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Chapter 12: Strategic Investment Decis24ns
Chapter 12
Strategic Investment Decisions
LEARNING OBJECTIVES
Chapter 12 addresses the following questions:
LO1 Explain how strategic investment decisions are made.
LO2 identify relevant cash flows and perform net present value (NPV) analysis.
LO3 Identify the uncertainties of NVP analysis.
LO4 Apply alternative methods in analyzing strategic investment decisions.
LO5 Identify additional issues to be considered for strategic investment decisions.
LO6 Explain how income taxes affect strategic investment decisions cash flows.
LO7 Explain how real and nominal methods are used to address inflation in an NPV analysis.
These learning questions (LO1 through LO7) are cross-referenced in the textbook to individual
exercises and problems.
© 2012 John Wiley and Sons Canada, Ltd. 25 Cost Management
QUESTIONS
12.1 After a number of years, the present value factors for all discount rates become quite
small, and the incremental effect of future cash flows is therefore small.According to the
present value tables, after about 20 years, the incremental values at rates above 8 to 10%
are small (less than 20% of the original value).If these cash flows are small, but include
error, the size of error would also be small and likely have little effect on the overall
analysis.
12.2 If several projects are being analyzed, their NPVs can be summed to determine the NPV
for that group or portfolio of projects, whereas IRR can be neither summed nor
averaged.In addition, NPV provides information about the value of the projects in terms
of today’s dollars.If projects are of different sizes, requiring large and small investments,
NPV reflects these differences.IRR provides only a rate of return, and comparing rates of
return does not take into consideration the size of return.In addition, the net present value
method is computationally simpler than the internal rate of return method. Determining
IRR can be time consuming, particularly for projects having uneven cash flows.
However, the use of a spreadsheet reduces the effort considerably.
An important difference between the two methods is that the IRR method assumes cash
inflows can be reinvested to earn the same return that the project would
generate.However, it may be difficult for an organization to identify other opportunities
that could achieve the same rate when IRR is high.In contrast, the NPV method assumes
that cash inflows can be reinvested and earn the discount rate—a more realistic
assumption.If the discount rate is set equal to the organization’s cost of capital, then
alternative uses of cash would include paying off creditors or buying back
stock.Therefore, if the results of analyses using the two methods are not the same, the
NPV method is preferable.
Both methods are used widely in business.One reason for the continued use of IRR is that
many people find it intuitively easier to understand than NPV.In addition, managers may
want to compare the IRR on prior projects to current project return rates as they consider
new investment.
12.3
(a) Net present value (NPV)
Pros:
• NPV is more accurate than the payback and accrual accounting rate of return
methods because it reflects the time value of money.
• Under NPV, discounted cash flows reflect today’s dollars, so several different
projects can be easily compared to determine the one with the highest NPV.
Cons:
• It is sometimes more difficult to estimate cash flows and choose an
appropriate discount rate for NPV than finding the internal rate of return or
calculating payback or an accounting rate of return.
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 26
(b) Internal Rate of Return (IRR)
Pros:
• Many managers find IRR intuitively easier to understand than NPV
• IRR has the same advantage as NPV of including the time value of money.
• IRR can be used to compare potential projects (choose the one with highest
IRR).
Cons:
• Assumes cash flows can be reinvested at the IRR
• When comparing projects, IRR does not take into consideration size of
investment and may be inappropriate when managers need to choose among
competing projects because capital is constrained.
• IRRs from several projects cannot be summed or averaged, while net present
values can.
• IRR is computationally more difficult than NPV and the other methods,
particularly with uneven cash flows.
(c) Payback Method
Pros:
• Used extensively, particularly outside of the U.S.
• Focuses on high risk of long payback period
Cons:
• Does not incorporate time value of money
• Ignores cash flows received after the investment is recovered
(d) Accrual Accounting Rate of Return
Pros:
• Use for division or department performance because data is readily available
Cons
• Cost of investment is double-counted (amortization is included in the
numerator, and the investment is the denominator)
• Not appropriate for capital budget decisions because it does not include the
time value of money
12.4 Estimating future cash flows becomes more difficult over longer periods of time because
the uncertainties increase.Changes in economic, political, and consumer tastes that affect
cash flows cannot be easily predicted.More information is usually available about near-
term economic factors than long-term.
12.5 Future cash flows are discounted with present value factors that become increasingly
small across time to reflect the fact that investors forego interest on cash flows that are
received in the future relative to cash flows that are received today and could be invested
© 2012 John Wiley and Sons Canada, Ltd. 27 Cost Management
today.This discounting reflects the opportunity cost (interest foregone) when money is
received in the future instead of today.
12.6 A nominal discount rate includes a factor for inflation, and the real rate does not.Both
rates include a risk-free rate and a risk premium.Using a nominal approach, different cash
flows can be inflated differentially.For example, gasoline prices might inflate at a
different rate than wages.If different types of cash flows are differentially inflated to
better reflect future expectations, the preciseness of the estimation and analysis process
increases and information quality increases.
12.7 Real assets tend to increase in nominal value under inflation, while monetary assets tend
to remain fixed.If a firm has cash in a bank earning interest, the after-tax return could be
less than the inflation rate.Therefore the firm’s cash would be losing purchasing power
over time.In this case it would be better for the firm to invest in a real asset that increases
at the inflation rate or greater.
12.8 Net present value.All investments with a positive net present value would be accepted,
assuming that the cost of capital is constant across investments.
12.9 Requiring a higher return rate for projects in developing countries may be the firm's way
of coping with increased problems of uncertainty and risk.Less developed countries
usually have less stable political systems, economies, inflation rates, and consumer
markets.In addition, infrastructure such as roads and utilities is sometimes unreliable, so
production and transportation problems could occur more frequently. These factors
increase the risk of doing business in developing countries.
From the host government's point of view, if a higher rate of return is not permitted under
such circumstances, the investment would probably never have been made at all, and the
developing country would be worse off as a result.The firm, however, must be careful to
avoid any perception of exploitation, as the long-term reputation effect could be
devastating.
12.10 There are two reasons to incorporate tax effects more formally into NPV analyses.From
an accounting standpoint, tax regulations permit a shift of both the amount and the timing
(sometimes permanently) of taxes; this will have an effect on present values.If tax
savings based on current tax rules are not incorporated into the analysis, these effects are
not captured and the analysis is less accurate.From a mathematical standpoint, the factors
in the tables are not linearly related (all of the formulas have exponents); e.g., the present
value factor for 20% is not one-half of the factor for 10%.
12.11 The return on the investment portfolio represents the centre's opportunity cost for
funds.They can earn at least that return; therefore, any other investment must yield a
higher return.
12.12 After a number of years, the present value factors for all discount rates become quite
small, and the incremental effect of future cash flows is therefore small. According to the
present value tables, after about 15 years, the incremental values at rates above 8 to 10%
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 28
are small. For example, at a discount rate of 15%, after 17 years the present value factor
is 0.093, meaning that the $1 inflow 17 years from today is worth to us just $0.093 when
measured in today’s dollars
12.13 The present value of an ordinary annuity table reflects the value of uniform cash flows
over time. If the cash flows were not discounted over time, the annuity factor would be
equal to the number of time periods in which cash flows are expected to occur. However,
the discount increases over time, so the incremental present value for each time period
decreases. Annuity factors increase over time because they are cumulative; they reflect
cash flows for additional time periods. However, the incremental increase for each
annuity factor becomes smaller over time. This is in contrast to the present value table,
which reflects the value of a single sum in the future. The factors decrease each time
period to reflect the time value of money; $1 received further into the future is worth less
than $1 received sooner.
12.14 Organizations expect to accept projects which contribute to organizational strategy and
for which the rate of return appropriately reflects the business risk. The following types
of boundary controls help to ensure that subordinates comply with top management’s
investment policies:
(1) Required rate of return: Each firm has a different risk appetite and boundaries such
as hurdle rates communicate these risk preferences to subordinates and constrain
them from investing in projects that exceed the firm’s risk appetite.
(2) Types of capital projects to consider: Each organization has an overarching strategy,
and a boundary control that restricts the types of projects to consider should reduce
the likelihood that investments will be made in projects that do not support planned
strategies.
(3) Maximum capital budget that can be spent without top management approval: To
facilitate timeliness of decision-making, especially in industries that compete on
cutting edge technology, subordinates are often given investment decision rights.
Placing a maximum amount on decision rights for capital expenditures can improve
organizational cash flow planning and reduce the likelihood that large investments
will fail to meet top management’s strategic plans.
12.15 When an NPV analysis includes taxes, the terminal value of any asset that is sold needs
to be adjusted for the effects of taxes on a loss or gain because the tax consequences will
affect cash flows during the year the sale is made. If an asset is sold at its tax basis, no
taxes will be paid.
© 2012 John Wiley and Sons Canada, Ltd. 29 Cost Management
MULTIPLE-CHOICE QUESTIONS
12.16 In analyzing capital budgeting decisions, a number of methods are commonly used.
Which of the following methods does not involve the discounting of cash flows?
a) Internal rate of return method
b) Net present value method
c) Real options method
d) Payback method
Ans: D
Use the following information to answer Question 12.17 to 12.20: Juno Manufacturing
Ltd. isconsidering replacing its existing equipment with an automated machine for
$133,950. Junoamortizes its capital assets using the straight-line amortization method.
Juno estimates that thenew machine will reduce production costs by $28,500 per year and
that it has a useful life of6 years.
12.17 What is the internal rate of return?
a) 6.84%
b) 7.46%
c) 7.66%
d) 8.14%
Ans: B Use excel or a financial calculator to solve this problem.
12.18 What is the payback period?
a) 1.27 years
b) 4.00 years
c) 4.70 years
d) 6.00 years
Ans: C ($133,950 / $28,500 = 4.7 years)
12.19 What is the net present value if the required rate of return is 8%?
a) $(2,194.50)
b) $0.00
c) $1,909.50
d) $37,050.00
Ans: A
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 30
12.20 What is the accounting rate of return?
a) 3.55%
b) 4.61%
c) 9.50%
d) 21.30%
Ans: B
© 2012 John Wiley and Sons Canada, Ltd. 31 Cost Management
EXERCISES
12.21 Time Value of Money
A. Using tables, the answer is ($8,000 x 0.5835) = $4,668.
Using Excel, the answer is $4,667.92.
B. Using the tables, the answer is ($125 x 1.7908) = $223.88.
Using Excel, the answer is $223.86.
C. Using tables, the answer is ($10,000 x 0.7473) = $7,473.
Using Excel, the answer is $7,472.58.
D. Using tables, the answer is ($1,000 x 0.5066) = $506.6
Using Excel, the answer is $506.63.
12.22 Capital Budgeting Process
The proper sequence is:4, 1, 5, 2, 3, and 6.
12.23 Payback in Months -- International Netherlands Group
Payback = $700,000/$2,900,000 = 0.24 years
0.24 years × 12 months per year = 2.88 months
12.24 NPV Calculations with Taxes - Overnight Laundry
Cash Flow Timeline:
Time 0 Years1-10 Year 10
Investment $(96,000)
Incremental cash flows:
Annual Savings $25,000
Taxes (5,128) (a)
Net cash flow $19,872
Terminal value $6,000
(a) The salvage value is ignored for income tax amortization, so the annual
amortization = $96,000/10 years = $9,600 per year
Taxes per year = ($25,000 - $9,600) * 33.3% = $5,128
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 32
NPV calculation:
NPV = $(96,000) + $19,872 (PVFA 18%, 10 years) + $6,000 (PVF 18%, 10 years)
= $(96,000) + ($19,872 x 4.4941) + ($6,000 x0.1911)
= $(96,000) + $89,307 + $1,147
= ($5,547)
Any tax affect of disposal value has been ignored in this question.
12.25 NPV and IRR Calculations - Axel Corporation
A. The net present value is $30,000 (5.0188) - 150,000 = $564.
B. The internal rate of return is a little higher than 15%.Using Excel, the actual rate is
15.098%.
12.26 NPV, IRR, ARR and Payback Methods - Amaro Clinic
A. The net present value is ($5,000 x 5.2161) - 20,000 = $6,080
B. The factor for the internal rate of return must be
20,000 = $5,000*Factor
Factor = 4.0
From the PVFA tables for 10 year, it would be just over 20% (PVFA = 4.192)
Using Excel’s IRR function, the rate is 21.4%
C. Assuming straight-line amortization, the earnings will be
$5,000 - $20,000/10 = $3,000
The accounting rate of return is $3,000/20,000 = 15%
D. The payback period is $20,000/$5,000 = 4 years
12.27 NPV, ARR and Payback Methods – Moosehead Community Centre
A sample spreadsheet showing the calculations for this problem is available on the Instructor’s
web site for the textbook (available at www.wiley.com/canada/eldenburg).
© 2012 John Wiley and Sons Canada, Ltd. 33 Cost Management
A.
NPV
Cash Discount PresentValue
Year Savings factor @12%
1 $5,200 0.893 4,643.08
2 4,800 0.797 3,826.56
3 4,400 0.712 3,131.92
4 3,600 0.636 2,287.80
5 3,200 0.567 1,815.68
6 2,800 0.507 1,418.48
7 2,200 0.452 995.06
8 1,800 0.404 727.02
PVof CashFlows 18,845.60
Less:Costof Investment (20,000.00)
NetPresentValue (1,154.40)
UsingExcel:PVof CashFlows 18,845.58
Less:Costof Investment (20,000.00)
NetPresentValue (1,154.42)
B.
ARR
Initial Investment 20,000
Life 8years
ExpectedReturn 12%
YearAmount
1 5,200 Averageannual savings
2 4,800 =28,000/ 8years 3,500
3 4,400
4 3,600 Annual amortization
5 3,200 =20,000/ 8years 2,500
6 2,800
7 2,200 Incremental income
8 1,800 =savings- amortization 1,000
Total 28,000
ARR Incremental Income/ Initial Investment
=1,000/ 20,000= 5.00%
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decision34
C.
PaybackPeriod
Balanceto
CashFlow berecovered
Investment 20,000
Year-1 5,200 14,800
2 4,800 10,000
3 4,400 5,600
4 3,600 2,000
5 3,200
6 2,800
7 2,200
8 1,800
Year5cashflowof $3,200will coverthebalanceof $2,000
Todeterminewhenduringyear5:
balance/ amountof year5cashflow
2,000/3,200= 0.6250 years
thisisequal to7.5months
Theinvestmentwill berecoveredin5.625yearsor5years7.5months
D. Based on the above analysis this snow plough would not be recommended. The net
present value is negative indicating that the cost savings are not sufficient enough to
cover the cost of the snow plough. The payback period is longer than 5 years which
exceeds their four-year cut-off for new project pay back periods. The accrual accounting
rate of return is only 5% which does not come close to their minimum expected return of
12%.
12.28 Present Value and Future Value Calculations - Crown Corporation
A. The PVFA for four payments discounted at 6% is 3.4651.Thus, the present value of the
note is $1,000 x 3.4651 = $3,465.With the down payment, the total is $4,465.
B. Because this is a single payment the factor is a present value single amount of 0.7350, so
the total is $4,000 x .7350 = $2,940.With the down payment it becomes a total present
value selling price of $3,940.
C. The selling price of the equipment is $5,000 no matter how the employee gets the cash
and what Crown does with the $5,000.The future value factor for three years hence is
1.2250, yielding:$5,000 x 1.225 = $6,125.
© 2012 John Wiley and Sons Canada, Ltd. 35 Cost Management
12.29 NPV, IRR, Payback Methods, and ARR – KTI Inc
A. Net Present Value:
($320,000
Initial Investment )
Working Capital 20,000
($300,000
)
Annual Cash Flows
Net Income 50,000
Add: Depreciation * 60,000
x3.790
Total Annual Cash flows 110,000 8 $416,988
Terminal Value
Residual Value 20,000
Requirement of Working Capital ($20,000) 0
Net Present Value $116,988
*Depreciation Expense = ($320,000 – $20,000) ÷ 5 = 60,000
B. IRR:
($300,000) + $110,000 X + 0 = 0
X = 2.7273
20% = 2.9906
X% = 2.7273
25% = 2.6893
X = (2.9906 – 2.7273) ÷ (2.9906 – 2.6893) = 0.8739
0.8739 x 5% = 4.3694% X = 24.3694%
IRR as per Excel = 24.319%
C. Payback Period
Annual Cash Flows:
$50,000 + $60,000 = $110,000
$320,000 ÷ $110,000 = 2.73 years
D. Accrual Accounting Rate of Return:
$50,000 ÷ $300,000 = 16.67%
E. Yes, KTI should invest in the project, because NPV is greater than 0, IRR = 24%, and
ARR = 16.67% are greater than the required rate of return,10%. Although the
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 36
acceptable cut off period is greater than the company’s benchmark, it is close to the
required payback period. Based on the quantitative analysis, the project will bring
financial benefit to KTI.
12.30 NPV Analysis with Taxes and CCA (Appendix 12A)
Year0 Year1 Year2 Year3 Year4 Year5 Year6 Year7
Costofnewmachine (1,200,000)
Installationcosts (130,000)
Totalcostofnewmachine (1,330,000)
Saleofoldmachine 75,000
NetInvestment (1,255,000)
AnnualSavings 130,000 140,000 150,000 175,000 180,000 185,000 195,000
Costsavings 45,000
Maintenancefees (40,000)
Salvageofnewmachine 120,000
Salvagelostonoldmachine (30,000)
Totalannual savings 130,000 140,000 195,000 175,000 140,000 185,000 285,000
Depreciationoncostofnewmachine 15% (199,500) (199,500) (199,500) (199,500) (199,500) (199,500) (199,500)
Totaltaxableincome (69,500) (59,500) (4,500) (24,500) (59,500) (14,500) 85,500
Incometaxes 35% (24,325) (20,825) (1,575) (8,575) (20,825) (5,075) 29,925
Totalannual savingsnetoftaxes (1,255,000)154,325 160,825 196,575 183,575 160,825 190,075 255,075
Discountrate;factor 12% 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523
Presentvalueofcashflows 825,505 137,797 128,210 139,922 116,662 91,252 96,292 115,370
Netpresentvalue (429,495)
NPVasperExcel (429,480)
The company should not buy the new machine because the NPV is negative.
12.31 Relevant Cash Flows, NPV Analysis with Taxes and CCA (Appendix 12A) –
Karisma Ltd.
A sample spreadsheet showing the calculations for this problem is available on the Instructor’s
web site for the textbook (available at www.wiley.com/canada/eldenburg).
A.
Assumptions:
Initial Investment 60,000 Annual Savings
Life 5 Materials 14,000
Lab
Terminal Value - our 6,000
After-tax Rate of Return 7%
Real Interest Rate 10% CCA Rate 20%
Income Tax Rate 30%
Annual Cost Savings
Schedule
© 2012 John Wiley and Sons Canada, Ltd. 37 Cost Management
Year 1 2 3 4 5
20,
0
0
Annual Cost Savings 20,000 20,000 20,000 0 20,000
6,00
Less Income Taxes 6,000 6,000 6,000 0 6,000
Total 14,000 14,000 14,000 14,000 14,000
Calculation of Amortization Tax
Shield
CCA Rate 20% declining
balance
st
½ year on 1 year
10,80
CCA Deduction 6,000 0 8,640 6,912 5,530
Tax Savings (tax shield) 1,800 3,240 2,592 2,074 1,659
Summary of Cost Savings
14,
0
0
Incremental Cost Savings 14,000 14,000 14,000 0 14,000
2,
0
7
Tax Savings 1,800 3,240 2,592 4 1,659
16,
0
7
Total 15,800 17,240 16,592 4 15,659
Present Value of Cost
Savings 61,779
Less Initial Investment (60,000)
Net Present Value 1,779
B. Profitability Index = Present Value of Cash Inflows
Present Value of Investment cash outflows
= 61,779= 1.0297
60,000
C.
Summary of Cost
Savings
Incremental Cost 14,000 14,000 14,000 14,000
Savings 1
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Deci38ons
4
,
0
0
0
3,2
4
Tax Savings 1,800 0 2,592 2,074 1,659
Total 15,800 17,240 16,592 16,074 15,659
Initial Investment
Cost
Savin
gs Cumulative Balance to Recover
15,80
0
15,800 44,200
33,04
0
17,240 26,960
49,63
2
16,592 10,368
65,70
6
16,074
15,659
The investment will be fully recovered in year 4. To determine when, divide the balance after
year 3 by the total to be recovered in year 4.
10,368/16,074 = 0.645 years
.645 years = 7.74 months
The payback period is 3.645 years or 3 years 7.7 months
D. Based on the above analysis the new machine should be purchased. The net present value
is positive indicating that the cost savings are sufficient enough to cover the cost of the
machine. The profitability index is greater than one, although this would be more
beneficial if they were ranking various projects. The payback period is less than the four-
year cut-off required for new project pay back periods.
© 2012 John Wiley and Sons Canada, Ltd. 39 Cost Management
12.32 Relevant Cash Flows, NPV Analysis with Taxes and Inflation (Appendix 12A)
-Clearwater Bottling Company
A sample spreadsheet showing the calculations for this problem is available on the Instructor’s
web site for the textbook (available at www.wiley.com/canada/eldenburg).
A.
Cash Flow Timeline:
Time 0 Years1-5 Year 10
Investment $(100,000)
Incremental cash flows:
Annual Savings $20,000 (a)
Taxes (0) (b)
Net cash flow $20,000
Terminal value $0
(a) Savings = Additional contribution margin – Increase in fixed costs
= ($9 - $7) x 20,000 cases - $20,000 = $20,000
(b) Amortization = $100,000/5 years = $20,000 per year
Incremental Taxes = (Savings – Amortization) * 25%
= ($20,000 - $20,000) * 25% = $0
B. The NPV for this part can easily be calculated manually as shown below. The sample
spreadsheet shows the NPV to be $(27,904). The difference is due to rounding.
NPV = $(100,000) + $20,000 (PVFA 12%, 5 years)
NPV = $(100,000) + $20,000 x 3.605
NPV = $(27,900)
C. To determine the amount of sales needed to bring the NPV to zero, first re-write the
incremental cash flows substituting Q for the volume of cases sold.
Cash Flow Timeline:
Time 0 Years1-5 Year 10
Investment $(100,000)
Incremental cash flows:
Annual contribution margin $2Q (a)
Incremental fixed costs (20,000)
Incremental taxes ($0.5Q - $5,000) (b)
Net cash flow $1.5Q - $15,000
Terminal value $0
(a) Annual contribution margin per case (Q) = ($9 - $7)Q = $2Q
(b) Amortization = $100,000/5 years = $20,000 per year
Incremental Taxes = ($2Q – $20,000) * 25%
= $0.5Q - $5,000
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 40
Next, set the NPV equal to zero and solve for Q:
0 = $(100,000) + ($1.5Q - $15,000) x 3.6048
0 = $(100,000) + 5.4072Q - $54,072
5.4072Q = $154,072
Q = 28,494 cases
12.33 NPV Analysis - Parish County
This problem is most easily solved in steps. First determine the present value of the
terminal cash flow:
Terminal value = $400,000 x 20% = $80,000
Present value = $80,000 x (PVF, 10%, 5 years) = $80,000 x 0.6209 = $49,672
Subtract the present value of the terminal value from the investment to determine the
present value needed from annual savings to justify the purchase:
Minimum PV of annual savings = $400,000 - $49,672 = $350,328
Finally, determine the annual savings needed to achieve the present value calculated
above.The following calculation assumes that the annual savings would be identical
during each of the 5 years.
Savings x (PVFA, 10%, 5 years) = $350,328
Savings x 3.7908 = $350,328
Savings = $350,328/3.791 = $92,415
The company must generate at least $92,415 per year in savings to justify purchasing the
plane.
© 2012 John Wiley and Sons Canada, Ltd. 41 Cost Management
12.34 NPV and Payback with Taxes - Equipment Investment
A.
Time 0 investment = -$60,000
Years 1-6: Year
1 2 3 4 5 6
Annual saving after-tax $18,000 $18,000 $18,000 $18,000 $18,000 $18,000
Amortization tax savings 4,000 4,000 4,000 4,000 4,000 4,000
Total annual after-tax flows$22,000 $22,000 $22,000 $22,000 $22,000 $22,000
Calculation details:
Annual after-tax savings = $30,000 * (1-0.40) = $18,000
Straight-line amortization = $60,000/6 years = $10,000 per year
Amortization tax savings per year = $10,000 * 0.40 = $4,000
B. NPV calculation:
NPV = -$60,000 + $22,000 x (PVFA 10% 6 years)
NPV = -$60,000 + $22,000 x 4.3553 = $35,817
C. To determine the payback period, first summarize the cumulative cash flows from the
project:
Year Cumulative Cash Inflows
1 22,000
2 44,000
3 66,000
The original investment is $60,000, which is expected to be paid back between 2 and 3
years. If the cash flows are assumed to occur evenly throughout each year, the payback
period is 2.73 years [(2 + (60,000 - 44,000)/22,000)]. Because cash flows are identical
across years, the payback can also be calculated as follows: $60,000/$22,000 = 2.73
years.
12.35 IRR - Ferris Industries
A sample spreadsheet showing the calculations for this problem is available on the Instructor’s
web site for the textbook (available at www.wiley.com/canada/eldenburg).
A. Internal rates of return were calculated using the Excel function IRR. The rates of return
are
Project IRR
1 15.67%
2 27.32%
3 26.59%
4 28.14%
Based solely on the internal rate of return, the projects would be ranked 4, 2, 3, and 1.
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 42
B. There appear to be considerable differences in risk among the projects. Projects 2 and 3
expect negative incremental operating cash flows during some of the years, and project 4
expects zero incremental operating cash flows during 2 of the 6 years. Projects 2, 3, and
4 show more variation across years than project 1. If there is a high rate of technological
change in this industry, management may prefer project 2, which pays back most of the
investment quickly.
12.36 Alternative Technologies and Capital Budgeting with Taxes - Lymbo Company, Inc.
A. Based on the NPV of the two alternatives, the company should choose Alternative 2 with
a less negative NPV than Alternative 1. Calculations for each alternative are shown
below.
Cash Flow Timeline for Alternative 1:
Time 0 Years 1-5 Years 6-15
Investment $(100,000)
Incremental cash flows:
Maintenance Cost $(20,000) $(20,000)
Taxes 12,000 (a) 6,000 (b)
Net cash flow $ (8,000) $(14,000)
(a) Amortization = $100,000/5 years = $20,000 per year
Incremental taxes deductions during years 1-5 = (Maintenance cost +
Amortization) * 30%
= ($20,000 + $20,000) * 30% = $12,000
(b) Incremental taxes deductions during years 6-15 = Maintenance cost * 30%
= $20,000 * 30% = $6,000
NPV Calculation for Alternative 1:
NPV = $(100,000) + [$(8,000) x (PVFA 12%, 5 years)] + [$(14,000) x (PVFA
12% 15 years – PVFA 12% 5 years)]
NPV = $(100,000) + [$(8,000) x 3.6048] + [$(14,000) x (6.8109 – 3.6048)]
NPV = $(100,000) + $(28,838) + $(44,886) = $(173,724)
Following is a different way to perform the same calculations for Alternative 1:
NPV of installation cost $(100,000)
NPV of annual maintenance cost
$(20,000) x (1-30%) x 6.8109 (95,353)
NPV of amortization tax shield
$20,000 x 30% x 3.6048 21,629
Total NPV $(173,724)
© 2012 John Wiley and Sons Canada, Ltd. 43 Cost Management
Cash Flow Timeline for Alternative 2:
Time 0 Years 1-5 Years 6-15
Investment $(150,000)
Incremental cash flows:
Maintenance Cost $(10,000) $(10,000)
Taxes 12,000 (a) 3,000 (b)
Net cash flow $ 2,000 $ (7,000)
(a) Amortization = $150,000/5 years = $30,000 per year
Incremental taxes deductions during years 1-5 = (Maintenance cost +
Amortization) * 30%
= ($10,000 + $30,000) * 30% = $12,000
(b) Incremental taxes deductions during years 6-15 = Maintenance cost * 30%
= $10,000 * 30% = $3,000
NPV Calculation for Alternative 2:
NPV = $(150,000) +[$2,000 x (PVFA 12%, 5 years)] + [$(7,000) x (PVFA 12%
15 years – PVFA 12% 5 years)]
NPV = $(150,000) + [$2,000 x 3.6048] + [$(7,000) x (6.8109 – 3.605)]
NPV = $(150,000) + $7,210 + $(22,443) = $(165,233)
Following is a different way to perform the same calculations for Alternative 2:
NPV of installation cost $(150,000)
NPV of annual maintenance cost
$(10,000) x (1-30%) x 6.8109 (47,676)
NPV of amortization tax shield
$30,000 x 30% x 3.6048 32,443
Total NPV $(165,233)
B. Following are the NPV calculations without the amortization tax shield:
NPV without income taxes for Alternative 1:
NPV of installation cost $(100,000)
NPV of annual maintenance cost
$(20,000) x 6.8109 (136,218)
Total NPV $(236,218)
NPV without income taxes for Alternative 2:
NPV of installation cost $(150,000)
NPV of annual maintenance cost
$(10,000) x 6.8109 (68,109)
Total NPV $(218,109)
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 44
The answer depends on management's time-frame used in the budget process. If the not-
for-profit organization intends to occupy the building for the next 15 years, alternative 2
is still the best choice. However, management may concern itself only with current year
outlays (a focus of many governmental units). In that case, alternative 1 might be chosen
because its initial cost is $100,000 less than alternative 2's. Although this is a common
approach, one might question whether it is "proper."
12.37 Equipment Replacement, NPV, IRR, and Payback - Garco
A.
Present Value Present
Factor Value
Initial net investment (1,000,000 - 60,000) 1.00 $ (940,000)
Annual savings 300,000 3.6048 1,081,440
Net present value $ 141,440
B. First calculate the present value factor for an annuity of 5 payments that equates the cash
inflows and outflows:
$300,000 * F = 940,000
F = 3.13333
A factor of 3.13333 represents an internal rate of return of slightly less than 18%.
A spreadsheet could be used to determine the exact answer of 17.913%.
C. Assuming the cash flows take place evenly throughout the year:
$940,000/$300,000 = 3.13 years
© 2012 John Wiley and Sons Canada, Ltd. 45 Cost Management
PROBLEMS
12.38 Capital Budgeting Methods, Sensitivity Analysis, Spreadsheet Development,
Uncertainties - Jackson
A. The choices are (1) hold the stock and work for $90,000 per year or (2) sell the stock, do
not take the job, and start the restaurant.
B. Either IRR or NPV methods could be used for this analysis. The decision is a long-term
decision and therefore needs to include the time value of money. Both of these methods
do that. With the NPV method, inflation rates for different categories of costs could be
used, so the results would be more precise. In addition, it may be easier to understand the
differences in these two plans in today’s dollars, rather than in rates of returns.
C. His opportunity costs are $90,000 plus benefits from the job offer, plus the return on the
stock.
D. The following categories would be set into an input box: Investment amount, risk free
rate, risk premium for the restaurant, risk premium for the stock, inflation rate, tax rates,
all of the cash flows from the restaurant (revenues and variable and fixed costs). Once
these are in the input box, formulas for calculating the incremental cash flows over time
need to be set up, and the real cash flows would need to be inflated and then discounted.
If amortization is relevant for the investment, a calculation would need to be included to
account for the amortization tax shield using the appropriate CCA rate.
E. Uncertainties about a new job include lack of information about the people Jackson
would work with, and also about the nature of the work to be done. The future of the
company is not guaranteed. Students may have thought of other uncertainties.
F. Jackson faces uncertainties about customer preferences, which will result in uncertainty
about revenues. He has not operated a restaurant, so he faces uncertainties about current
costs and cost trends over time. He also faces uncertainties about the quality and quantity
of employees available to cook, wait tables, and perform other tasks that need to be done.
G. Jackson faces many uncertainties, no matter which alternative he chooses. If he performs
sensitivity analyses around each alternative and formally incorporates qualitative factors,
such as the amount of enjoyment he takes in his current position and his perceptions of
this aspect of owning a restaurant, he will be able to make a high quality decision.
© 2012 John Wiley and Sons Canada, Ltd. Chapter 12: Strategic Investment Decisions 46
12.39 NPV, Payback Methods, and ARR – TubeFab Inc.
A. Net Present Value:
PV
Initial Investment: ($60,000)+($5,000)+$20,500 = $(44,500)
Old New Incremental
Annual Cash Flows: Machine Machine Inflow Factor
Direct labour 13,500 7,900 5,600
Machinery costs
3,000 3,400 (400)
Cleaning & setup 2,500 1,200 1,300 PVIFA (10,8%)
Outflows 19,000 12,500 6,500 6.7101 43,616
PVIF (10, 8%)
Terminal Value inflow 2000 4000 2000 0.4632 926
Working capital inflow 5,000 0.4632 2,316
NPV $2,358
B. Point of Indifference:
(44,500) + 6.7101X + 926+2,316 = 0
6.7101X = 44,500-926-2,316
6.7101X = 41,258
X= $6,148.64 annual cost savings
C. Payback Period:
$44,500 / 6,500=6.85 year
D. AARR:
Amortization difference = 4,000 – 5,600 = - $1,600
(6,500-1,600) / 44,500 =11%
E.
Quantitative:
1. NPV >0 (go)
2. Payback Period > Cutoff period (no go).
3. Accounting Rate of Return > RRR (go)
Qualitative:
The management should consider if there is any impact on morale due to the layoff of
personnel. Also, the quality of the product, efficiency of the production, and the lesser need
for rework should also be considered.
Yes, TubeFab Inc. should proceed with this investment:.
© 2012 John Wiley and Sons Canada, Ltd. 47 Cost Management
12.40 IRR, Developing a Discount Rate, Evaluating Risk - Homeless Shelter
A. Advantages of IRR
• It is easy to explain
• It can be calculated using a spreadsheet
Disadvantages
• Without spreadsheets, it is time consuming to calculate
• It does not take into consideration the relative size of projects
• It does not give information about the dollar value of the
investment.
B. The discount rate should be different for every project because the risk of every project is
different. Part of the discount rate is the risk premium, and that should be higher for
projects that are riskier.
C. For discount rates, the following information would be helpful: current and historical
inflation rates and T-bill rates. In addition, historical financial information about the
three alternative projects or similar projects would be important to develop the risk
premium. Information about demand for rooms, apartments, and boxes would be needed.
Information about the availability of management and employees for the three
alternatives would be useful.
D. The answer to this question depends in part upon the assumptions made about the current
operations of the homeless shelter. If the shelter’s current op

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