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.. A one-year
Trang 1CHAPTER 26 CAPITAL INVESTMENT ANALYSIS
DISCUSSION QUESTIONS
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
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
example, the average rate of return will include the impact of depreciation, but the internal
rate of return will not In addition, the internal rate of return approach will use time value of money concepts, while the average rate of return does not
4 A one-year payback will not equal a 100% average rate of return because the payback period
is based on cash flows, while the average rate of return is based on income The depreciation
on the project will prevent the two methods from reconciling
5 The cash payback period ignores cash flows occurring after the payback period, which will
often include large residual values
6 The majority of the cash flows of a new motion picture are earned within two years of
release Thus, the time value of money aspect of the cash flows is less significant for motion pictures than for projects with time-extended cash flows This would favor the use of a cash payback 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
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,assume one project required an investment of $10,000 and the other an investment of
$100,000 The present value indexes would be calculated as 0.9 and 0.09, respectively, for
the two projects That is, a $9,000 net present value on a $10,000 investment would be more desirable than the same net present value on a $100,000 investment
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 proposal during its useful life will be reinvested at the rate of return used to compute the
present 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 proposal 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
12 Quicker delivery of products, higher production quality, and greater manufacturing flexibility
are examples of qualitative factors that should be considered
26-1
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Trang 210% [($74,035 ÷ $17,000) = 4.355, the present value of an annuity factor for six
periods at 10%, from Exhibit 2]
PE 26–4B
15% [($362,672 ÷ $76,000) = 4.772, the present value of an annuity factor for nine
periods at 15%, from Exhibit 2]
CHAPTER 26 Capital Investment Analysis
Trang 3PE 26–5A
a Present value of $5,000 per year at 12% for 6 years*……… $20,555 Present value of $12,000 at 12% at the end of 6 years**……… 6,084 Total present value of Project A……… $26,639 Less total cost of Project A……… 22,500 Net present value of Project A……… $ 4,139
* [$15,000 × 2.589 (Exhibit 2, 20%, 4 years)]
** [$38,000 × 0.482 (Exhibit 1, 20%, 4 years)]
b Project 2 Project 1’s net present value of $2,151 is less than the net present
value of Project 2, $5,000.
Trang 4Ex 26–1
Estimated average annual income:
Testing Equipment Vehicle
(Beginning Cost + Residual Value) ÷ 2
Trang 5Average Revenues – Annual Product Costs*
(Beginning Cost + Residual Value) ÷ 2
Operating cash flows:
Annual revenues (4,000 units × 68)……… $ 272,000 $ 272,000 $ 272,000 Selling expenses (5% × $272,000)………
Cost to manufacture
(13,600) (13,600) (13,600)
(4,000 units × $49.65)*……… (198,600 ) (198,600 ) (198,600 ) Net operating cash flows……… $ 59,800 59,800 $ $ 59,800 Total for Year 1……… $ (47,200 )
Total for Years 2–9 (operating cash flow)………… $ 59,800
* The fixed overhead relates to the depreciation on the equipment Depreciation is not a cash
flow and should not be considered in the analysis Thus, $9.00 + $36.00 + $4.65 = $49.65
Trang 6Location 1: $380,000 ÷ $76,000 = 5-year cash payback period
Location 2: 4-year cash payback period, as indicated below.
Cumulative Net Cash Net Cash
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
Net Cash Flow
Cumulative Net Cash Flows
Net Cash Flow
Cumulative Net Cash Flows
Liquid Soap has a four-year cash payback period, and Body Lotion has a six-
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
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
emphasizes the initial years’ net cash flows in determining the cash payback
period Thus, the project with the greatest net cash flows in the early years of
the project life will be favored over the one with less net cash flows in the initial years.
CHAPTER 26 Capital Investment Analysis
Ex 26–5
Trang 7b Yes The $7,158 net present value indicates that the return on the proposal is
greater than the minimum desired rate of return of 15%.
Ex 26–8
Revenues……… $ 58,000 $ 58,000 $ 58,000 $ 58,000 $ 58,000 Driver salary……… (42,000) (43,000) (44,000) (45,000) (46,000)
Total present value of cash flows……… $48,973
Less investment in delivery truck……… 55,000
Net present value of delivery truck……… $ (6,027 )
c The total present value of cash flows from the delivery truck investment is
less than the total purchase price of the truck That is, the net present value
is negative Thus, this analysis does not support investment in the truck.
CHAPTER 26 Capital Investment Analysis
Trang 8Ex 26–9
Annual revenues……… $47
Total expenses……… $32
Less noncash depreciation expense*……… 4
Annual cash expenses……… 28
Annual net cash flow……… $19
* Annual depreciation expense, $120 million ÷ 30 years = $4 million per year 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 except present value factor) $ 19 7.00266 * $ 133 120
$ 13
c The present value of the hotel’s operating cash flows exceeds the construction costs by $13 million That is, the net present value is positive Therefore,
construction of the new hotel can be supported by this analysis.
Trang 9Ex 26–10
a Cash inflow s :
Hours of operation……… 1,500 × Revenue per hour……… $ 110
Revenue per year……… $165,000 Cash outflow s :
Hours of operation……… 1,500 Fuel cost per hour……… $46
Labor cost per hour………
× Total fuel and labor costs per hour………
28
$ 74
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
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%.
d 3.791 [(Hrs × $110) – (Hrs × $74) – $8,000] = $132,000
(Hrs × $417) – (Hrs × $281) – $30,328 = $132,000
Hrs × $136 = $162,328
Hrs = 1,194 (rounded)
Thus, the bulldozer operating hours must exceed 1,194 annually in order for
the investment to be justified.
Trang 10Ex 26–11
a Revenues (3,600 × 330 days × $340)……… $403,920,000 Less: Variable expenses (3,600 × 330 days × $140)……… (166,320,000) Fixed expenses (other than depreciation)……… (80,000,000 ) Annual net cash flow……… $157,600,000
b Present value of annual net cash flows ($157,600,000 × 5.650)……… $890,440,000 Present value of residual value ($140,000,000 × 0.322)……… 45,080,000
Less amount to be invested……… 750,000,000
Ex 26–12
a Present Value Index =
Total Present Value of Net Cash Flow
b The analysis supports investing in Blue Springs because the present value
index is greater than one The Lee’s Summit investment is not supported.
Trang 11Ex 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 Machin e :
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 2)………… 4.487 Present value of annual net cash flows……… $361,832 Less amount to be invested……… 260,000
Packing Machin e :
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 2)………… 4.487 Present value of annual net cash flows……… $131,918 Less amount to be invested……… 85,000 Net present value……… 46,918 $
b Present Value Index =
Total Present Value of Net Cash Flow
Amount to Be Invested
Present value index
of the sewing machine: =
Present value index
of the packing machine: =
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 over triple the
investment than the packing machine ($260,000 vs $85,000), for barely
double the extra net present value ($101,832 vs $46,918) Thus, the present
value index indicates the packing machine is favored If there were sufficient
capital for both investments, then they would both be attractive opportunities
This solution does not consider the alternative use of remaining cash, which is
an additional complexity beyond the scope of this text.
Trang 12* Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2.
Ex 26–15
a Payback period: $1,400,000 $350,000 = 4 years
b Net present value:
Present value factor for an annuity of $1, 10 periods at 10%: 6.145
Net present value = (6.145 × $350,000) – $1,400,000 = $750,750
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
Instead, the equipment should allow the company to assemble the product
with higher quality and higher flexibility This should translate into greater
sales volume, better pricing, and lower inventories All of these could be
brought into the 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.
● There will likely be a start-up or learning curve with this new technology that
will cause the benefits to be delayed.
● The analysis fails to account for taxes.
Trang 13Ex 26–16
a Present Value Factor for an
Annuity of $1 for 6 Periods =
=
Amount to Be Invested Annual Net Cash Flow
$82,220
$20,000
b 12%
= 4.111 Row 6 in Exhibit 2 The column associated with the factor 4.111 is 12%.
Ex 26–17
a Present Value Factor for an
Annuity of $1 for 10 Periods =
=
Amount to Be Invested Annual Net Cash Flow
$415 million
$99 million
= 4.192 4.192 is the present value of an annuity factor for 10 years at 20% from Exhibit 2; thus, the internal rate of return on the cash flows for 10 years is 20%.
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:
1 warm weather conditions, or no snow.
2 recessionary economic conditions that reduce the demand for ski holidays.
3 competitor property improvements that siphon demand from the project.
4 increased fuel costs that increase the cost of travel to ski resorts, thus reducing demand from non-local patrons.
5 industry overbuilding that causes a price war to maintain volume.
Trang 14Ex 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
Present Value Factor for an Annuity
of $1 for 7 Periods =
=
Amount to Be Invested Annual Net Cash Flow
$43,056
$10,350
= 4.160 Internal Rate of Return = 15% (from text Exhibit 2 for 7 periods)
Bagging Machine
Direct labor savings (3 hrs./day × $18/hr × 250 days/yr.)……… $13,500
Present Value Factor for an Annuity
of $1 for 7 Periods =
=
Amount to Be Invested Annual Net Cash Flow
$61,614
$13,500
= 4.564 Internal Rate of Return = 12% (from text Exhibit 2 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
machine is 12%, while the delivery truck is 15% (detailed analysis available).
The bagging machine fails to exceed our minimum rate of return requirement of 13% In addition, there do not appear to be any qualitative considerations that
would favor the bagging machine Therefore, the recommendation is to invest in the delivery truck.
Trang 15Ex 26–19
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 2.
b The rate of return is less than 12% because there is a negative net present
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
would not be recovered during the useful life of the asset In addition, there would
be no positive average rate of return because a net loss would result If the 20%
average rate of return and useful life are correct, the cash payback period must
be less than five years Alternatively, if both the 20% average rate of return and 5.5
years for the cash payback period are correct, the machinery must have a useful life much more than five years.
Trang 16Ex 26–21
Processing Mill
Present Value Net Cash Present Value of
260,000 260,000
196,560 171,080
4 (residual value) 0.572 280,000 160,160 Total………
Less amount to be invested………
Net present value………
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.
Note to Instructors: Since the investment amount is the same, the net present value
can be compared to determine preference That is, the present value index will show the same preference ordering.
Trang 17Ex 26–22
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 Residual value at end of fifth year……… $15,000
× Present value of $1 at 10% for five periods……… 0.621
Present value of of residual value……… 9,315
Less amount to be invested……… 75,000 Net present value……… $ 6,344 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
b Present value index of blending equipment:
Present value index of computer system:
Both the net present value calculations in part (a) and the present value index
calculations in part (b) suggest that the computer system should be selected
between the two options if there is sufficient capital for only one project
investment.
Trang 18Prob 26–1A
1 a Average annual rate of return for both projects:
$35,000 ÷ 5 ($80,000 + $0) ÷ 2
… Less amount to be invested……… 80,000 80,000
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 flows, the greenhouse offers a larger net present value The greenhouse
has a larger net present value because larger cash flows occur earlier in time
compared to the front end loader Thus, if only one of the two projects can be
accepted, the greenhouse would be the more attractive.
Trang 19Prob 26–2A
1 a Cash payback period for both projects: 2 years (the year in which
accumulated net cash flows equal $750,000), shown as follows:
b Net present value analysis:
Present Value of Net Cash Flow
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.
c Because of the timing of the receipt of the net cash flows, the plant
expansion offers a higher net present value.
d Both projects provide a positive net present value This means both
projects would be acceptable, since they exceed the minimum rate of
return.
Trang 20Prob 26–3A
Present Value Net Cash Present Value of
3 0.579 4,000,000 2,316,000
Less amount to be invested……… 7,000,000
Route Expansion Present Value Net Cash Present Value of
Trang 21Prob 26–3A (Concluded)
2 Present Value Index = Total Present Value of Net Cash Flow Amount to Be Invested
1, indicating that it does not meet the minimum rate of return standard.)
Present value index of $9,257,000 new maintenance yard: $7,000,000 Present value index of $18,629,000 route expansion: $16,000,000 Present value index of $9,257,000
acquiring railcars: $10,000,000
Trang 22Prob 26–4A
1 a Wind Turbines:
Annual net cash flow (at the end of each of 4 years)……… $ 320,000
× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)……… 3.465 Present value of annual net cash flows……… $1,108,800 Less amount to be invested……… 971,840
Bio
Fuel Equipment :
Annual net cash flow (at the end of each of 4 years)……… $ 350,000
× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)……… 3.465 Present value of annual net cash flows……… $1,212,750 Less amount to be invested……… 1,109,500 Net present value……… $ 103,250
b Present Value Index = Total Present Value of Net Cash Flow
Amount to Be Invested
Present value index of
wind turbines:
Present value index of the
bio fuel equipment:
2 a Present Value Factor for an Annuity of $1 = Amount to Be Invested
Annual Net Cash Flow