Topic 10
CAPITAL BUDGETING: NPV &
CAPITAL DECISIONS (Part 1)
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems
require multiple steps. Due to space and readability constraints, when these intermediate
steps are included in this solutions manual, rounding may appear to have occurred.
However, the final answer for each problem is found without rounding during any step in
the problem.
Q8.3
Calculating Payback. Kleimner Manufacturing N.V. imposes a payback cutoff
of three years for its international investment projects. If the company has the
following two projects available, should it accept either of them?
Year
Cashflow ($) A
Cashflow ($) B
-45,000
17,000
23,000
19,000
100,000
-90,000
19,000
24,000
35,000
5,000
0
1
2
3
4
Project A has cash flows of:
Cash flows = $17,000 + 23,000
Cash flows = $40,000
during the first two years. The cash flows are still short by $5,000 of recapturing the
initial investment, so the payback for Project A is:
Payback = 2 + ($5,000 / $19,000)
Payback = 2.26 years
Project B has cash flows of:
Cash flows = $19,000 + 24,000 + 35,000
Cash flows = $78,000
during the first three years. The cash flows are still short by $12,000 of recapturing
the initial investment. Since the project’s cash flow in the fourth year is less than
$12,000 the payback for Project B is never.
Using the payback criterion and a cutoff of 3 years, accept project A and reject
project B.
2
Q8.4
Calculating AAR. You're trying to determine whether or not to expand your
business by building a new manufacturing plant. The plant has an installation cost
of $17 million, which will be depreciated straight-line to zero over its four-year
life. If the plant has projected net income of $1,735,000, $2,105,000, $1,945,000,
and $1,342,000 over these four years, what is the project's average accounting
return (AAR)?
Our definition of AAR is the average net income divided by the average book value.
The average net income for this project is:
Average net income = ($1,735,000 + 2,105,000 + 1,945,000 + 1,342,000) / 4
Average net income = $1,781,750
And the average book value is:
Average book value = ($17,000,000 + 0) / 2
Average book value = $8,500,000
So, the AAR for this project is:
AAR = Average net income / Average book value
AAR = $1,781,750 / $8,500,000
AAR = .2096 or 20.96%
Q8.5 Calculating IRR. A firm evaluates all of its projects by applying the IRR rule. If
the required return is 13 percent, should the firm accept the following project?
Year
0
1
2
3
Cashflow ($)
-4,550
1,750
2,550
540
The IRR is the interest rate that makes the NPV of the project equal to zero. So, the
equation that defines the IRR for this project is:
0 = – $4,550 + $1,750/(1+IRR) + $2,550/(1+IRR)2 + $540/(1+IRR)3
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
IRR = 3.61%
Since the cash flows are conventional and the IRR is less than the required return, we
would reject the project.
3
Topic 10
CAPITAL BUDGETING: NPV &
CAPITAL DECISIONS (Part 2)
Answers to Concepts Review and Critical Thinking Questions
Q9.5
Cash Flow and Depreciation. “When evaluating projects, we're only concerned
with the relevant incremental aftertax cash flows. Therefore, because depreciation
is a noncash expense, we should ignore its effects when evaluating projects.”
Critically evaluate this statement.
Depreciation is a non-cash expense, but it is tax-deductible on the income
statement. Thus depreciation causes taxes paid, an actual cash outflow, to be
reduced by an amount equal to the depreciation tax shield TCD. A reduction in
taxes that would otherwise be paid is the same thing as a cash inflow, so the
effects of the depreciation tax shield must be added in to get the total incremental
aftertax cash flows.
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems
require multiple steps. Due to space and readability constraints, when these intermediate
steps are included in this solutions manual, rounding may appear to have occurred.
However, the final answer for each problem is found without rounding during any step in
the problem.
Q9.2
Relevant Cash Flows. Chinco Ltd., currently sells 28,000 motor homes per year
at $73,000 each, and 7,000 luxury motor coaches per year at $115,000 each. The
company wants to introduce a new portable camper to fill out its product line; it
hopes to sell 23,000 of these campers per year at $19,000 each. An independent
consultant has determined that if Chinco introduces the new campers, it should
boost the sales of its existing motor homes by 2,600 units per year, and reduce the
sales of its motor coaches by 850 units per year. What is the amount to use as the
annual sales figure when evaluating this project? Why?
Sales due solely to the new product line are:
23,000($19,000) = $437,000,000
Increased sales of the motor home line occur because of the new product line
introduction; thus:
4
2,600($73,000) = $189,800,000
in new sales is relevant. Erosion of luxury motor coach sales is also due to the new
mid-size campers; thus:
850($115,000) = $97,750,000 loss in sales
is relevant. The net sales figure to use in evaluating the new line is thus:
Net sales = $437,000,000 + 189,800,000 – 97,750,000
Net sales = $529,050,000
Q9.4
Calculating OCF. Consider the following income statement:
Sales
Variable costs
Depreciation
EBIT
Taxes@35%
Net income
$62,000
39,500
76,000
?
?
?
Fill in the missing numbers and then calculate the OCF. What is the depreciation
tax shield?
To find the OCF, we need to complete the income statement as follows:
Sales
$
62,000
Variable costs
(39,500)
Depreciation
(76,000)
EBIT
$ (53,500)
Taxes@35%
0
Net income / loss $(53,500)
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = -$53,500+ 76,000 – (0)
OCF = $22,500
The depreciation tax shield is the depreciation times the tax rate, so:
Depreciation tax shield = Depreciation(T)
Depreciation tax shield = .35($76,000)
Depreciation tax shield = $26,600
In the example above where the company has a loss (negative EBIT), the full benefit of
the depreciation tax shield could not be utilized. However for a company with positive
EBIT, the depreciation tax shield shows us an increase in OCF by being able to expense
depreciation.
5
Q9.13 Project Evaluation. Agro Foods is looking at a new sausage system with an
installed cost of $625,000. 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 $95,000. The sausage system will save the firm $183,000 per year in pretax
operating costs, and the system requires an initial investment in net working
capital of $41,000. If the tax rate is 34 percent and the discount rate is 8 percent,
what is the NPV of this project?
First, we will calculate the annual depreciation of the new equipment.
It will be:
Annual depreciation = $625,000/5
Annual depreciation = $125,000
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)T
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)T
Aftertax salvage value = MV(1 – T)
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 = $95,000(1 – 0.34)
Aftertax salvage value = $62,700
Using the tax shield approach, we find the OCF for the project is:
OCF = $183,000(1 – 0.34) + 0.34($125,000)
OCF = $163,280
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 = –$625,000 – 41,000 + $163,280(PVIFA8%,5) + [($62,700 + 41,000) / 1.085]
NPV = $56,506.17