1. The principal objections to the use of the average rate of return method are its failure to consider
the expected cash flows from the proposals and the timing of these flows.
5. The cash payback period ignores cash flows occurring after the payback period, which
often includes large residual values.
6. The majority of the cash flows of a new motion picture are earned within 2 years of
release. Thus, the time value of money aspect of the cash flows is less significant for motion
p
ictures than for projects with time-extended cash flows. This would favor the use of a cash
p
ayback period for evaluating the cash flows of the project.
7. The $7,900 net present value indicates that the proposal is desirable because the proposal is
expected to recover the investment and provide more than the minimum rate of return.
9. The computations for the net present value method are more complex than those for the
methods that ignore present value. Also, the method assumes that the cash received from the
p
roposal during its useful life will be reinvested at the rate of return used to compute the
p
resent value of the proposal. This assumption may not always be reasonable.
10. The computations for the internal rate of return method are more complex than those for the
methods that ignore present value. Also, the method assumes that the cash received from the
p
roposal during its useful life will be reinvested at the internal rate of return. This assumption
may not always be reasonable.
11. The major advantages of leasing are that it avoids the need to use funds to purchase assets
and reduces some of the risk of loss if the asset becomes obsolete. There may also be some
income tax advantages to leasing.
b
CHAPTER 26
CAPITAL INVESTMENT ANALYSIS
DISCUSSION QUESTIONS
CHAPTER 26 Capital Investment Analysis
PE 26-1A
Estimate average annual income $42,000 ($210,000 ÷ 5 years)
Average investment $175,000 [($325,000 + $25,000) ÷ 2]
Average rate of return 24% ($42,000 ÷ $175,000)
PE 26-1B
PE 26-2A
5.9 years ($467,870 ÷ $79,300)
PE 26-2B
PE 26-3A
a. $2,520 [($24,000 × 3.605) – $84,000]
b. 1.03 ($86,520 ÷ $84,000)
PE 26-3B
a. $(9,510) [($147,000 × 3.170) – $475,500]
PE 26-4A
[($58,995 ÷ $9,500) = 6.210, the present value of an annuity factor for 8
periods at 6%, from Exhibit 5]
PE 26-4B
PRACTICE EXERCISES
6%
CHAPTER 26 Capital Investment Analysis
PE 26-5A
a. Present value of $21,000 per year at 12% for 6 years*……………………
$ 86,331
Present value of $46,000 at 12% at the end of 6 years**…………………… 23,322
Total present value of Project A………………………………………………
$109,653
Less total cost of Project A……………………………………………………… 97,800
PE 26-5B
a. Present value of $74,000 per year at 20% for 4 years*……………………
$191,586
Present value of $106,000 at 20% at the end of 4 years**…………………
51,092
Total present value of Project 1………………………………………………… $242,678
Less total cost of Project 1……………………………………………………… 219,120
Net present value of Project 1…………………………………………………
$ 23,558
CHAPTER 26 Capital Investment Analysis
Ex. 26-1
3D
Printer Truck
Estimated average annual income:
$24,080 ÷ 7…………………………………………………………… $3,440
$36,400 ÷ 10…………………………………………………………
…
$3,640
Average investment:
($40,000 + $3,000) ÷ 2………………………………………………
…
$21,500
($50,000 + $6,000) ÷ 2………………………………………………
…
$28,000
Ex. 26-2
EXERCISES
Average Rate
of Return =
=Average Savings* – Annual Depreciation – Additional Operating Costs
(Beginning Cost + Residual Value) ÷ 2
Average Annual Income
Average Investment
CHAPTER 26 Capital Investment Analysis
Ex. 26-3
Ex. 26-4
Year 1 Years 2–9 Last Year
Initial investment……………………………………
…
$(411,200)
Operating cash flows:
Annual revenues (2,400 units × $80)………… $ 192,000 $ 192,000 $ 192,000
Selling expenses (5% × $192,000)……………
…
(9,600) (9,600) (9,600)
Cost to manufacture
(2,400 units × $74)*…………………………
…
(177,600) (177,600) (177,600)
Average Annual Income
Average Investment
Average Rate
of Return =
=Average Revenues – Annual Product Costs*
(Beginning Cost + Residual Value) ÷ 2
CHAPTER 26 Capital Investment Analysis
Ex. 26-5
Location 1: $280,000 ÷ $56,000 = 5-year cash payback period.
Location 2: 4-year cash payback period, as indicated below.
Cumulative
Net Cash Net Cash
Flow Flows
Year 1…………………………………………………………………………… $84,000 $ 84,000
Ex. 26-6
a. The Liquid Soap product line is recommended, based on its shorter cash
payback period. The cash payback period for both products can be determined
using the following schedule:
Initial investment: $540,000
Cumulative Cumulative
Net Cash Net Cash Net Cash Net Cash
Flow Flows Flow Flows
Year 1………………………………
…
$170,000 $170,000 $90,000 $ 90,000
Year 2………………………………
…
150,000 320,000 90,000 180,000
…
…
…
…
Liquid Soap has a 4-year cash payback period, and Body Lotion has a 6-year
cash payback.
b. The cash payback periods are different between the two product lines because
Liquid Soap earns cash faster than does Body Lotion. Even though both
Body LotionLiquid Soap
CHAPTER 26 Capital Investment Analysis
Ex. 26-7
a. Year
1
2
3
b. Yes. The $29,424 net present value indicates that the return on the proposal is
greater than the minimum desired rate of return of 15%.
Ex. 26-8
a. 20Y1 20Y2 20Y3 20Y4 20Y5
Revenues…………………
…
$ 58,000 $ 58,000 $ 58,000 $ 58,000 $ 58,000
Driver salary……………
…
(42,000) (43,000) (44,000) (45,000) (46,000)
b. Year
20Y1
20Y2
20Y3
20Y4
20Y5
78,000
60,000
58,968
39,480
Present Value of
Net Cash Flow
$ 83,520
0.658
0.870
0.756
Present Value
of $1 at 15%
Net Cash
Flow
$ 96,000
[from part (a)] of $1 at 12% Net Cash Flow
Net Cash Flow Present Value Present Value of
$13,000 0.893 $11,609
12,000 0.797 9,564
11,000 0.712 7,832
10,000 0.636 6,360
24,000
0.567 13,608
CHAPTER 26 Capital Investment Analysis
Ex. 26-9
a.
Annual revenues……………………………………………………………
…
$35
Total expenses………………………………………………………………
…
$20
Less noncash depreciation expense*……………………………………
…
4
b.
Annual cash flows……………………………………………………………
…
× Present value of an annuity of $1 at 14% for 30 periods……………
…
Present value of hotel project cash flows, rounded……………………
Less hotel construction costs……………………………………………
…
Net present value of hotel project…………………………………………
…
*
From Appendix A in the text
(in millions)
value factor)
(in millions
except present
$19
7.00266
$ 133
120
$13
*
…
CHAPTER 26 Capital Investment Analysis
Ex. 26-10
a. Cash inflows:
Hours of operation…………………………………
…
1,500
× Revenue per hour…………………………………
…
$110
Revenue per year…………………………………… $ 165,000
Cash outflows:
Hours of operation…………………………………
…
1,500
Fuel cost per hour………………………………
…
$46
b. Annual net cash flow (at the end of each of 5 years)………
…
$ 46,000
× Present value of annuity of $1 at 10% for 5 periods………
…
3.791
Present value of annual net cash flows………………………
…
$ 174,386
Less amount to be invested……………………………………… 132,000
Net present value…………………………………………………… $ 42,386
c. Yes. Briggs should accept the investment because the bulldozer cost is less
than the present value of the cash flows at the minimum desired rate of return
of 10%.
CHAPTER 26 Capital Investment Analysis
Ex. 26-11
a. Revenues (3,600 × 330 days × $250)……………………………………
…
$297,000,000
Less:
V
ariable expenses (3,600 × 330 days × $110)…………………
…
130,680,000
Fixed expenses (other than depreciation)………………………
…
20,000,000
Annual net cash flow………………………………………………………
…
$146,320,000
Ex. 26-12
$727,500
$750,000
a. Total Present Value of Net Cash Flow
Amount to Be Invested
Present Value Index =
Present value index
of Carolina: = = 0.97
CHAPTER 26 Capital Investment Analysis
Ex. 26-13
a. Annual net cash flow—Sewing Machine:
$80,640 = 1,800 hours × (290 baseballs – 150 baseballs) × $0.32 per baseball
Annual net cash flow—Packing Machine:
$29,400 = 1,400 hours × $21 labor cost saved per hour
Sewing Machine:
Packing Machine:
Annual net cash flow (at the end of each of 8 years)………………………
…
$ 29,400
× Present value of an annuity of $1 at 15% for 8 years (Exhibit 5)………
…
4.487
Present value of annual net cash flows………………………………………
…
$131,918
Less amount to be invested……………………………………………………
…
85,000
Net present value…………………………………………………………………
…
$ 46,918
c. The present value index indicates that the packing machine would be the
preferred investment, assuming that all other qualitative considerations are
equal. Note that the net present value of the sewing machine is greater than
the packing machine’s. However, the sewing machine requires more than triple
the investment than the packing machine ($260,000 vs. $85,000) for barely
…
…
…
…
…
CHAPTER 26 Capital Investment Analysis
Ex. 26-14
$63,000
($840,000 + $0) ÷ 2
*
The annual earnings are equal to the cash flow less the annual depreciation expense,
shown as follows:
$168,000 – ($840,000 ÷ 8 years) = $63,000
Ex. 26-15
b. Net present value:
Present value of annual net cash flows ($350,000 × 6.145*)………………
…
$2,150,750
Less amount to be invested……………………………………………………
…
1,400,000
Net present value…………………………………………………………………
…
$ 750,750
*
Present value of an annuity of $1 at 10% for 10 periods from Exhibit 5.
c. Some critical elements that are missing from this analysis:
●
The cost of the automated assembly equipment does not stop with the initial
purchase price and installation costs. The equipment will require the company
to hire engineers and support personnel to keep the machines running, to
program the software, and to debug new programs. The operators will require
new training. Thus, extensive training costs will likely be incurred. It would not
be surprising to see a large portion of the direct labor savings lost by hiring
expensive indirect labor support for the technology.
4 years=
Average rate of return on investment:
a. Payback period: $1,400,000
$350,000
a. = 15%
*
…
…
…
CHAPTER 26 Capital Investment Analysis
Ex. 26-16
b. Row 6 in Exhibit 5. The column associated with the factor 4.111 is 12%.
b. Many uncertainties could adversely impact a project of this scale and scope.
There are uncertainties affecting the initial investment and the annual cash flow
assumptions. Regarding the initial investment, the construction cost could be
higher than $415 million due to delays, labor issues, and other construction site
problems. The annual cash flow assumptions could be adversely impacted by
uncertainties such as these:
●Warm weather conditions or no snow
●Recessionary economic conditions that reduce the demand for ski holidays
Present Value Factor for an
Annuity of $1 for 6 Periods =
a.
Amount to Be Invested
Annual Net Cash Flow
12%
CHAPTER 26 Capital Investment Analysis
Ex. 26-18
a. Delivery Truck
Cash received from additional delivery (95,000 bags × $0.45)……………
…
$42,750
Cash used for operating expenses (24,000 miles × $1.35)…………………
…
32,400
Net cash flow for delivery truck…………………………………………………
…
$10,350
Internal Rate of Return = 15% (from text Exhibit 5 for 7 periods)
Bagging Machine
Direct labor savings (3 hrs./day × $18/hr. × 250 days/yr.)…………………
…
$13,500
b. To: Management
Re: Investment Recommendation
An internal rate of return analysis was performed for the delivery truck and
bagging machine investments. The internal rate of return for the bagging
machine is 12%, while that of the delivery truck is 15% (detailed analysis available).
Present Value Factor for an Annuity
of $1 for 7 Periods =Amount to Be Invested
Annual Net Cash Flow
CHAPTER 26 Capital Investment Analysis
Ex. 26-19
a. Present value of annual net cash flows ($76,000 × 5.335*)…………………
…
$405,460
Less amount to be invested………………………………………………………
…
471,960
Net present value……………………………………………………………………
…
$ (66,500)
*Present value of an annuity of $1 at 10% for 8 periods from text Exhibit 5.
b. The rate of return is less than 10% because there is a negative net present
value.
Ex. 26-20
With an expected useful life of 5 years, the cash payback period cannot be greater
than 5 years. This would indicate that the cost of the initial investment would not be
recovered during the useful life of the asset. In addition, there would be no positive
CHAPTER 26 Capital Investment Analysis
Ex. 26-21
Processing Mill
Present Value
Year of $1 at 15%
1 0.870
2 0.756
3 0.658
Electric Shovel
Present Value
Year of $1 at 15%
1 0.870
2 0.756
3 0.658
The net present value of both proposals is positive; thus, both pieces of equipment
are acceptable. However, the net present value of the processing mill exceeds that
of the electric shovel. Thus, the processing mill should be preferred if there is enough
investment money for only one of the projects.
$ 330,000 $287,100
325,000 213,850
325,000 245,700
Net Cash Present Value of
Flow Net Cash Flow
260,000
260,000
196,560
Present Value of
Net Cash Flow
Net Cash
Flow
$ 310,000 $269,700
171,080
CHAPTER 26 Capital Investment Analysis
Ex. 26-22
a. Blending Equipment
Equal annual cash flows for Years 1–5……………………………
…
$19,000
× Present value of a $1 annuity at 10% for 5 periods…………… 3.791
Present value of operating cash flows……………………………
…
$72,029
Computer System
Equal annual cash flows for Years 1–5……………………………
…
$27,000
× Present value of a $1 annuity at 10% for 5 periods…………… 3.791
Present value of operating cash flows……………………………
…
$102,357
Less amount to be invested…………………………………………
…
90,000
Net present value………………………………………………………
…
$ 12,357
$81,344
$75,000
Present value index of blending equipment: b. = 1.08
…
…
…
CHAPTER 26 Capital Investment Analysis
Ex. 26-23
b. Megawatt hour capacity…………………………………………………… 2
× Operating days per year………………………………………………… 90
× Hours per day……………………………………………………………
…
24
Wind turbine mwh generated per year…………………………………
…
4,320
V
ariable operating cost per mwh: natural gas………………………
…
$95
Operating cost per mwh: wind turbine…………………………………
…
(10)
Megawatt hour cost savings using wind turbine……………………
…
$85
Annual savings (4,320 mwh × $85)……………………………………… $367,200
…
CHAPTER 26 Capital Investment Analysis
Ex. 26-24
a.
Silica-Blended
Tires
b. Annual cash flows:
Annual contribution margin with silica-blended tires………………
…
$5,200,000
Less annual contribution margin of lost sales in
conventional tires…………………………………………………………
…
4,060,000
Net annual cash flows from selling silica tires………………………… $1,140,000
* ($140 – $70 – $12) × 70,000 tires
*
…
CHAPTER 26 Capital Investment Analysis
b. Net present value analysis:
Front-End Greenhouse Front-End Greenhouse
Year Loader Loader
1 $ 40,000 $35,720 $23,441
2 35,000 27,895 20,921
3 22,000 15,664 18,690
4 18,000 11,448 16,695
516,250 9,214 14,884
Total…………………………
…
$131,250 $99,941 $94,631
Less amount to be invested……………………………………
…
75,000 75,000
Net present value…………………………………………………
…
$24,941 $19,631
2. The report to the capital investment committee can take many forms. The report
should, at a minimum, present the following points:
a. Both projects offer the same average annual rate of return.
PROBLEMS
Present Value of
Present
0.893 $ 26,250
Fixtures
Net Cash FlowNet Cash Flow
Fixtures$1 at 12%
Value of
$131,250
0.797
0.712
0.636
0.567
26,250
26,250
26,250
26,250