Chapter 12 Capital Investment Decisions and the Time Value of Money
Chapter 12
Capital Investment Decisions and the Time Value of
Money
Quick Check
Answers:
Short Exercises
(10 min.) S12-1
1.
(f)
Identify potential capital investments
2.
(b)
Project investments’ cash flow
3.
(g)
Screen / analyze investments using one or more of the methods discussed
4.
(a)
Budget capital investments
5.
(d)
Make investments
6.
(c)
Perform post-audits
7.
(e)
Use feedback to reassess investments already made
(5 min.) S12-2
Payback period
=
=
$1,000,000
$371,500
=
If the investment had a $100,000 residual value, the payback period would not be affected. The cash inflow from any
Managerial Accounting 4e Solutions Manual
(5 min.) S12-3
Full years
+
=
Payback
2
+
($80,000
/
$330,000)
=
2.24 years
If the investment had a $100,000 residual value, the payback period would not be affected. The cash inflow from any
residual value would occur at the end of the asset’s useful operating life and is not taken into account when calculating
the payback period.
The payback period if the DVR project had a residual value of $100,000 is 2.24 years.
The payback period is less than 3.5 years, so it passes Arpegio’s initial screening.
(5-10 min.) S12-4
Accounting rate
of return
=
Average annual operating
income from asset
Initial Investment
=
Average annual
net cash
−
Annual depreciation
expense on asset
inflow from asset
Initial Investment
=
$371,500 − $200,000*
$1,000,000
=
$171,500
$1,000,000
=
17.15%
* Depreciation expense:
[$1,000,000 − $0] ÷ 5 = $200,000
Amount to complete recovery in next year
Projected net cash inflow in next year
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) S12-4
If the MP3 player project had a $100,000 residual value, the ARR would change. Specifically, the residual value would
cause the yearly depreciation expense to decrease, which will cause the average annual operating income from the
investment to increase.
Accounting rate
of return
=
Average annual operating income from
investment
Initial Investment
=
Average annual
net cash
−
Annual depreciation
expense on asset
inflow from asset
Initial Investment
=
$371,500 − $180,000*
$1,000,000
=
$191,500
$1,000,000
=
19.15%
* Depreciation expense:
[$1,000,000 − $100,000] ÷ 5 = $180,000
The ARR, in either case, exceeds Arpegio’s minimum required ARR. Therefore, the MP3 player project passes the
company’s screening rule in both cases.
(5-10 min.) S12-5
Accounting rate
of return
=
Average annual operating
income from investment
Initial Investment
=
Average annual
net cash
−
Annual depreciation
expense on asset
inflow from asset
Initial Investment
=
$309,000a − $200,000*
$1,000,000
=
$109,000
$1,000,000
=
10.90%
a Average net cash inflow =
$1,545,000 total net cash inflow ÷ 5 years = $309,000
* Depreciation expense: $1,000,000 ÷ 5 = $200,000
Managerial Accounting 4e Solutions Manual
(continued) S12-5
If the DVR project had a $100,000 residual value, the ARR would change. Specifically, the residual value would cause
the yearly depreciation expense to decrease, which will cause the average annual operating income from the
investment to increase.
Accounting rate
of return
=
Average annual operating
income from investment
Initial Investment
=
Average annual
net cash
−
Annual depreciation
expense on asset
inflow from asset
Initial Investment
=
$309,000 − $180,000*
$1,000,000
=
$129,000
$1,000,000
=
12.9%
* Depreciation expense:
[$1,000,000 − $100,000] ÷ 5 = $180,000
The ARR, in either case, exceeds Arpegio’s minimum required ARR. Therefore, the DVR project passes the company’s
screening rule in both cases.
(5-10 min.) S12-6
Payback period
=
Initial Investment
Expected annual net cash inflow
Expected annual net cash inflow
=
Initial Investment
Payback period
=
$8,000,000
4 years
=
$ 2,000,000
Chapter 12 Capital Investment Decisions and the Time Value of Money
(10-15 min.) S12-7
Note: This is the 1st example of several problems that will have 2nd answers using a programmed calculator.
Using an 8% interest rate, the present values are:
Scenario #1
Present value
=
$ 8,550 × (Annuity PV factor, i = 8%, n = 8)
=
$ 8,550 x 5.747
=
$49,137 (rounded)
Scenario #2
Present value
=
$50,250 (since it would be received now)
Scenario #3
Present value
=
$99,350 × (PV factor, i = 8%, n = 8)
=
$99,350 x 0.540
=
$ 53,649 (rounded)
Scenario #1
Present value
=
$ 8,550 × (Annuity PV factor, i = 12%, n = 8)
=
$ 8,550 x 4.968
=
$42,476 (rounded)
Scenario #2
Present value
=
$50,250
Scenario #3
Present value
=
$99,350 × (PV factor, i = 12%, n = 8)
=
$99,350 × 0.404
=
$ 40,137 (rounded)
Chapter 12 Capital Investment Decisions and the Time Value of Money
(10-15 min.) S12-9
a.
Payment Options
Future Value of Lottery Payout
(Principal amount × FV factor
i = 6%, n = 9)
Option #1
$975,000 now
$1,646,775
($975,000 × 1.689)
Option #2
$153,000 annually for 9 years
$1,758,123
($153,000 x 11.491)
Option #3
$1,550,000 9 years from now
$1,550,000
(already stated at its
future value)
b. Based on the future values, our preference among payout options is:
Option 2
– most preferable
Option 1
– next preferable
Option 3
– least preferable
Chapter 12 Capital Investment Decisions and the Time Value of Money
(5-10 min.) S12-12
We solve for the IRR by first finding the Annuity PV factor associated with the investment:
$650,000
=
Annuity PV factor (n = 9, i = ?)
$90,000
7.22
=
Annuity PV factor (n = 9, i = ?)
7.22 falls between 6% and 8% at a period of 9 years. Therefore, the IRR is between 6% and 8%.
(5-10 min.) S12-13
Year
Net Cash Inflow
PV factor
i =10%
Present Value
1
$12,000
0.909
$ 10,908
2
19,000
0.826
15,694
3
26,000
0.751
19,526
Present value of net cash inflows
$ 46,128
Less: Initial Investment
(46,000)
NPV
$ 128
Chapter 12 Capital Investment Decisions and the Time Value of Money
(5-10 min.) S12-17
1.
Julie does not include an estimate of maintenance costs
associated with a new computer system. She knows that
her department needs the computer system. If the
maintenance costs were included in the estimate, the
computer system purchase might not be approved.
Credibility – Disclose all relevant information that
could reasonably be expected to influence an
intended user’s understanding of the reports,
analyses, or recommendations.
2.
Geoffrey is a staff accountant. He has recently been
moved into a position where he will be working on capital
budgeting proposals. Geoffrey does not know how to
make an NPV calculation, but he does not take the steps
to acquire the skills. He figures he can just use ARR and
payback for investment analysis instead.
Competence – Maintain an appropriate level of
professional expertise by continually developing
knowledge and skills.
3.
Terrance’s company is in negotiations to purchase a
complex computer system from one of its suppliers.
Terrance, a management accountant, does not disclose
that his mother is a major stockholder of the supplier.
Integrity – Mitigate actual conflicts of interest,
regularly communicate with business associates t
avoid apparent conflicts of interest. Advise all
parties of any potential conflicts.
4.
Anthony is anxious to impress his date, Sonja. Sonja
works in Purchasing, while Anthony works in Accounting.
When they start talking about people they work with,
Anthony shares salary information about each person.
Confidentiality – Keep information confidential
except when disclosure is authorized or legally
required.
5.
Marcella accepts a kickback payment from a contractor to
make sure that the contactor’s bid is accepted.
Integrity – Refrain from engaging in any conduct
that would prejudice carrying out duties ethically
Copyright © 2015 Pearson Education, Inc.
12–12
(5-10 min.) E12-18A
Payback period
=
Initial Investment
Expected annual net cash inflow
=
$1,860,000
$310,000
=
6 years
Decision: The payback occurs well after the plant must be replaced, so the payback method does not support
purchasing the plant.
(5-10 min.) E12-19A
(10-15 min.) E12-20A
Accounting rate of return
=
Average annual
operating income from asset
Initial investment
=
$118,500
$1,450,000
=
8.17%
(10-15 min.) E12-21A
Accounting rate of return
=
Average annual
operating income from asset
Initial investment
Accounting rate of return on Rouse
=
$160,000
$1,000,000
Accounting rate of return on Rouse
=
16.00%
Accounting rate of return on Vargas
=
$249,750
$1,350,000
Accounting rate of return on Vargas
=
18.50%
Decision: Vargas offers the higher rate of return.
Chapter 12 Capital Investment Decisions and the Time Value of Money
(15-20 min.) E12-22A
Req. 1
Your “out–of–pocket” cost is $120,000 either way: ($4,800 × 25 years) vs. ($10,000 × 12 years).
Req. 2
Future Value
=
Annuity × (Annuity FV factor, i = 12%, n = 25)
=
$4,800 × (133.334)
=
$640,003 (rounded)
Future Value
=
Annuity × (Annuity FV factor, i = 12%, n = 12)
=
$10,000 × (24.133)
=
$241,330
Future Value
=
$640,003 × (FV factor, i = 12%, n = 9)
=
$640,003 × (2.773)
=
$1,774,728 (rounded)
Future Value
=
$241,330 × (FV factor, i = 12%, n = 9)
=
$241,330 × (2.773)
=
$669,208
(15-20 min.) E12-23A
Req. 1
Payback = 14.44 years ($650,000/45,000)
Req. 2
Chapter 12 Capital Investment Decisions and the Time Value of Money
(10-15 min.) E12-26A
Question #1:
Future value
=
$2,500 × (FV factor, i = 12%, n = 6)
=
$2,500 × 1.974
=
$4,935
Question #2:
Present value
=
$ 5,000 × (Annuity PV factor, i = 8%, n = 20)
=
$ 5,000 × 9.818
=
$49,090
Present value
=
$135,000 × (PV factor, i = 6%, n = 7)
=
$135,000 × 0.665
=
$89,775
Future value
=
$3,000 × (Annuity FV factor, i = 14%, n = 10)
=
$3,000 × 19.337
=
$58,011
Future value
=
$ annuity × (Annuity FV factor, i = 8%, n = 4)
$54,500
=
$ annuity × 4.506
$12,905
=
$ annuity
Managerial Accounting 4e Solutions Manual
(continued) E12-27A
Decision: Invest in Project A, but not in Project B.
(15 min.) E12-28A
(15-20 min.) E12-29A
1) The equipment’s net present value (NPV) is calculated as follows. Since each annual cash inflow is unique, we
cannot use the annuity table. We must discount each annual cash inflow using the PV Factors found in the Present
Value of $1 table:
Year
Net cash inflow
PV of $1 factor
(i =16%)
Present Value of Net
Cash inflow
Year 1 (n = 1)
$261,000
0.862
$224,982
Year 2 (n = 2)
$250,000
0.743
185,750
Year 3 (n = 3)
$228,000
0.641
146,148
Year 4 (n = 4)
$214,000
0.552
118,128
Year 5 (n = 5)
$203,000
0.476
96,628
Year 6 (n = 6)
$176,000
0.410
72,160
Present value of net cash inflows
$843,796
Less: Initial Investment
($925,000)
Net present value
($ 81,204)
Kerwin Industries should not invest in the equipment because its NPV is negative.
2) Kerwin must determine whether the equipment investment becomes favorable (positive NPV) if the equipment is
refurbished, used for one more year, and then sold. The following analysis needs to be added to the NPV
computations above:
Year
Cash (outflow) /
inflow
PV of $1 factor
(i = 16%)
Present Value
Refurbishment at the end of Year 6 (n = 6)
($106,000)
0.410
($43,460)
Cash inflows in Year 7 (n = 7)
$ 75,000
0.354
26,550
Residual value (n=7)
$ 53,000
0.354
18,762
Additional NPV provided from
refurbishment
$ 1,852
NPV from part 1
($81,204)
New NPV
($79,352)
The refurbishment provides a positive NPV. The refurbishment NPV ($79,352) is not large enough to overcome the
original negative NPV of the equipment ($81,352). Therefore, the refurbishment should not alter Kerwin Industries’
decision to turn down the equipment investment.
(15-20 min.) E12-30A
The NPV at 10% is $41,882.
Chapter 12 Capital Investment Decisions and the Time Value of Money
(15 min.) E12-33A
Req. 1
The initial payback period of 4.27 years will not change since the method does not consider any cash flows that occur
after the payback period. The residual value will not affect cash flows until the end of the asset’s life, so it was not