
8
$8,318,626
T1
T2
T3
T4
Revenue
COGS
Net Income
Operating cash
flows
Incremental cash
flows
T0
Capital Spending
-24,000,000
Change in NWC
-480,000
OCF
T5
480,000
5,575,500
7,273,440
7,033,949
7,308,848
Disposal cash flow
8,318,626
2,054,016
Incremental Cash
Flow
-24,480,000
NPV @ 9%
$ 4,419,790.77
5,575,500
7,273,440
7,033,949
©2013 Pearson Education, Inc. Publishing as Prentice Hall 7,308,848
10,852,642
Chapter 10 n Cash Flow Estimation 367 Operating Cash Flows(sales growth rate= 0%)
Year
1
2
3
4
5
$16,500,000
$16,500,000
$16,500,000
$16,500,000
$16,500,000
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
$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
$5,575,500
$6,554,700
$5,510,220
$4,883,532
$4,883,532
T1
T2
T3
T4
T5
Revenue
COGS
Net Income
Operating cash flows
Incremental cash flows
T0
Capital
Spending
Change in
NWC
–24,000,000
–480,000
OCF
480,000
5,575,500
6,554,700
5,510,220
4,883,532
Disposal
cash flow
4,883,532
2,054,016
Incremental
Cash Flow
–24,480,000
NPV @ 9%
$(1,312,487.24)
5,575,500
6,554,700
5,510,220
4,883,532
7,417,548
NPV is quite sensitive to the growth rate of sales. Doubling the growth rate almost triples
the NPV, while a flat growth rate leads to a negative NPV and the project would be
rejected. This sensitivity suggests that the project may be riskier than it seemed from the
most likely scenario of 6% growth.
©2013 Pearson Education, Inc. Publishing as Prentice Hall 368 Brooks n Financial Management: Core Concepts, 2e Additional Problems with Solutions 1. Erosion cost. Volvo is looking to introduce a new “hybrid” car in the US. 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-­‐35 to 10-­‐36) OLD SEDAN
Current EBIT = # of cars sold × (Price – Cost)=25,000 × ($20,000-$15,000)
= $125,000,000
EBIT (after launch) = 18,000 × ($5000) = $90,000,000
Lost EBIT = $125,000,000 – $90,000,000 = $35,000,000= Erosion Cost
HYBRID
EBIT = 20,000 × ($22,000-$18,000) = $80,000,000
COMBINED EBIT
= $80,000,000 + $90,000,000 = $170,000,000
Since the Combined EBIT is higher than the current EBIT by $45,000, 000 it would be a
worthwhile move for Volvo.
2. Depreciation rates. R.K. Boats Inc. has just installed a new hydraulic lift system
which is being categorized as a 5-year class-life asset under MACRS. The total
purchase cost plus installation amounted to $750,000. RKB has always used straightline 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
since the total depreciation under each method will still sum up to $750,000 and be
spread over 6 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-­‐37 to 10-­‐38) Under straight-line depreciation:
Annual dep.exp. = Cost + Installation / Life = $750,000/5 = $150,000
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 369 Using “half-year” convention the comparison of yearly depreciation under the 2 methods
is as follows:
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
750000
750000
0
0
Year
Total
100%
NPV
@10%
$2,265.82
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 – 7 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-­‐39 to 10-­‐40) The 7-year MACRS rates are as follows:
After 5 years, the book value would be (0893+.0893+.0445) × $3,000,000
Book value = 0.2231 × $3,000,000 = $669, 300
Loss on sale = Selling Price – Book value = $500,000 – $669,300 = -$169,300
©2013 Pearson Education, Inc. Publishing as Prentice Hall 370 Brooks n Financial Management: Core Concepts, 2e 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 5 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
5 years? Hint: Use a spreadsheet and round units to the nearest whole number.
ANSWER (Slides 10-­‐41 to 10-­‐43) Based on 5-year MACRS rates, the annual depreciation expense is as follows:
Dep. Basis è
2,200,000
Year
Rate
Depreciation
1
0.2
440000
2
0.32
704000
3
0.192
422400
4
0.1152
253440
5
0.1152
253440
6
0.0576
126720
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
Prod. Costs
$1,050,000 $1,146,600 $1,252,087 $1,367,279 $1,493,069
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
($147,500) ($358,370)
($18,752)
$213,564
$282,748
($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
$422,400
$253,440
$253,440
EBIT
Taxes
35%
$704,000
©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 10 n Cash Flow Estimation 371 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 5 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 5-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-­‐44 to 10-­‐47) In addition to the operating cash flow for years 1-5, we need to calculate the initial year
and terminal year cash flow and add them in.
Initial Year Cash Flow (Year 0)
Cost of Equipment = $2,200,000
Increase in NWC = .10 × (Year 1 production cost) = 0.1 × $472,500 = $47,250
Total cost at start up = -2, 247,250
Terminal Year Cash Flow
Recovery of NWC = +$47, 250
After-tax Salvage Value of Equipment = Selling Price –Tax on Gain
Where; Tax on gain = Tax rate × (Selling Price – Book Value)
Selling Price = 20% of Cost = .2 × (2,200,000) = $440,000
Book Value = Year 6 MACRS Dep. Rate × Dep. Basis=.0576 × 2200000=$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!
©2013 Pearson Education, Inc. Publishing as Prentice Hall