Chapter 10
Questions and Problems
1. Relevant Cash Flows
Precious Metals Ltd. is looking at setting up a new
manufacturing plant in South Africa to produce gold
bracelets. The company bought some land six years ago
for 5 million rand in anticipation of using it as a
warehouse and distribution site, but the company has
since decided to rent these facilities from a competitor
instead. If the land were sold today, the company would
net 5.4 million rand. The company wants to build its new
manufacturing plant on this land; the plant will cost 10.4
million rand to build, and the site requires 850,000 rand
worth of grading before it is suitable for construction.
What is the proper cash flow amount to use as the initial
investment in fixed assets when evaluating this project?
Why?
• ZAR 5,400,000 + 10,400,000 + 850,000 =
ZAR 16,650,000
• 2. Relevant Cash Flows
• Winnebagel Corp. currently sells 30,000 motor homes
per year at $45,000 each, and 12,000 luxury motor
coaches per year at $95,000 each. The company wants
to introduce a new portable camper to fill out its product
line; it hopes to sell 20,000 of these campers per year at
$12,000 each. An independent consultant has
determined that if Winnebagel introduces the new
campers, it should boost the sales of its existing motor
homes by 5,000 units per year, and reduce the sales of
its motor coaches by 1,300 units per year. What is the
amount to use as the annual sales figure when
evaluating this project? Why?
•
•
•
•
2.
Sales due solely to the new product line are:
20,000($12,000) = $240,000,000
Increased sales of the motor home line occur because of
the new product line introduction; thus:
• 5,000($45,000) = $225,000,000 in new sales is relevant.
• Erosion of luxury motor coach sales is also due to the
new mid-size campers; thus: 1,300($95,000) =
$123,500,000 loss in sales is relevant.
• The net sales figure to use in evaluating the new line is
thus: $240,000,000 + 225,000,000 – 123,500,000 =
$341,500,000
• 4. Calculating OCF
• Consider the following income statement:
• Fill in the missing numbers and then
calculate the OCR What is the
depreciation tax shield?
Sales
$912,400
Costs
593,600
Depreciation
135,000
EBIT
Taxes (34)
Net income
?
?
?
Sales
$ 912,400
Costs
593,600
Depreciation
135,000
EBT
Taxes@34%
Net income
$ 183,800
62,492
$ 121,308
•
•
•
•
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = $183,800 + 135,000 – 62,492
OCF = $256,308
• The depreciation tax shield is the
depreciation times the tax rate, so:
• Depreciation tax shield = tc X Depreciation
• Depreciation tax shield = .34($135,000)
• Depreciation tax shield = $45,900
• The depreciation tax shield shows us the
increase in OCF by being able to expense
depreciation.
• 5. OCF from Several Approaches
• A proposed new project has projected
sales of ¥9,200,000, costs of ¥5,120,000,
and depreciation of ¥287,400. The tax rate
is 35 percent. Calculate operating cash
flow using the four different approaches
described in the chapter and verify that the
answer is the same in each case.
Sales
Variable costs
Depreciation
EBT
Taxes@35%
Net income
¥ 9,200,000
5,120,000
287,400
¥ 3,792,600
1,327,410
¥ 2,465,190
Using the most common financial calculation for
OCF, we get:
• OCF = EBIT + Depreciation – Taxes =
¥3,792,600 + 287,400 – 1,327,410
• OCF = ¥ 2,752,590
• The top-down approach to calculating OCF
yields:
• OCF = Sales – Costs – Taxes = ¥9,200,000 –
5,120,000 – 1,327,410
• OCF = ¥ 2,752,590
•
•
•
•
The tax-shield approach is:
OCF = (Sales – Costs)(1 – tC) + tC X Depreciation
OCF = (¥9,200,000 – 5,120,000)(1 – .35) + .35(287,400)
OCF = ¥ 2,752,590
• And the bottom-up approach is:
• OCF = Net income + Depreciation = ¥2,465,190 +
287,400
• OCF = ¥ 2,752,590
• All four methods of calculating OCF should always give
the same answer.
• 13. Project Evaluation
• Dog Up! Franks is looking at a new sausage
system with an installed cost of $420,000. This
cost will be depreciated straight-line to zero over
the project's five-year life, at the end of which
the sausage system can be scrapped for
$60,000. The sausage system will save the firm
$130,000 per year in pretax operating costs, and
the system requires an initial investment in net
working capital of $28,000. If the tax rate is 34
percent and the discount rate is 10 percent, what
is the NPV of this project?
• 13. First we will calculate the annual
depreciation of the new equipment. It will be:
• Annual depreciation = $420,000/5
• Annual depreciation = $84,000
• Now, we calculate the aftertax salvage value.
The aftertax salvage value is the market price
minus (or plus) the taxes on the sale of the
equipment, so:
• Aftertax salvage value = MV + (BV – MV)tc
• Very often the book value of the equipment is zero as it
is in this case. If the book value is zero, the equation for
the aftertax salvage value becomes:
• Aftertax salvage value = MV + (0 – MV)tc
• Aftertax salvage value = MV(1 – tc)
• We will use this equation to find the aftertax salvage
value since we know the book value is zero. So, the
aftertax salvage value is:
•
• Aftertax salvage value = $60,000(1 – 0.34)
• Aftertax salvage value = $39,600
• Using the tax shield approach, we find the OCF for the
project is:
• OCF = $130,000(1 – 0.34) + 0.34($84,000)
• OCF = $114,360
• Now we can find the project NPV. Notice we include the
NWC in the initial cash outlay. The recovery of the NWC
occurs in Year 5, along with the aftertax salvage value.
• NPV = –$420,000 – 28,000 + $114,360(PVIFA 10%,5) +
[($39,600 + 28,000) / 1.15]
• NPV = $27,488.66
• 17. Calculating EAC
• You are evaluating two different silicon wafer milling
machines. The Techron I costs $210,000, has a threeyear life, and has pretax operating costs of $34,000 per
year. The Techron II costs $320,000, has a five-year life,
and has pretax operating costs of $23,000 per year. For
both milling machines, use straight-line depreciation to
zero over the project's life and assume a salvage value
of $20,000. If your tax rate is 35 percent and your
discount rate is 12 percent, compute the EAC for both
machines. Which do you prefer? Why?
• 17.We will need the aftertax salvage value
of the equipment to compute the EAC.
Even though the equipment for each
product has a different initial cost, both
have the same salvage value. The aftertax
salvage value for both is:
• Both cases: aftertax salvage value =
$20,000(1 – 0.35) = $13,000
• To calculate the EAC, we first need the OCF and
NPV of each option. The OCF and NPV for
Techron I is:
•
• OCF = – $34,000(1 – 0.35) + 0.35($210,000/3) =
$2,400
•
• NPV = –$210,000 + $2,400(PVIFA 12%,3) +
($13,000/1.123) = –$194,982.46
• EAC = –$194,982.46 / (PVIFA 12%,3)= –
$81,180.75
• And the OCF and NPV for Techron II is:
• OCF = – $23,000(1 – 0.35) + 0.35($320,000/5) = $7,450
•
• NPV = –$320,000 + $7,450(PVIFA 12%,5) +
($13,000/1.145) = –$285,767.87
•
• EAC = –$285,767.87 / (PVIFA 12%,5) = –$79,274.79
• The two milling machines have unequal lives, so they
can only be compared by expressing both on an
equivalent annual basis, which is what the EAC method
does. Thus, you prefer the Techron II because it has the
lower (less negative) annual cost.
• 18. Calculating a Bid Price
• Osaka Enterprises needs someone to supply it with
150,000 cartons of machine screws per year to support
its manufacturing needs over the next five years, and
you've decided to bid on the contract. It will cost you
¥17,580,000 to install the equipment necessary to start
production; you'll depreciate this cost straight-line to zero
over the project's life. You estimate that in five years, this
equipment can be salvaged for ¥480,000. Your fixed
production costs will be ¥4,245,000 per year, and your
variable production costs should be ¥106.20 per carton.
You also need an initial investment in net working capital
of ¥652,800. If your tax rate is 35 percent and you
require a 16 percent return on your investment, what bid
price should you submit?
• 18. To find the bid price, we need to calculate all
other cash flows for the project, and then solve
for the bid price. The aftertax salvage value of
the equipment is:
• Aftertax salvage value = ¥480,000(1 – 0.35) =
¥312,000
• Now we can solve for the necessary OCF that
will give the project a zero NPV. The equation for
the NPV of the project is:
• NPV = 0 = – ¥17,580,000 – 652,800 +
OCF(PVIFA 16%,5) + [(¥652,800 + 312,000) /
1.165]
• Solving for the OCF, we find the OCF that makes
the project NPV equal to zero is:
• OCF = ¥17,773,446.17 / PVIFA 16%,5 =
¥5,428,177.20
• The easiest way to calculate the bid price is the
tax shield approach, so:
• OCF = ¥5,428,177.20 = [(P – v)Q – FC ](1 – tc) +
tcXD
• ¥5,428,177.20 = [(P – ¥106.20)(150,000) –
¥4,245,000 ](1 – 0.35) + 0.35(¥17,580,000/5)
• P = ¥177.55
• 19. Cost-Cutting
• Proposals Massey Machine Shop is considering a fouryear project to improve its production efficiency. Buying
a new machine press for $480,000 is estimated to result
in $180,000 in annual pretax cost savings. The press
falls in the MACRS five-year class, and it will have a
salvage value at the end of the project of $70,000. The
press also requires an initial investment in spare parts
inventory of $20,000, along with an additional $3,000 in
inventory for each succeeding year of the project. If the
shop's tax rate is 35 percent and its discount rate is 15
percent, should Massey buy and install the machine
press?
• 19. First, we will calculate the depreciation each
year, which will be:
•
D1 = $480,000(0.2000) = $96,000
•
D2 = $480,000(0.3200) = $153,600
•
D3 = $480,000(0.1920) = $92,160
•
D4 = $480,000(0.1152) = $55,296
• The book value of the equipment at the end of
the project is:
• BV4 = $480,000 – ($96,000 + 153,600 + 92,160
+ 55,296) = $82,944
• The asset is sold at a loss to book value, so this creates
a tax refund.
• After-tax salvage value = $70,000 + ($82,944 –
70,000)(0.35) = $74,530.40
• So, the OCF for each year will be:
• OCF1 = $180,000(1 – 0.35) + 0.35($96,000) =
$150,600.00
• OCF2 = $180,000(1 – 0.35) + 0.35($153,600) =
$170,760.00
• OCF3 = $180,000(1 – 0.35) + 0.35($92,160) =
$149,256.00
• OCF4 = $180,000(1 – 0.35) + 0.35($55,296) =
$136,353.60
• Now we have all the necessary
information to calculate the project NPV.
• We need to be careful with the NWC in
this project. Notice the project requires
$20,000 of NWC at the beginning, and
$3,000 more in NWC each successive
year.
• We will subtract the $20,000 from the initial cash flow,
and subtract $3,000 each year from the OCF to account
for this spending.
• In Year 4, we will add back the total spent on NWC,
which is $29,000.
• The $3,000 spent on NWC capital during Year 4 is
irrelevant. Why?
• Well, during this year the project required an additional
$3,000, but we would get the money back immediately.
• So, the net cash flow for additional NWC would be zero.
With all this, the equation for the NPV of the project is:
• NPV = – $480,000 – 20,000 + ($150,600 –
3,000)/1.15 + ($170,760 – 3,000)/1.152
+ ($149,256 – 3,000)/1.153 + ($136,353.60
+ 29,000 + 74,530.40)/1.154
• NPV = –$11,481.36
Example: Setting the Bid Price設定
投標價格
• Consider the following information:
– Army has requested bid for multiple use digitizing
devices (MUDDs)
– Deliver 4 units each year for the next 3 years
– Labor and materials estimated to be $10,000 per unit
– Production space leased for $12,000 per year
– Require $50,000 in fixed assets with expected
salvage of $10,000 at the end of the project
(depreciate straight-line)
– Require initial $10,000 increase in NWC
– Tax rate = 34%
– Required return = 15%