21-1
Difference in after-tax cash flow from terminal disposal of machines:
$23,020 – $14,720 = $8,300 (in favor of new machine)
2. The Frooty Company should retain the old equipment because the net present value of the
incremental cash flows from the new machine is negative. The computations, using the results of
requirement 1, are presented below. In this format, the present value factors appear at the bottom.
All cash flows, year by year, are then converted into present values.
After-Tax Cash Flows
2013a
2014
2015
2016
2017
2018
Initial machine investment
$(190,000)
Current disposal price of old machine
68,000
Tax savings from loss on disposal of
old machine
11,305
Recurring after-tax cash-operating savings
Variable
$18,810
$18,810
$18,810
$18,810
$18,810
Fixed
660
660
660
660
660
Income tax cash savings from difference in
depreciation deductions
5,695
5,695
5,695
5,695
5,695
Additional after-tax cash flow from
terminal disposal of new machine
over old machine
_________
_______
_______
_______
_______
_ 8,300
Net after-tax cash flows
$(110,695)
$25,165
$25,165
$25,165
$25,165
$33,465
Present value discount factors (at 12%)
_ 1.000
0.893
0.797
0.712
0.636
0.567
Present value
$(110,695)
$22,472
$20,057
$17,917
$16,005
$18,975
Net present value
$ (15,269)
a More precisely, January 1, 2014
3. Let $X be the additional recurring after-tax cash operating savings required each year to
make NPV = $0.
The present value of an annuity of $1 per year for 5 years discounted at 12% = 3.605.
To make NPV = 0, Frooty needs to generate cash savings with NPV of $15,269.
That is $X × (3.605) = $15,269
X = $15,269 ÷ 3.605 = $4,235.51
Frooty must generate additional annual after-tax cash operating savings of $4,235.51.
21-35 (35 min.) Recognizing cash flows for capital investment projects.
Johnny Buster owns Entertainment World, a place that combines fast food, innovative beverages,
and arcade games. Worried about the shifting tastes of younger audiences, Johnny contemplates
bringing in new simulators and virtual reality games to maintain customer interest.
As part of this overhaul, Johnny is also looking at replacing his old Guitar Hero equipment with
a Rock Band Pro machine. The Guitar Hero setup was purchased for $25,200 and has accumulated
depreciation of $23,000, with a current trade-in value of $2,700. It currently costs Johnny $600
per month in utilities and another $5,000 a year in maintenance to run the Guitar Hero equipment.
Johnny feels that the equipment could be kept in service for another 11 years, after which it would
have no salvage value.
21-2
The Rock Band Pro machine is more energy-efficient and durable. It would reduce the utilities
costs by 30% and cut the maintenance cost in half. The Rock Band Pro costs $49,000 and has an
expected disposal value of $5,000 at the end of its useful life of 11 years.
Johnny charges an entrance fee of $5 per hour for customers to play an unlimited number of
games. He does not believe that replacing Guitar Hero with Rock Band Pro will have an impact
on this charge or materially change the number of customers who will visit Entertainment World.
Required:
1. Johnny wants to evaluate the Rock Band Pro project using capital budgeting techniques. To
help him, read through the problem and separate the cash flows into four groups: (1) net initial
investment cash flows, (2) cash flow savings from operations, (3) cash flows from terminal
disposal of investment, and (4) cash flows not relevant to the capital budgeting problem.
2. Assuming a tax rate of 40%, a required rate of return of 8%, and straight-line depreciation over
the remaining useful life of equipment, should Johnny purchase Rock Band Pro?
SOLUTION
1. Partitioning relevant cash flows into categories:
(1) Net initial investment cash flows
— The $49,000 cost of the new Rock Band Pro
—The disposal value of Guitar Hero, $2,700, is a cash inflow.
—The book value of Guitar Hero $2,200 ($25,200 − $23,000), relative to the
disposal value of $2,700, yields a taxable gain of $500 ($2,700 − $2,200) that
leads to a cash outflow for taxes of $500 Tax Rate.
(2) Cash flow savings from operations
–—The 30% savings in utilities cost per year of $2,160 (30% × $600 per month ×
12 months) results in cash inflow from operations after tax of $2,160 (1 − Tax
Rate).
–—The savings of half the maintenance costs per year of $2,500 (50% × $5,000)
results in a cash inflow from operations after tax of $2,500 (1 − Tax Rate).
—Annual depreciation of ($49,000 − $5,000) ÷ 11 years = $4,000 on Rock Band
Pro, relative to the ($2,200 − $0) ÷ 11 years = $200 depreciation on current Guitar
Hero leads to additional tax savings of $3,800 × Tax Rate.
(3) Cash flows from terminal disposal of investment
—The $5,000 salvage value of Rock Band Pro minus the $0 salvage value of the
old Guitar Hero equipment is a terminal cash flow at the end of Year 11. There
are no tax effects because both systems are planned to be disposed of at book
value.
21-3
(4) Data not relevant to the capital budgeting decision
—The $5 per hour charge for customers, since it would not change whether or not
Johnny got the new machine
—The $25,200 original cost of the Guitar Hero setup
21-4
2. Net present value of the investment:
Net initial investment
Initial investment in Rock Band Pro
$(49,000)
Current disposal value of Guitar Hero
2,700
Tax on gain on sale of Guitar Hero, 40% × $500
(200)
Net initial investment
$(46,500)
Annual after-tax cash flow from operations (excl. deprn. effects)
After-tax savings in utilities costs, $2,160 × (1−0.40)
$ 1,296
After-tax savings in maintenance costs, $2,500 × (1−0.40)
1,500
Annual after-tax cash flow from operations
$ 2,796
Income-tax cash savings from annual additional depreciation
deductions ($4,000 − $200) × 40%
$ 1,520
After-tax cash flow from terminal disposal of machines
$ 5,000
These four amounts can be combined to determine the NPV at an 8% discount rate.
Present value of net initial investment, $(46,500) × 1.000
$(46,500)
Present value of 11-year annuity of annual after-tax cash flow
from operations (excl. deprcn. effects), $2,796 × 7.139
19,961
Present value of 11-year annuity of income-tax cash savings from
annual depreciation deductions, $1,520 × 7.139
10,851
Present value of after-tax cash flow from terminal disposal of
machines, $5,000 × 0.429
2,145
Net present value
$(13,543)
At the required rate of return of 8%, the net present value of the investment in the Rock Band Pro
machine is substantially negative. Johnny should therefore not make the investment.
21-36 (25 min.) NPV, inflation and taxes.
Cheap-O Foods is considering replacing all 10 of its old cash registers with new ones. The old
registers are fully depreciated and have no disposal value. The new registers cost $899,640 (in
total). Because the new registers are more efficient than the old registers, Cheap-O will have annual
incremental cash savings from using the new registers in the amount of $192,000 per year. The
registers have a 7-year useful life and no terminal disposal value and are depreciated using the
straight-line method. Cheap-O requires an 8% real rate of return.
Required:
1. Given the preceding information, what is the net present value of the project? Ignore taxes.
2. Assume the $192,000 cost savings are in current real dollars and the inflation rate is 5.5%.
Recalculate the NPV of the project.
3. Based on your answers to requirements 1 and 2, should Cheap-O buy the new cash registers?
4. Now assume that the company’s tax rate is 30%. Calculate the NPV of the project assuming
no inflation.
5. Again assuming that the company faces a 30% tax rate, calculate the NPV of the project under
an inflation rate of 5.5%.
6. Based on your answers to requirements 4 and 5, should Cheap-O buy the new cash registers?
SOLUTION
1. Without inflation or taxes, this is a simple net present value problem using an 8%
discount rate
Present value of initial investment, $(899,640) × 1.000
$(899,640)
Present value of 7-year annuity of annual cash savings:
$192,000 × 5.206
999,552
Net present value
$ 99,912
2. With inflation, we adjust each year’s cash flow for the inflation rate to get nominal cash
flows and then discount each cash flow separately using the nominal discount rate.
Nominal rate = (1 + real rate) × (1 + inflation rate) − 1
Nominal rate = (1.08) × (1.055) − 1 = 1.1394 – 1 = 0.1394 or 14% (approx.)
Cash Flow
Cumulative
Cash Inflows
Present Value
Period
(Real Dollars)
Inflation Rate
(Nominal Dollars)
Factor, 14%
Present Value
(1)
(2)
(3) = (1) × (2)
(4)
(5) = (3) × (4)
1
$192,000
1.055
$202,560
0.877
$177,645
2
192,000
1.1131
213,696
0.769
164,332
3
192,000
1.174
225,408
0.675
152,150
4
192,000
1.239
237,888
0.592
140,830
5
192,000
1.307
250,944
0.519
130,240
6
192,000
1.379
264,768
0.456
120,734
7
192,000
1.455
279,360
0.400
111,744
Total present value of annual net cash inflows in nominal dollars
997,675
Present value of initial investment, $(899,640) × 1.000
(899,640)
Net present value
$ 98,035
11.113 = (1.055)2
3. Both the unadjusted and adjusted NPV are positive. Based on financial considerations
alone, Cheap-O Foods should buy the new cash registers. However, the effect of taxes should
also be considered, as well as any pertinent nonfinancial issues, such as potential improvements
in customer response time from moving to the new cash registers.
4.
Initial equipment investment
$(899,640)
Annual cash flow from operations (excl. deprn. effects)
$192,000
Deduct income tax payments (0.30 × $192,000)
57,600
Annual after-tax cash flow from operations (excl. deprn. effects)
$ 134,400
Income tax cash savings from annual depreciation deductions
(0.30 × $128,520)1
$ 38,556
1 Depreciation deductions = ($899,640 – $0) / 7 = $128,520
The terminal disposal price of the equipment is equal to the book value at disposal = $0, so the
above three amounts suffice to determine the NPV at a 8% discount rate.
Present value of net initial investment, $(899,640) × 1.000
$(899,640)
Present value of 7-year annuity annual after-tax cash flow from operations,
$134,400 × 5.206
699,686
Present value of 7-year annuity of income tax cash savings from
annual depreciation deductions, $38,556 × 5.206
200,723
Net present value
$ 769
5. As in the previous section, with inflation, we adjust each year’s cash flow for the
inflation rate to get nominal cash flows and then discount each cash flow separately using the
nominal discount rate.
Nominal rate = (1 + real rate) × (1 + inflation rate) −1
Nominal rate = (1.08)(1.055) −1 = 1.1394 – 1 = .1394 or 14% (approx.)
Cash Flow
Cumulative
Cash Inflows
After Tax
Cash
Present Value
Period
(Real Dollars)
Inflation Rate
(Nominal Dollars)
Flows
Factor, 14%
Present Value
(1)
(2)
(3) = (1) × (2)
(4) = 0.7 × (3)
(5)
(6) = (4) × (5)
21-7
1
$192,000
1.055
$202,560
$141,792
0.877
$124,352
2
192,000
1.113
213,696
149,587
0.769
115,033
3
192,000
1.174
225,408
157,786
0.675
106,505
4
192,000
1.239
237,888
166,522
0.592
98,581
5
192,000
1.307
250,944
175,661
0.519
91,168
6
192,000
1.379
264,768
185,338
0.456
84,514
7
192,000
1.455
279,360
195,552
0.400
78,221
Total present value of annual net cash inflows (excl. depreciation. effects)
$698,374
Present value of 7-year annuity of income-tax cash savings from
annual depreciation deductions, $38,556 × 5.206
200,723
Present value of initial investment $(899,640) × 1.000
(899,640)
Net present value
$ (543)
6. Without inflation, we obtain a positive NPV; however, with inflation NPV is negative,
and Cheap-O Foods would be better off not purchasing the new registers. Negative NPV is
obtained with an inflation estimate of 5.5%. If a careful review of this forecasted inflation rate
results in a lower rate of inflation, Cheap-O Foods should recalculate the NPV to determine
whether the purchase of the registers is in its best interest.
21-37 (60 min.) NPV of information system, income taxes.
Saina Supplies leases and sells materials, tools, and equipment and also provides add-on services
such as ground maintenance and waterproofing to construction and mining sites. The company has
grown rapidly over the past few years. The owner, Saina Torrance, feels that for the company to
continue to scale, it needs to install a professional information system rather than relying on
intuition and Excel analyses. After some research, Saina’s CFO reports back with the following
data about a data warehousing and analytics system that she views as promising:
▪ The system will cost $750,000. For tax purposes, it can be depreciated straight-line to a zero
terminal value over a 5-year useful life. However, the CFO expects that the system will still
be worth $50,000 at that time.
▪ There is an additional $75,000 annual fee for software upgrades and technical support from
the vendor.
▪ The ability to provide better services and to target and reach more clients as a result of the
new system will directly result in a $500,000 increase in revenues for Saina in the first year
after installation. Revenues will grow by 5% each year thereafter. Saina’s contribution
margin is 60%.
▪ Due to greater efficiency in ordering and dispatching supplies, as well as in collecting
receivables, the firm’s working-capital requirements will decrease by $100,000.
▪ Saina will also be able to reduce the amount of warehouse space it currently leases, saving
$40,000 annually in the process.
▪ Saina Supplies pays an income tax of 30% and requires an after-tax rate of return of 12%.
Assume that all cash flows occur at year-end except for initial investment amounts.
21-8
Required:
1. If Saina decides to purchase and install the new information system, what is the expected
incremental after-tax cash flow from operations during each of the 5 years?
2. Compute the net present value of installing the information system at Saina Supplies.
3. In addition to the analysis in requirement 2, what nonfinancial factors you would consider in
making the decision about the information system?
SOLUTION
1. Initial investment (Year 0): $750000
Working-capital investment:
Reduced working capital of $100000 at end of Year 0.
Increased working capital of $100000 at end of Year 5.
Depreciation on initial investment: $750000 5 years = $150000 per year
Income tax cash savings from annual depreciation deductions: $150000 × 0.30 = $45000
After-tax cash flow from disposal of JIT system at end of Year 5: $50000 × (1– 0.30) = $35000
Annual after-tax cash flow from operations:
Year 1
Year 2
Year 3
Year 4
Year 5
Incremental revenues
(5% annual growth)
$500,000
$525,000
$551,250
$578,813
$607,753
Incremental contribution margin
(60%
incremental revenues)
$300,000
$315,000
$330,750
$347,288
$364,652
Rent savings
40,000
40,000
40,000
40,000
40,000
Deduct increase in software
upgrades and tech support costs
(75,000)
(75,000)
(75,000)
(75,000)
(75,000)
Annual pre-tax incremental
cash inflow from operations
265,000
280,000
295,750
312,288
329,652
Deduct income tax payments
(30%)
79,500
84,000
88,725
93,686
98,896
Annual after-tax incremental
cash inflow from operations
$185,500
$196,000
$207,025
$218,602
$230,756
2. Solution Exhibit 21-37 reports the net present value to be $214,506.
3. Saina will have a NPV of $214,506 with the new data warehousing and analytics system.
Based on financial quantitative factors, this is an attractive investment. Qualitative factors could
make the system even more attractive. For example, if a competitor adopts the new information
system but Saina does not, Saina could be at a sizable competitive disadvantage. Not adopting the
information system does not mean the status quo will remain. Saina’s workers can also gain
21-9
additional expertise when using the data warehousing and analytics system that can be beneficially
employed on other projects.
21-10
SOLUTION EXHIBIT 21-37
Total
Present
Value
Present
Value
Discount
Factors
at 12%
Sketch of Relevant After-Tax Cash Flows
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
1a. Net initial
investment
$(750000)
1.000
$(750000)
1b. Working
capital decrease
100,000
1.000
$100000
2a. Annual after-
tax cash flow
from operations
Year 1
165,652
0.893
$185,500
Year 2
156,212
0.797
$196000
Year 3
147,402
0.712
$207,025
Year 4
139,031
0.636
$218,602
Year 5
130,839
0.567
$230,756
2b. Income tax cash
savings from annual
depreciation charges
Year 1
40,185
0.893
$45000
Year 2
35,865
0.797
$45000
Year 3
32,040
0.712
$45000
Year 4
28,620
0.636
$45000
Year 5
25,515
0.567
$45000
3. After-tax cash flow from:
a. Terminal
disposal of
machine
19,845
0.567
$35000
b. Increase in
working capital
(56,700)
0.567
$(100000)
Net
present value
$214,506