2. The principal limitations of the cash payback method are its failure to consider cash flows
occurring after the payback period and its failure to use present value concepts.
3. The average rate of return is not based on cash flows, but on operating income. Thus, for
4. A one-year payback will not equal a 100% average rate of return because the payback period
6. The majority of the cash flows of a new motion picture are earned within two years of
p
p
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.
8. The net present values indicate that both projects are desirable, but not necessarily equal in
desirability. The present value index can be used to compare the two projects. For example,
9. The computations for the net present value method are more complex than those for the
p
p
10. The computations for the internal rate of return method are more complex than those for the
p
11. The major advantages of leasing are that it avoids the need to use funds to purchase assets
CHAPTER 25 (FIN MAN); CHAPTER 10 (MAN)
CAPITAL INVESTMENT ANALYSIS
DISCUSSION QUESTIONS
25-1
CHAPTER 25 Capital Investment Analysis
PE 25–1A (FIN MAN); PE 10–1A (MAN)
PE 25–1B (FIN MAN); PE 10–1B (MAN)
PE 25–2A (FIN MAN); PE 10–2A (MAN)
PE 25–2B (FIN MAN); PE 10–2B (MAN)
PE 25–3A (FIN MAN); PE 10–3A (MAN)
a. $1,389 [($6,800 × 3.605) – $23,125]
PE 25–3B (FIN MAN); PE 10–3B (MAN)
a. ($10,546) [($96,200 × 3.170) – $315,500]
PE 25–4A (FIN MAN); PE 10–4A (MAN)
PE 25–4B (FIN MAN); PE 10–4B (MAN)
PRACTICE EXERCISES
25-2
CHAPTER 25 Capital Investment Analysis
PE 25–5A (FIN MAN); PE 10–5A (MAN)
a. Present value of $7,000 per year at 12% for 6 years*………………………
…
$28,777
Present value of $15,000 at 12% at the end of 6 years**……………………
…
7,605
Total present value of Project A…………………………………………………
…
$36,382
b. Project A. Project A’s net present value of $3,782 is more than the net present
value of Project B, $3,500.
PE 25–5B (FIN MAN); PE 10–5B (MAN)
a. Present value of $15,000 per year at 20% for 4 years*………………………
…
$38,835
Present value of $38,000 at 20% at the end of 4 years**……………………
…
18,316
Total present value of Project 1…………………………………………………
…
$57,151
25-3
CHAPTER 25 Capital Investment Analysis
Ex. 25–1 (FIN MAN); Ex. 10–1 (MAN)
Testing
Equipment Vehicle
Estimated average annual income:
$18,060 ÷ 6…………………………………………………………… $3,010
$12,000 ÷ 8…………………………………………………………… $1,500
Average investment:
Average rate of return:
$3,010 ÷ $43,000……………………………………………………
…
7%
$1,500 ÷ $15,000……………………………………………………
…
10%
Ex. 25–2 (FIN MAN); Ex. 10–2 (MAN)
Average Annual Income
Average Investment
EXERCISES
Average Rate
of Return =
25-4
CHAPTER 25 Capital Investment Analysis
Ex. 25–3 (FIN MAN); Ex. 10–3 (MAN)
Ex. 25–4 (FIN MAN); Ex. 10–4 (MAN)
Year 1 Years 2–9 Last Year
Initial investment……………………………………
…
$(227,000)
Operating cash flows:
Annual revenues (2,500 units × 60)…………
…
$ 150,000 $ 150,000 $ 150,000
Selling expenses (5% × $150,000)……………
…
(7,500) (7,500) (7,500)
…
Average Rate
of Return =
=Average Revenues – Annual Product Costs*
(Beginning Cost + Residual Value) ÷ 2
Average Annual Income
Average Investment
25-5
CHAPTER 25 Capital Investment Analysis
Ex. 25–5 (FIN MAN); Ex. 10–5 (MAN)
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……………………………………………………………………
…
$90,000 $90,000
Ex. 25–6 (FIN MAN); Ex. 10–6 (MAN)
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
…
…
…
…
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
products earn the same total net cash flow over the eight-year planning horizon,
Liquid Soap returns cash faster in the earlier years. The cash payback method
Body LotionLiquid Soap
25-6
…
…
…
CHAPTER 25 Capital Investment Analysis
Ex. 25–7 (FIN MAN); Ex. 10–7 (MAN)
a. Year
2
4
b. Yes. The $4,238 net present value indicates that the return on the proposal is
greater than the minimum desired rate of return of 15%.
Ex. 25–8 (FIN MAN); Ex. 10–8 (MAN)
a. 2016 2017 2018 2019 2020
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
2016
2017
2018
11,000 0.712 7,832
$13,000 0.893 $11,609
12,000 0.797 9,564
[from part (a)] of $1 at 12% Net Cash Flow
Net Cash Flow Present Value Present Value of
Present Value of
Net Cash Flow
0.572 12,000 6,864
0.756
Present Value
of $1 at 15%
Net Cash
Flow
18,000
13,608
$61,000 $43,838
25-7
CHAPTER 25 Capital Investment Analysis
Ex. 25–9 (FIN MAN); Ex. 10–9 (MAN)
a.
Annual revenues……………………………………………………………
…
$55
Total expenses………………………………………………………………
…
$38
b.
Annual cash flows……………………………………………………………
…
× Present value of an annuity of $1 at 14% for 30 periods……………
…
Present value of hotel project cash flows, rounded……………………
in millions
value factor)
(in millions
except present
$22
7.00266
$ 154
*
25-8
…
…
CHAPTER 25 Capital Investment Analysis
Ex. 25–10 (FIN MAN); Ex. 10–10 (MAN)
a. Cash inflows:
Hours of operation…………………………………
…
1,500
× Revenue per hour………………………………… $ 110
Revenue per year…………………………………… $ 165,000
Cash outflows:
Hours of operation…………………………………
…
1,500
b. Annual net cash flow (at the end of each of five years)……
…
$ 46,000
× Present value of annuity of $1 at 10% for five periods……
…
3.791
Present value of annual net cash flows………………………
…
$ 174,386
d. 3.791 [(Hrs. × $110) – (Hrs. × $74) – $8,000] = $132,000
(Hrs. × $417) – (Hrs. × $281) – $30,328 = $132,000
25-9
CHAPTER 25 Capital Investment Analysis
Ex. 25–11 (FIN MAN); Ex. 10–11 (MAN)
a. Revenues (3,600 × 330 days × $340)……………………………………
…
$ 403,920,000
Less: Variable expenses (3,600 × 330 days × $140)…………………
…
(166,320,000)
Ex. 25–12 (FIN MAN); Ex. 10–12 (MAN)
$607,600
$620,000
Present value index
of Ft. Collins: = = 0.98
a. Total Present Value of Net Cash Flow
Amount to Be Invested
Present Value Index =
25-10
CHAPTER 25 Capital Investment Analysis
Ex. 25–13 (FIN MAN); Ex. 10–13 (MAN)
a. Annual net cash flow—Sewing Machine:
Sewing Machine:
Annual net cash flow (at the end of each of 8 years)………………………
…
$ 80,640
× Present value of an annuity of $1 at 15% for 8 years (Exhibit 5)………
…
4.487
Present value of annual net cash flows………………………………………
…
$361,832
…
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
…
…
$361,832
$260,000
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
Present value index
of the sewing machine: = 1.39
b. =
=
Total Present Value of Net Cash Flow
Amount to Be Invested
Present Value Index
25-11
CHAPTER 25 Capital Investment Analysis
Ex. 25–14 (FIN MAN); Ex. 10–14 (MAN)
$39,000
($520,000 + $0) ÷ 2
Ex. 25–15 (FIN MAN); Ex. 10–15 (MAN)
b. Net present value:
c. Some critical elements that are missing from this analysis are:
●The manager is viewing the acquisition of automated assembly equipment as
a labor-saving device. This is probably a limited way to view the investment.
●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
a. = 15%
$520,000
Cash payback period:
a. Payback period: $1,400,000
$350,000
b. $104,000
4 years=
Average rate of return on investment:
= 5 years
*
25-12
CHAPTER 25 Capital Investment Analysis
Ex. 25–16 (FIN MAN); Ex. 10–16 (MAN)
b. Row 6 in Exhibit 5. The column associated with the factor 3.785 is 15%.
Ex. 25–17 (FIN MAN); Ex. 10–17 (MAN)
b. There are many uncertainties that 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:
2. Recessionary economic conditions that reduce the demand for ski holidays
4. Increased fuel costs that increase the cost of travel to ski resorts, thus
reducing demand from nonlocal patrons
15%
a. Present Value Factor for an
Annuity of $1 for 10 Periods =
Present Value Factor for an
Annuity of $1 for 6 Periods =
a.
Amount to Be Invested
Annual Net Cash Flow
Amount to Be Invested
Annual Net Cash Flow
25-13
CHAPTER 25 Capital Investment Analysis
Ex. 25–18 (FIN MAN); Ex. 10–18 (MAN)
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
Internal Rate of Return = 12% (from text Exhibit 5 for 7 periods)
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
Amount to Be Invested
Annual Net Cash Flow
Present Value Factor for an Annuity
of $1 for 7 Periods =Amount to Be Invested
Annual Net Cash Flow
Present Value Factor for an Annuity
of $1 for 7 Periods =
25-14
CHAPTER 25 Capital Investment Analysis
Ex. 25–19 (FIN MAN); Ex. 10–19 (MAN)
a. Present value of annual net cash flows ($35,000 × 4.968*)…………………
…
$173,880
Less amount to be invested………………………………………………………
…
186,725
Net present value……………………………………………………………………
…
$ (12,845)
*Present value of an annuity of $1 at 12% for 8 periods from text Exhibit 5.
b. The rate of return is less than 12% because there is a negative net present
value.
Ex. 25–20 (FIN MAN); Ex. 10–20 (MAN)
With an expected useful life of five years, the cash payback period cannot be
greater than five years. This would indicate that the cost of the initial investment
c.
Amount to Be Invested
Annual Net Cash Flow
Present Value Factor
for an Annuity of $1 =
25-15
CHAPTER 25 Capital Investment Analysis
Ex. 25–21 (FIN MAN); Ex. 10–21 (MAN)
Processing Mill
Present Value
Year of $1 at 15%
1 0.870
3 0.658
4 0.572
Total…………………………………………
…
Electric Shovel
Year
1
3
4
…
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
260,000
Present Value of
Net Cash Flow
Net Cash
Flow
$ 310,000 $269,700
171,080
Present Value Net Cash Present Value of
of $1 at 15% Flow Net Cash Flow
0.658 325,000 213,850
0.572 320,000 183,040
0.870 $ 330,000 $287,100
$1,370,000 $946,220
(residual value)
25-16
CHAPTER 25 Capital Investment Analysis
Ex. 25–22 (FIN MAN); Ex. 10–22 (MAN)
a. Blending Equipment
Equal annual cash flows for Years 1–5……………………………
…
$19,000
× Present value of a $1 annuity at 10% for five 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 five periods………… 3.791
…
…
$81,344
$75,000
Present value index of blending equipment: b. = 1.08
25-17
…
…
…
CHAPTER 25 Capital Investment Analysis
Prob. 25–1A (FIN MAN); Prob. 10–1A (MAN)
1. a. Average annual rate of return for both projects:
b. Net present value analysis:
Front-End Greenhouse Front-End Greenhouse
Year Loader Loader
1 $ 35,000 $31,255 $19,825
2 32,000 25,504 17,693
3 24,000 17,088 15,806
2. The report to the capital investment committee can take many forms. The report
should, as a minimum, present the following points:
a. Both projects offer the same average annual rate of return.
b. Although both projects exceed the selected rate established for discounted cash
0.797
0.712
22,200
22,200
0.893 $ 22,200
Fix.
Net Cash FlowNet Cash Flow
Fix.$1 at 12%
Value of
PROBLEMS
Present Value of
Present
25-18
CHAPTER 25 Capital Investment Analysis
Prob. 25–2A (FIN MAN); Prob. 10–2A (MAN)
1. a. Cash payback period for both projects: 2 years (the year in which
accumulated net cash flows equal $900,000), shown as follows:
Net Cash Cumulative Net Cash Cumulative
Year Flow Net Cash Flow Year Flow Net Cash Flow
b. Net present value analysis:
Present
Value of Plant Retail Store Plant Retail Store
Year $1 at 15% Expansion Expansion Expansion Expansion
1 0.870 $ 450,000 $ 500,000 $ 391,500 $ 435,000
3 0.658 340,000 350,000 223,720 230,300
5 0.497 180,000 200,000 89,460 99,400
Total………………………
…
$1,700,000 $1,700,000 $1,205,040 $1,210,100
2. The report can take many forms and should include, as a minimum, the
following points:
a. Both projects offer the same total net cash flow.
b. Both projects offer the same cash payback period.
Plant Expansion
Net Cash FlowNet Cash Flow
Present Value of
Retail Store Expansion
25-19
CHAPTER 25 Capital Investment Analysis
Prob. 25–3A (FIN MAN); Prob. 10–3A (MAN)
1.
Present Value Net Cash Present Value of
Year of $1 at 20% Flow Net Cash Flow
1 0.833 $ 4,000,000 $3,332,000
3 0.579 2,500,000 1,447,500
…
…
Present Value Net Cash Present Value of
Year of $1 at 20% Flow Net Cash Flow
1 0.833 $12,000,000 $ 9,996,000
3 0.579 9,000,000 5,211,000
Total……………………………………………
…
$31,000,000 $22,147,000
…
Present Value Net Cash Present Value of
Year of $1 at 20% Flow Net Cash Flow
1 0.833 $ 6,000,000 $ 4,998,000
3 0.579 4,000,000 2,316,000
Total……………………………………………
…
$15,000,000 $10,784,000
…
Ramp Facilities
Computer Network
Maintenance Equipment
25-20