(5-10 min.) E12-36B
Payback period
=
Initial Investment
Expected annual net cash inflow
=
$1,600,000
$320,000
=
5 years
The payback occurs well before the plant must be replaced, so the payback method supports purchasing the plant.
(5-10 min.) E12-37B
Full years
+
Amount to complete
recovery in next year
/
Projected net cash
inflow in next
year
=
Payback
5
+
( $135,000
/
$230,000 )
=
5.59 years
(10-15 min.) E12-38B
Accounting rate of return
=
Average annual operating
income from asset
Initial Investment
ARR
=
$101,500
$1,450,000
ARR
=
7.00%
Managerial Accounting 4e Solutions Manual
(10-15 min.) E12-39B
Accounting rate of return
=
Average annual operating
income from asset
Initial Investment
Accounting rate of return on Atlas
=
$170,500
$1,100,000
=
15.5%
Accounting rate of return on Kyler
=
$247,500
$1,375,000
=
18.0%
(15-20 min.) E12-40B
Req. 1
Your “out–of–pocket” cost is $127,500 either way: ($5,100 × 25 years) vs. ($10,625 × 12 years).
Req. 2
Future Value
=
Annuity × (Annuity FV factor, i = 12%, n = 25)
=
$5,100 × (133.334)
=
$680,003 (rounded)
Future Value
=
Annuity × (Annuity FV factor, i = 12%, n = 12)
=
$10,625 × (24.133)
=
$256,413 (rounded)
=
$680,003 × (2.476)
=
$1,683,687
Future Value
=
$256,413 × (FV factor, i = 12%, n = 8)
=
$256,413 × (2.476)
=
$634,879
(15-20 min.) E12-41B
Req. 1
Payback = 15 years ($600,000/40,000)
(5-10 min.) E12-42B
Req. 1
With the 8% interest rate, Laurel needs:
Present Value
=
Annuity × (Annuity PV factor, n = 4, i = 8%)
=
$27,000 × (3.312)
=
$89,424
=
$27,000 × (3.465)
=
$93,555
Present Value
$15,000,000 × (PV factor, i = 10%, n = 4)
$15,000,000 × 0.683
$10,245,000
Present Value
$2,200,000 × (Annuity PV factor, i = 10%, n = 5)
$2,200,000 × 3.791
$8,340,200
Present Value
$11,000,000 × (PV factor, i = 10%, n = 3)
$11,000,000 × 0.751
$8,261,000
Managerial Accounting 4e Solutions Manual
(10-15 min.) E12-44B
Scenario #1:
Future value
=
$3,500 × (FV factor, i = 10%, n = 6)
=
$3,500 × 1.772
=
$6,202
Scenario #2:
Present value
=
$ 4,000 × (Annuity PV factor, i = 8%, n = 20)
=
$ 4,000 × 9.818
=
$39,272
Scenario #3:
Present value
=
$145,000 × (PV factor, i = 6%, n = 7)
=
$145,000 × 0.665
=
$ 96,425
Scenario #4:
Future value
=
$4,000 × (Annuity FV factor, i = 14%, n = 10)
=
$4,000 × 19.337
=
$77,348
Scenario #5:
Future value
=
$ annuity × (Annuity FV factor, i = 6%, n = 4)
$51,000
=
$ annuity × 4.375
$11,657
=
$ annuity
(15-20 min.) E12-45B
Smith Products
Net Present Value Analysis
Annuity PV Factors
at I = 16%; 12%
Net Cash Inflow
Total Present
Value
Project A:
Present value of annuity of equal
annual net cash inflows for 7
years at 16%
4.039* × $59,000 per year =
$ 238,301
Less: Initial Investment
(260,000)
Net present value of Project A
$ (21,699)
Project B:
Present value of annuity of equal
annual net cash inflows for
9 years at 12%
5.328** × $71,000 per year =
$ 378,288
Less: Initial investment
(390,000)
Net present value of Project B
$ (11,712)
Managerial Accounting 4e Solutions Manual
(15-20 min.) E12-47B
Req. 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)
$264,000
0.862
$227,568
Year 2 (n = 2)
$253,000
0.743
$187,979
Year 3 (n = 3)
$224,000
0.641
$143,584
Year 4 (n = 4)
$213,000
0.552
$117,576
Year 5 (n = 5)
$204,000
0.476
$97,104
Year 6 (n = 6)
$177,000
0.410
$72,570
Present value of net cash inflows
$846,381
Less: Initial Investment
($915,000)
Net present value
($68,619)
Alderman Industries should not invest in the equipment because its NPV is negative.
Req. 2
Alderman 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)
($104,000)
0.410
($42,640)
Cash inflows in Year 7 (n = 7)
$ 76,000
0.354
26,904
Residual value (n=7)
$ 55,000
0.354
19,470
Additional NPV provided from
refurbishment
$ 3,734
NPV from part 1
($68,619)
New NPV
($64,885)
The refurbishment provides a positive NPV. The refurbishment NPV is not large enough to overcome the original NPV
of the equipment ($68,619). Therefore, the refurbishment should not alter Alderman Industries’ original decision to
turn down the equipment investment.
(15-20 min.) E12-48B
NPV at 12%
Year
Net Cash Inflow
PV factor
i = 12%
Present Value
1
$498,000
0.893
$444,714
2
400,000
0.797
$318,800
3
296,000
0.712
$210,752
Present value of net cash inflows
$974,266
Less: Initial investment
(935,000)
NPV
$ 39,266
Net Cash Inflow
400,000
296,000
Net Cash Inflow
$429,276
400,000
$297,200
296,000
$189,736
$916,212
(935,000)
$1,705,000
$1,955,000
$2,215,000
Managerial Accounting 4e Solutions Manual
(10-15 min.) E12-50B
Req. 1
Avg. net cash inflow per
day
x
Number of ski days per year
=
Avg. annual net cash
inflow
$12,120
x
163
=
$1,975,560
Req. 2
Avg. annual net cash inflow
–
Annual depreciation expense
=
Avg. annual operating income
from asset
$1,975,560
–
$810,000
=
$1,165,560
Req. 3
Initial Investment
/
Expected annual net cash inflow
=
Payback period
$9,000,000
/
$1,975,560
=
4.56 years
Req. 4
Avg. annual operating income
from asset
/
Initial investment
=
Accounting
rate of return
$1,165,560
/
$9,000,000
=
12.95%
(5-10 min.) E12-51B
Req. 1
The payback period of 4.56 years will not change since the method does not consider any cash flows that occur after
=
Payback period
=
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) E12-51B
Req. 2
The ARR will change if the asset has no residual value. The average annual operating income will be lower since there
$9,000,000
(10-15 min.) E12-52B
Req. 1
PV factor at
12%
Net Cash Inflow
Total Present Value
Present value of annuity of equal
annual net cash inflows for 10
years at 12%
5.650 × $1,975,560a
$11,161,914
Present value of residual value*
0.322 b × $900,000
289,800
Total present value
$11,451,714
Less: Initial investment
(9,000,000)
Net present value of expansion
$ 2,451,714
a From E12-51B
b The residual value is a single lump sum (not an annuity) that will occur at the end of the investment’s useful life. The
Present Value of $1 table is used to find the correct PV factor for i = 12%, n = 10.
The expansion is an attractive project because its NPV is positive.
Req. 2
Annuity PV
factor at i =
12%, n = 10
Net Cash Inflow
Total Present Value
Present value of annuity of equal
annual net cash inflows for 10
years at 12%
5.650 × $1,975,560a
$11,161,914
Less: Initial investment
(9,000,000)
Net present value of expansion
$ 2,161,914
__________
a From E12-51B
Without a residual value, the expansion is still attractive because of the project’s positive NPV.
Managerial Accounting 4e Solutions Manual
(20 min.) E12-53B
Req. 1
(a)
Net Present
Value
(b)
Profitability Index
(c)
Internal Rate of
Return
(d)
Payback
Period
(e)
Accounting
Rate of Return
1st preferred
C
A
B
C
D
2nd preferred
D
C
A
A
A
3rd preferred
A
B
C
D
B
4th preferred
B
D
D
B
C
Req. 2
Net Present Value (NPV) – This method indicates profitability by comparing the present value of the investment’s net
cash inflows with the cost of the investment (already stated at its present value). This method is superior because it
incorporates the time value of money.
Profitability index – This method helps to compare the NPV across alternative investments of varying sizes.
Internal rate of return (IRR) – This method also indicates profitability and incorporates the time value of money. This
method will show us the actual rate of return being earned on the investment by equating the present value of the net
cash inflows to the investment’s cost. In other words, it is the interest rate, which brings the investment’s NPV to zero.
Payback Period – This method will show the company how quickly it recoups its initial investment. This method will be
good for screening out those potential investments that are too risky because the payback period is too long. However,
the payback period will not be the sole criterion for accepting capital investments since it does not give the company
any insight about the investment’s profitability. Additionally, it does not incorporate the time value of money.
Accounting rate of return (ARR) – This method will give the company an indication of how profitable the investment
will be. However, since it does not consider the time value of money, it is not the best indicator of profitability. This
method is the only method that uses accrual accounting figures. Therefore it will help the company assess the impact
of investments on the financial statements. The other methods use net cash flows.
Present value
=
Annuity × (Annuity PV factor, i = 10%, n = 20)
$2,000,000
=
Annuity × 8.514
$234,907
=
Annuity
Future value
=
$ 3,000 × (Annuity FV factor, i = 14%, n = 8)
=
$ 3,000 × 13.233
=
$39,699
Scenario #5:
Present value
=
$15,000 × (Annuity PV factor, i = 12%, n = 10)
=
$15,000 × 5.650
=
$84,750
=
$300,000 × 0.926 =
=
$206,000 × 0.857 =
=
$100,000 × 0.794 =
Total Present value
Less: Initial Investment
Net Present Value (NPV)
(30-45 min.) P12-54A
Scenario #1:
Future value
=
$ 35,000 × (FV factor, i = 10%, n = 15)
=
$ 35,000 × 4.177
=
$146,195
Scenario #2:
Present value
=
$3,500,000 × (PV factor, i = 12%, n = 30)
=
$3,500,000 × 0.033
=
$ 115,500
Managerial Accounting 4e Solutions Manual
(continued) P12-54A
Scenario #7:
The IRR is the interest rate at which the investment’s NPV = 0. Since the NPV was positive at 8% (in Scenario 6), we’ll
Chapter 12 Capital Investment Decisions and the Time Value of Money
(continued) P12-55A
Req. 1
Present Value
=
Annual cash withdrawals × (Annuity PV factor, i = 12%, n = 40)
=
$ 250,000 × (8.244)
=
$2,061,000
Amount of annual cash savings × (Annuity FV factor, i =12%, n = 15)
Amount of annual cash savings × (37.280)
$55,284
Amount of annual cash savings
Managerial Accounting 4e Solutions Manual
(20-30 min.) P12-56A
Req. 1
Payback
=
Initial investment
period
Expected annual net cash inflow
=
$2,000,000
$520,000
=
3.8 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
=
$520,000 − $200,000
$2,000,000
=
$320,000
$2,000,000
=
16%