Chapter 26Capital investment analysis
EYE OPENERS
1
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.The cash payback period ignores the cash flows that occur after the cash payback period, while the net present value method includes all cash flows in the analysis. The cash payback period also ignores the time value of money, which is also included in the net present value method.
5.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.
6.The cash payback period ignores cash flows occurring after the payback period, which will often include large residual values.
7.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.
8.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 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.
10.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.
11.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.
12.Allowable deductions for depreciation.
13.The life of the proposal with the longer life can be adjusted to a time period that is equal to the life of the proposal with the shorter life.
14.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.
15.Quicker delivery of products, higher production quality, and greater manufacturing flexibility are examples of qualitative factors that should be considered.
16.Monsanto indicated that it recognized that the market was demanding higher product quality that could be achieved only with a large investment in process control technology and automated laboratory equipment. The process control technology could reduce the variation in the size of fibers. More uniform fibers, in turn, improve the efficiency of the processes used by carpet manufacturers. The local area network (LAN) was not a stand-alone investment, but it linked the process control information to operators and management via computer linkages. Thus, the LAN was an integral part of the investment portfolio. Monsanto indicated the following considerations in making its investment:
a.After-tax cash flows.
b.Labor savings.
c.Accepting projects that do not have a quantifiable payback, such as enablers that allow projects with more visible benefits to be put into place (such as LAN enabling the process control technology to communicate information).
d.Allowing estimates of increased sales due to higher quality.
e.Considering inventory reductions in the cost of savings.
f.Avoiding reactive investment but considering the organizational vision and long-term strategic direction in the investment decision.
1
PRACTICE EXERCISES
PE 26–1A
Estimated average annual income$12,000 ($36,000/3 years)
Average investment$40,000 ($65,000 + $15,000)/2
Average rate of return30% ($12,000/$40,000)
PE 26–1B
Estimate average annual income$27,200 ($136,000/5 years)
Average investment$200,000 ($380,000 + $20,000)/2
Average rate of return13.6% ($27,200/$200,000)
PE 26–2A
4.5 years ($37,800/$8,400)
PE 26–2B
6.2 years ($706,800/$114,000)
PE 26–3A
a.($1,520)[($9,000 × 3.170) – $30,050]
b.0.95($28,530/$30,050)
PE 26–3B
a.$36,610[($82,000 × 3.605) – $259,000]
b.1.14($295,610/$259,000)
PE 26–4A
6%[($427,779/$87,000) = 4.917, the present value of an annuity factor for six
periods at 6%, from Exhibit 2]
PE 26–4B
20%[($56,434/$14,000) = 4.031, the present value of an annuity factor for nineperiods at 20%, from Exhibit 2]
PE 26–5A
a.
Present value of $3,000 per year at 20% for 4 years...... $ 7,767*
Present value of $9,000 at 20%at the end of 4 years...... 4,338**
Total present value of Project 1...... $ 12,105
Total cost of Project 1...... 10,000
Net present value of Project 1...... $ 2,105
*[$3,000 × 2.589 (Exhibit 2, 20%, 4years)]
**[$9,000 × 0.482 (Exhibit 1, 20%, 4years)]
b.Project 2. Project 1’s net present value of $2,105is less than the net present value of Project 2, $2,500.
PE 26–5B
a.
Present value of $24,000 per year at 12% for 6 years...... $ 98,664*
Present value of $60,000 at 12%at the end of 6 years...... 30,420**
Total present value of Project A...... $129,084
Total cost of Project A...... 125,000
Net present value of Project A...... $ 4,084
*[$24,000 × 4.111 (Exhibit 2, 12%, 6years)]
**[$60,000 × 0.507 (Exhibit 1, 12%, 6years)]
b.Project A. Project A’s net present value of $4,084is more than the net present value of Project B, $2,400.
EXERCISES
Ex. 26–1
Testing
EquipmentVehicle
Estimated average annual income:
$13,200/6...... $2,200
$14,000/8...... $1,750
Average investment:
($80,000 + 0)/2...... $40,000
($28,000+ 0)/2...... $14,000
Average rate of return:
$2,200/$40,000...... 5.5%
$1,750/$14,000...... 12.5%
Ex. 26–2
=
=
=
=
= 16%
*The effect of the savings in wages expense is an increase in income.
Ex. 26–3
=
=
=
=
= 40%
*The depreciation of the equipment is included in the factory overhead cost per unit.
Ex. 26–4
Year 1Years 2–9Last Year
Initial investment...... $(156,000)
Operating cash flows:
Annual revenues (9,000 units × $42).....$378,000$378,000$ 378,000
Selling expenses (5% × $378,000)...... (18,900) (18,900) (18,900)
Cost to manufacture
(9,000 units × $34.00)*...... (306,000) (306,000) (306,000)
Net operating cash flows...... $53,100$53,100$53,100
Total for Year 1...... $ (102,900)
Total for Years 2–9 (operating cash flow)...$53,100
Residual value...... 12,000
Total for last year...... $65,100
*The fixed overhead relates to the depreciation on the equipment [($156,000 – $12,000)/10 years/9,000 units = $1.60]. Depreciation is not a cash flow and should not be considered in the analysis.
Ex. 26–5
Location 1: $360,000/$60,000 = 6-year cash payback period.
Location 2: 4-year cash payback period, as indicated below.
Net CashCumulative
FlowNet Cash Flows
Year 1...... $120,000$120,000
Year 2...... 90,000210,000
Year 3...... 75,000285,000
Year 4...... 75,000360,000
Ex. 26–6
a.The Liquid Soapproduct 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: $500,000
Liquid SoapBody Lotion
Net CashCumulative NetNet CashCumulative Net
FlowCash FlowsFlowCash Flows
Year 1$190,000$190,000$100,000$100,000
Year 2180,000370,000100,000200,000
Year 3130,000500,000100,000300,000
Year 4100,000400,000
Year 5100,000500,000
Liquid Soap has a three-year cash payback period, and Body Lotion has a five-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.
Ex. 26–7
a.
Present ValueNet CashPresent Value of
Yearof $1 at 15%FlowNet Cash Flow
10.870$64,000$55,680
20.75649,00037,044
30.65837,00024,346
40.57225,00014,300
Total...... $175,000$131,370
Amount to be invested...... 104,000
Net present value...... $27,370
b.Yes. The $27,370 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.
20102011201220132014
Revenues $60,000$60,000$60,000$60,000$ 60,000
Driver salary.....(43,000)(45,000)(47,000)(49,000)(51,000)
Insurance...... (4,000)(4,000)(4,000)(4,000)(4,000)
Residual value...______5,000
Annual net cash
flow...... $13,000$11,000$9,000$7,000$ 10,000
b.
Net Cash FlowPresent Value ofPresent Value of
Year[from part (a)]$1 at 12%Net Cash Flow
2010$13,0000.893$11,609
201111,0000.7978,767
20129,0000.7126,408
20137,0000.6364,452
201410,0000.5675,670
Total present value of cash flows...... $36,906
Investment in delivery truck...... 38,000
Net present value of delivery truck...... $(1,094)
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.
Ex. 26–9
a.
(in millions)
Annual revenues...... $44
Total expenses...... $25
Less noncash depreciation expense...... 5
Annual cash expenses...... 20
Annual net cash flow...... $24
*Annual depreciation expense, $150 million/30 years = $5 million per year
b.
(in millions,
except present
value factor)
Annual net cash flow...... $ 24
Present value of an annuity of $1 at 14% for 30 periods...... ×7.0027*
Present value of hotel project cash flows...... $168
Less hotel construction costs...... 150
Net present value of hotel project...... $18
*From Appendix A in the text.
c.The present value of the hotel’s operating cash flows exceeds the construction costs by $18 million. That is, the net present value is positive. Therefore, construction of the new hotel can be supported by this analysis.
Ex. 26–10
a.Cash inflows:
Hours of operation...... 1,500
Revenue per hour...... ×$130.00
Revenue per year...... $ 195,000
Cash outflows:
Hours of operation...... 1,500
Fuel cost per hour...... $42.00
Labor cost per hour...... 32.00
Total fuel and labor costs per hour...... ×$74.00
Fuel and labor costs per year...... (111,000)
Maintenance costs per year...... (15,000)
Annual net cash flow...... $ 69,000
b.Annual net cash flow (at the end of each of five years)...... $69,000
Present value of annuity of $1 at 10% for five periods...... ×3.791
Present value of annual net cash flows...... $261,579
Less amount to be invested...... 245,000
Net present value...... $(16,579)
c.Yes. E&Tshould 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%.
Ex. 26–11
a.Revenues (3,600 × 300 days × $450)...... $486,000,000
Less:Variable expenses (3,600 × 300 days × $90)...... (97,200,000)
Fixed expenses (other than depreciation)...... (100,000,000)
Annual net cash flow...... $288,800,000
b.Present value of annual net cash flows ($288,800,000 × 5.650).$1,631,720,000
Present value of residual value ($120,000,000 × 0.322)...... 38,640,000
Total present value...... $1,670,360,000
Initial investment...... 750,000,000
Net present value...... $920,360,000
Ex. 26–12
Present Value Index =
Present value index of Location A: = 1.07
Present value index of Location B: = 0.96
Ex. 26–13
a.Annual net cash flow—
Sewing Machine:$97,920 = 1,700 hours × 120 incremental baseballs × $0.48
Annual net cash flow—
Packing Machine:$41,600 = 1,600×$26labor cost saved per hour
Sewing Machine:
Annual net cash flow (at the end of each of 8 years)...... $97,920
Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)...×4.487
Present value of annual net cash flows...... $439,367
Less amount to be invested...... 384,600
Net present value...... $54,767
Packing Machine:
Annual net cash flow (at the end of each of 8 years)...... $41,600
Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)...×4.487
Present value of annual net cash flows...... $186,659
Less amount to be invested...... 157,900
Net present value...... $28,759
b.Present Value Index =
Present value index of the sewing machine: = 1.14
Present value index of the packing machine: = 1.18
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 double the investment that the packing machine does ($384,600 vs. $157,900), for less than double extra net present value ($54,767 vs. $28,759). Thus, the present value index indicates the packing machine is favored.
Ex. 26–14
a.Average rate of return on investment: = 30%
*The annual earnings are equal to the cash flow less the annual depreciation expense, shown as follows:
$61,500 – ($246,000/10 years) = $36,900
b.Cash payback period: = 4 years
c.Present value of annual net cash flows ($61,500 × 6.145*)...... $377,918
Amount to be invested...... 246,000
Net present value...... $ 131,918
*Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2.
Ex. 26–15
a.Payback period: = 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×$600,000) – $2,400,000 = $1,287,000
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.
Ex. 26–16
a.=
=
=3.326
b.20%Row 6 in Exhibit 2. The column associated with the factor 3.326 is 20%.
Ex. 26–17
=
=
=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%.
Ex. 26–18
a.Delivery Truck
Cash received from additional delivery (48,200 bags × $0.42).....$20,244
Cash used for operating expenses (18,000 miles × $0.60)...... 10,800
Net cash flow for delivery truck...... $9,444
=
=
=4.160
Internal Rate of Return = 15% (from text Exhibit 2 for 7 periods)
Bagging Machine
Direct labor savings (3.0 hrs./day × $18/hr. × 250 days/yr.)...... $13,500
=
=
=4.868
Internal Rate of Return = 10% (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 10%, 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.
Ex. 26–19
a.Present value of annual net cash flows ($22,000 × 4.487*)...... $98,714
Amount to be invested...... 109,296
Net present value...... $ (10,582)
*Present value of an annuity of $1 at 15% for 8 periods from text Exhibit 2.
b.The rate of return is less than 15% because there is a negative net present value.
c.Present Value Factor for an Annuity of $1 =
=
=4.968
Internal Rate of Return=12% (from text Exhibit 2)
Ex. 26–20
With an expected useful life of five years, the cash payback period could not 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. However, there would be no average rate of return in such a case 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 of more than five years.
Ex. 26–21
Apartment Complex
Present ValueNet CashPresent Value of
Yearof $1 at 15%FlowNet Cash Flow
10.870$225,000$195,750
20.756200,000151,200
30.658200,000131,600
40.572140,00080,080
4 (residual value)0.572325,000185,900
Total...... $1,090,000$744,530
Amount to be invested...... (720,000)
Net present value...... $24,530
OfficeBuilding
Present ValueNet CashPresent Value of
Yearof $1 at 15%FlowNet Cash Flow
10.870$290,000$252,300
20.756290,000219,240
30.658230,000151,340
40.572220,000125,840
Total...... $1,030,000$748,720
Amount to be invested...... (720,000)
Net present value...... $28,720
The net present value of both projects is positive; thus, both proposals are acceptable. However, the net present value of the office building exceeds that of the apartment complex. Thus, the office building 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.
Ex. 26–22
a.
Blending Equipment
Equal annual cash flows for Years 1–5...... $12,000
Present value of a $1 annuity at 10% for five periods....×3.791
Present value of operating cash flows...... $45,492
Residual value at end of fifth year...... $8,000
Present value of $1 at 10% for five periods...... × 0.621
Present value of residual value...... 4,968
Total present value of cash flows...... $50,460
Amount to be invested...... (40,000)
Net present value...... $10,460
Computer System
Equal annual cash flows for Years 1–5...... $15,500
Present value of a $1 annuity at 10% for five periods....×3.791
Present value of cash flows...... $58,761
Amount to be invested...... (45,000)
Net present value...... $13,761
b.
Present value index of blending equipment: = 1.26