Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) P12-56A
(Req. 1 continued)
Managerial Accounting 4e Solutions Manual
(continued) P12-57A
Accounting
rate of return
=
Average annual operating income from asset
Initial investment
Average annual net
cash inflow from asset − Annual depreciation expense on asset
Initial investment
Plan A
=
$1,600,000 − $937,778a
$8,440,000
=
$662,222
$8,440,000
=
7.8%
Plan B
=
$1,250,000 − $793,333b
$8,240,000
=
$456,667
$8,240,000
=
5.5%
__________
a Annual depreciation = $8,440,000 / 9 = $937,778
b Annual depreciation = ($8,240,000 − $1,100,000) / 9 = $793,333
PV factor at
i = 10%, n = 9
Net Cash Inflow
Total Present Value
Plan A:
Present value of annuity of
equal annual net cash
inflows for 9 years at 10%
5.759 c × $1,600,000 per year
$ 9,214,400
Less: Initial Investment
(8,440,000)
Net present value of Plan A
$ 774,400
Plan B:
Present value of annuity of
equal annual net cash
inflows for 9 years at 10%
5.759c × $1,250,000 per year
$ 7,198,750
Present value of residual value (lump sum, not
annuity)
0.424 d × $1,100,000
466,400
Less: Initial investment
(8,240,000)
Net present value of Plan B
$ (574,850)
c Present Value of Annuity of $1 (n = 9, i = 10%)
d Present Value of $1 (n = 9, i = 10%)
Net present value is based on cash flows, can be used to assess profitability, and takes into account the time value of
money. It has none of the weaknesses of the other two models.
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) P12-57A
Payback method is easy to understand, is based on cash flows, and highlights risks. However, payback ignores
profitability and the time value of money.
Managerial Accounting 4e Solutions Manual
Problems (Group B)
(30-45 min.) P12-58B
Scenario #1:
Future value
=
$ 55,000 × (FV factor, i = 12%, n = 15)
=
$ 55,000 × 5.474
=
$301,070
Scenario #2:
Present value
=
$4,000,000 × (PV factor, i = 14%, n = 40)
=
$4,000,000 × 0.005
=
$ 20,000
Scenario #3:
Present value
=
Annuity × (Annuity PV factor, i = 8%, n = 20)
$2,000,000
=
Annuity × 9.818
$203,707
=
Annuity (rounded)
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) P12-58B
Scenario #4:
Future value
=
$ 4,500 × (Annuity FV factor, i = 10%, n = 7)
=
$ 4,500 × 9.487
=
$42,692 (rounded)
Scenario #5:
Present value
=
$9,000 × (Annuity PV factor, i = 10%, n = 9)
=
$9,000 × 5.759
=
$51,831
=
$302,000 × 0.926 =
=
$208,000 × 0.857 =
=
$98,000 × 0.794 =
Total Present value
Less: Initial Investment
Net Present Value (NPV)
=
$302,000 × 0.909 =
$ 274,518
=
$208,000 × 0.826 =
=
$98,000 × 0.751 =
Total Present value
Less: Initial investment
Net Present Value (NPV)
Managerial Accounting 4e Solutions Manual
(15-20 min.) P12-59B
Retirement planning involves two separate annuities:
1) the annual cash savings (from age 20 to age 40) and
2) the annual withdrawals (from age 40 to age 85).
To find the amount of annual savings needed, we perform a two– step process:
First, we discount the retirement withdrawals back to their present value (at age 40).
Second, we set that amount equal to the future value of the savings annuity.
Req. 1
Present Value
=
Annual cash withdrawals × (Annuity PV factor, i = 10=4%, n = 45)
=
$ 220,000 × (7.123)
=
$1,567,060
By age 40, you need to have accumulated a sum of $1,567,060.
Amount of annual cash savings × (91.023)
Amount of annual cash savings
AT AGE 40:
PV of future
retirement
withdrawals =
FV of the
annual savings
installments
Annual savings installments
Annual retirement
withdrawals
45 years
20 years
(20-30 min.) P12-60B
Req. 1
Payback
=
Initial Investment
period
Expected annual net cash inflow
=
$1,850,000
$495,000
=
3.7 years
Accounting
=
Average annual operating income from asset
rate of return
Initial investment
Average annual net
cash inflow from asset
−
Annual depreciation
expense on asset
Initial investment
=
$495,000 − $205,556a
$1,850,000
=
$289,444
$1,850,000
=
15.6% (rounded)
__________
aAnnual depreciation
=
$1,850,000
=
$205,556
9
Annuity PV factor at i
= 10%, n= 9
Net Cash Inflow
Total Present Value
Net present value:
Present value of annuity of
equal annual net cash
inflows for 9 years at 10%
5.759 $495,000 per year =
$ 2,850,705
Less: Initial Investment
(1,850,000)
Net present value
$ 1,000,705
Managerial Accounting 4e Solutions Manual
(30-45 min.) P12-61B
Req. 1
Payback period
=
Initial investment
Expected annual net cash inflow
Plan A
=
$8,740,000
$1,550,000
=
5.6 years
Plan B
=
$8,140,000
$1,050,000
=
7.8 years
Accounting
rate of return
=
Average annual operating income from asset
Initial investment
Average annual net
cash inflow from asset − Annual depreciation expense on asset
Initial investment
Plan A
=
$1,550,000 − $971,111
$8,740,000
=
$578,889
$8,740,000
=
6.6 %
Plan B
=
$1,050,000 − $785,000
$8,140,000
=
$265,000
$8,140,000
=
3.3%
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) P12-61B
PV factor at
i = 6%, n = 9
Net Cash Inflow
Total Present Value
Plan A:
Present value of annuity of
equal annual net cash
inflows for 9 years at 6%
6.802c × $1,550,000 per year
$10,543,100
Less: Initial investment
(8,740,000)
Net present value of Plan A
$ 1,803,100
Plan B:
Present value of annuity of
equal annual net cash
inflows for 9 years at 6%
6.802c × $1,050,000 per year
$ 7,142,100
Present value of residual value (lump sum, not
annuity)
0.592 d × $1,075,000
636,400
Less: Initial investment
(8,140,000)
Net present value of Plan B
$ (361,500)
c Present Value of Annuity of $1 (n = 9, i = 6%)
d Present Value of $1 (n = 9, i = 6%)
Annuity PV factor (i = ?, n = 9)
Managerial Accounting 4e Solutions Manual
Discussion & Analysis
A12-62
1. Describe the capital budgeting process in your own words.
2. Define capital investment. List at least three examples of capital investments other than the examples provided
3. “As the required rate of return increases, the net present value of a project also increases.” Explain why you
agree or disagree with this statement.
4. Summarize the net present value method for evaluating a capital investment opportunity. Describe the
circumstances that create a positive net present value. Describe the circumstances that may cause the net
present value of a project to be negative. Describe the advantages and disadvantages of the net present value
method.
5. Net cash inflows and net cash outflows are used in the net present value method and in the internal rate of
return method. Explain why accounting net income is not used instead of cash flows.
6. Suppose you are a manager and you have three potential capital investment projects from which to choose.
Funds are limited, so you can only choose one of the three projects. Describe at least three methods you can
7. The net present value method assumes that future cash inflows are immediately reinvested at the required rate
of return, while the internal rate of return method assumes that future cash inflows are immediately invested at
8. The decision rule for NPV analysis states that the project with the highest NPV should be selected. Describe at
least two situations when the project with the highest NPV may not necessarily be the best project to select.
9. List and describe the advantages and disadvantages of the internal rate of return method.
10. List and describe the advantages and disadvantages of the payback method.
11. Oftentimes, investments in sustainability projects do not meet traditional investment selection criteria. Suppose
you are a manager and have prepared a proposal to install solar panels to provide lighting for the office. The
12. Think of a company with which you are familiar. What are some examples of possible sustainable investments
Managerial Accounting 4e Solutions Manual
Application & Analysis
1. Research the cost of each model (includes taxes and title costs). Also, obtain an estimate of the miles per gallon
fuel efficiency of each model.
7. What qualitative factors might affect your decision about which model to purchase?
record.
A12-64
1.
a. The ethical issues in this situation are:
Competence: “Provide decision support information and recommendations that are accurate, clear, concise,
2. Instead of simply accepting or rejecting the proposal, Peter could consult upper management to discuss the
A12-65
1. Apple made its announcement in 2012 to beat these other large technology companies to the punch. Apple
2. Americans like things that are made in America. There is also a possibility that the products will be of better quality
than if they were made in China.
4. The stakeholders that are impacted are: the former (Chinese) employees who would have been manufacturing the
5. Potentially, if the company is not producing at its greatest margin, it could become the victim of a takeover
attempt. It also hurts the employees who work for lower wages so that they could keep their jobs.