10
Risk CHAPTER and Refinements
in Capital Budgeting
INSTRUCTORS RESOURCES
Overview
Chapters 8 and 9 developed the major decision-making aspects of capital budgeting.
Cash flows and budgeting models have been integrated and discussed in providing the
principles of capital budgeting. However, there are more complex issues beyond those
presented. Chapter 10 expands capital budgeting to consider risk with such methods as
sensitivity analysis, scenario analysis, and simulation. Capital budgeting techniques used
to evaluate international projects, as well as the special risks multinational companies
face, are also presented. Additionally, two basic risk-adjustment techniques are
examined: certainty equivalents and risk-adjusted discount rates.
PMF DISK
PMF Tutor
A topic covered for this is risk-adjusted discount rates (RADRs).
PMF Problem-Solver: Capital Budgeting Techniques
This module allows the student to compare the annualized net present value of projects
with unequal lives.
PMF Templates
No spreadsheet templates are provided for this chapter.
Study Guide
There are no particular Study Guide examples suggested for classroom presentation.
7
Part 3 Long-Term Investment Decisions
ANSWERS TO REVIEW QUESTIONS
10-1
There is usually a significant degree of uncertainty associated with capital
budgeting projects. There is the usual business risk along with the fact that future
cash flows are an estimate and do not represent exact values. This uncertainty
exists for both independent and mutually exclusive projects. The risk associated
with any single project has the capability to change the entire risk of the firm.
The firm's assets are like a portfolio of assets. If an accepted capital budgeting
project has a risk different from the average risk of the assets in the firm, it will
cause a shift in the overall risk of the firm.
10-2
Risk, in terms of cash inflows from a project, is the variability of expected cash
flows, hence the expected returns, of the given project. The breakeven cash
inflow level of cash inflow necessary in order for the project to be
the
acceptable
may be compared with the probability of that inflow occurring. When
comparing two projects with the same breakeven cash inflows, the project with
the higher probability of occurrence is less risky.
10-3
a. Sensitivity analysis uses a number of possible inputs (cash inflows) to assess
their impact on the firm's return (NPV). In capital budgeting, the NPVs are
estimated for the pessimistic, most likely, and optimistic cash flow estimates.
By subtracting the pessimistic outcome NPV from the optimistic outcome
NPV, a range of NPVs can be determined.
b. Scenario analysis is used to evaluate the impact on return of simultaneous
changes in a number of variables, such as cash inflows, cash outflows, and the
cost of capital, resulting from differing assumptions relative to economic and
competitive conditions. These return estimates can be used to roughly assess
the risk involved with respect to the level of inflation.
c. Simulation is a statistically based approach using random numbers to simulate
various cash flows associated with the project, calculating the NPV or IRR on
the basis of these cash flows, and then developing a probability distribution of
each project's rate of returns based on NPV or IRR criterion.
10-4
a. Multinational companies (MNCs) must consider the effect of exchange rate
risk, the risk that the exchange rate between the dollar and the currency in
which the project's cash flows are denominated will reduce the project's future
cash flows. If the value of the dollar depreciates relative to that currency, the
market value of the project's cash flows will decrease as a result. Firms can
use hedging to protect themselves against this risk in the short term; for the
long term, financing the project using local currency can minimize this risk.
8
Chapter 10 Risk and Refinements in Capital Budgeting
b. Political risk, the risk that a foreign government's actions will adversely affect
the project, makes international projects particularly risky, because it cannot
be predicted in advance. To take this risk into account, managers should
either adjust expected cash flows or use risk-adjusted discount rates when
performing the capital budgeting analysis. Adjustment of cash flows is the
preferred method.
c. Tax laws differ from country to country. Because only after-tax cash flows
are relevant for capital budgeting decisions, managers must account for all
taxes paid to foreign governments and consider the effect of any foreign tax
payments on the firm's U.S. tax liability.
d. Transfer pricing refers to the prices charged by a corporation's subsidiaries for
goods and services traded between them; the prices are not set by the open
market. In terms of capital budgeting decisions, managers should be sure that
transfer prices accurately reflect actual costs and incremental cash flows.
e. MNCs cannot evaluate international capital projects from only a financial
perspective. The strategic viewpoint often is the determining factor in
deciding whether or not to undertake a project. In fact, a project that is less
acceptable on a purely financial basis than another may be chosen for strategic
reasons. Some reasons for MNC foreign investment include continued market
access, the ability to compete with local companies, political and/or social
reasons (for example, gaining favorable tax treatment in exchange for creating
new jobs in a country), and achievement of a particular corporate objective
such as obtaining a reliable source of raw materials.
10-5
Risk-adjusted discount rates reflect the return that must be earned on a given
project in order to adequately compensate the firm's owners. The relationship
between RADRs and the CAPM is a purely theoretical concept. The expression
used to value the expected rate of return of a security k i (ki = RF + [b x (km - RF)])
is rewritten substituting an asset for a security. Because real corporate assets are
not traded in efficient markets and estimation of a market return, k m, for a
portfolio of such assets would be difficult, the CAPM is not used for real assets.
10-6
A firm whose stock is actively traded in security markets generally does not
increase in value through diversification. Investors themselves can more
efficiently diversify their portfolio by holding a variety of stocks. Since a firm is
not rewarded for diversification, the risk of a capital budgeting project should be
considered independently rather than in terms of their impact on the total portfolio
of assets. In practice, management usually follows this approach and evaluates
projects based on their total risk.
9
Part 3 Long-Term Investment Decisions
10-7
Yet RADRs are most often used in practice for two reasons: 1) financial decision
makers prefer using rate of return-based criteria, and 2) they are easy to estimate
and apply. In practice, risk is subjectively categorized into classes, each having a
RADR assigned to it. Each project is then subjectively placed in the appropriate
risk class.
10-8
A comparison of NPVs of unequal-lived mutually exclusive projects is
inappropriate because it may lead to an incorrect choice of projects. The
annualized net present value converts the net present value of unequal-lived
projects into an annual amount that can be used to select the best project. The
expression used to calculate the ANPV follows:
ANPV =
10-9
NPVj
PVIFAk%, nj
Real Options are opportunities embedded in real assets that are part of the capital
budgeting process. Managers have the option of implementing some of these
opportunities to alter the cash flow and risk of a given project. Examples of real
options include:
Abandonment the option to abandon or terminate a project prior to the end of its
planned life.
Flexibility - the ability to adopt a project that permits flexibility in the firms
production process, such as be able to reconfigure a machine to accept various
types of inputs.
Growth - the option to develop follow-on projects, expand markets, expand or
retool plants, and so on, that would not be possible without implementation the
project that is being evaluated.
Timing - the ability to determine the exact timing of when various action of the
project will be undertaken.
10-10 Strategic NPV incorporates the value of the real options associated with the
project while traditional NPV includes only the identifiable relevant cash flows.
Using strategic NPV could alter the final accept/reject decision. It is likely to lead
to more accept decisions since the value of the options is added to the traditional
NPV as shown in the following equation.
NPVstrategic = NPVtraditional = Value of real options
10-11 Capital rationing is a situation where a firm has only a limited amount of funds
available for capital investments. In most cases, implementation of the acceptable
projects would require more capital than is available. Capital rationing is
common for a firm, since unfortunately most firms do not have sufficient capital
available to invest in all acceptable projects. In theory, capital rationing should
not exist because firms should accept all projects with positive NPVs or IRRs
greater than the cost of capital. However, most firms operate with finite capital
10
Chapter 10 Risk and Refinements in Capital Budgeting
expenditure budgets and must select the best from all acceptable projects, taking
into account the amount of new financing required to fund these projects.
10-12 The internal rate of return approach and the net present value approach to capital
rationing both involve ranking projects on the basis of IRRs. Using the IRR
approach, a cut-off rate and a budget constraint are imposed. The NPV first ranks
projects by IRR and then takes into account the present value of the benefits from
each project in order to determine the combination with the highest overall net
present value. The benefit of the NPV approach is that it guarantees a maximum
dollar return to the firm, whereas the IRR approach does not.
11
Part 3 Long-Term Investment Decisions
SOLUTIONS TO PROBLEMS
10-1
LG 1: Recognizing Risk
a. & b.
Project
A
Risk
Low
B
Medium
C
Medium
D
High
Reason
The cash flows from the project can be easily
determined since this expenditure consists strictly of
outflows. The amount is also relatively small.
The competitive nature of the industry makes it so
that Caradine will need to make this expenditure to
remain competitive. The risk is only moderate
since the firm already has clients in place to use the
new technology.
Since the firm is only preparing a proposal, their
commitment at this time is low. However, the
$450,000 is a large sum of money for the company
and it will immediately become a sunk cost.
Although this purchase is in the industry in which
Caradine normally operates, they are encountering a
large amount of risk. The large expenditure, the
competitiveness of the industry, and the political
and exchange risk of operating in a foreign country
adds to the uncertainty.
NOTE: Other answers are possible depending on the assumptions a student may
make. There is too little information given about the firm and industry to
establish a definitive risk analysis.
10-2
LG 2: Breakeven Cash Flows
a.
$35,000 = CF(PVIFA14%,12)
$35,000 = CF(5.66)
CF = $6,183.75
Calculator solution: $6,183.43
b.
$35,000 = CF(PVIFA10%,12)
$35,000 = CF(6.814)
CF = $5,136.48
Calculator solution: $5,136.72
The required cash flow per year would decrease by $1,047.27.
12
Chapter 10 Risk and Refinements in Capital Budgeting
10-3
LG 2: Breakeven Cash Inflows and Risk
a.
Project X
PVn = PMT x (PVIFA15%,5 yrs.)
PVn = $10,000 x (3.352)
PVn = $33,520
Project Y
PVn = PMT x (PVIFA15%,5 yrs.)
PVn = $15,000 x (3.352)
PVn = $50,280
NPV = PVn - Initial investment
NPV = $33,520 - $30,000
NPV = $3,520
Calculator solution: $3,521.55
NPV = PVn - Initial investment
NPV = $50,280 - $40,000
NPV = $10,280
Calculator solution: $10,282.33
b.
Project X
$CF x 3.352 = $30,000
$CF = $30,000 3.352
$CF = $8,949.88
Project Y
$CF x 3.352 = $40,000
$CF = $40,000 3.352
$CF = $11,933.17
c.
Project X
Probability = 60%
Project Y
Probability = 25%
d.
Project Y is more risky and has a higher potential NPV. Project X has less risk
and less return while Project Y has more risk and more return, thus the risk-return
trade-off.
e.
Choose Project X to minimize losses; to achieve higher NPV, choose Project Y.
10-4
LG 2: Basic Sensitivity Analysis
a.
Range A = $1,800 - $200 = $1,600
Range B = $1,100 - $900 = $200
b.
NPV
Outcome
Pessimistic
Most likely
Optimistic
Range
Project A
Table Value
- $ 6,297
514
7,325
$13,622
Calculator
Solution
- $ 6,297.29
513.56
7,324.41
$13,621.70
Project B
Calculator
Table Value
Solution
- $ 337
- $ 337.79
514
513.56
1,365
1,364.92
$1,702
$1,702.71
c.
Since the initial investment of projects A and B are equal, the range of cash flows
and the range of NPVs are consistent.
d.
Project selection would depend upon the risk disposition of the management. (A
is more risky than B but also has the possibility of a greater return.)
13
Part 3 Long-Term Investment Decisions
10-5
LG 4: Sensitivity Analysis
a.
Range P = $1,000 - $500
Range Q = $1,200 - $400
= $500
= $800
b.
NPV
Outcome
Pessimistic
Most likely
Optimistic
c.
Project A
Table Value
$73
1,609
3,145
Calculator
Solution
$ 72.28
1,608.43
3,144.57
Project B
Calculator
Table Value
Solution
-$ 542
-$ 542.17
1,609
1,608.43
4,374
4,373.48
Range P = $3,145 - $73
= $3,072 (Calculator solution: $3,072.29)
Range Q = $4,374 - (-$542) = $4,916 (Calculator solution: $4,915.65)
Each computer has the same most likely result. Computer Q has both a greater
potential loss and a greater potential return. Therefore, the decision will depend
on the risk disposition of management.
10-6
LG 2: Simulation
a.
Ogden Corporation could use a computer simulation to generate the respective
profitability distributions through the generation of random numbers. By tying
various cash flow assumptions together into a mathematical model and repeating
the process numerous times, a probability distribution of project returns can be
developed. The process of generating random numbers and using the probability
distributions for cash inflows and outflows allows values for each of the variables
to be determined. The use of the computer also allows for more sophisticated
simulation using components of cash inflows and outflows. Substitution of these
values into the mathematical model yields the NPV. The key lies in formulating a
mathematical model that truly reflects existing relationships.
b.
The advantages to computer simulations include the decision maker's ability to
view a continuum of risk-return trade-offs instead of a single-point estimate. The
computer simulation, however, is not feasible for risk analysis.
14
Chapter 10 Risk and Refinements in Capital Budgeting
10-7
LG 4: RiskAdjusted Discount Rates-Basic
a.
Project E:
PVn = $6,000 x (PVIFA15%,4)
PVn = $6,000 x 2.855
PVn = $17,130
NPV = $17,130 - $15,000
NPV = $2,130
Calculator solution: $2,129.87
Project F: Year
PVIF15%,n
$6,000
4,000
5,000
2,000
1
2
3
4
CF
.870
.756
.658
.572
PV
$5,220
3,024
3,290
1,144
$12,678
NPV = $12,678 - $11,000
NPV = $1,678
Calculator solution: $1,673.05
Project G: Year
1
2
3
4
CF
PVIF15%,n
$ 4,000
6,000
8,000
12,000
.870
.756
.658
.572
NPV = $20,144 - $19,000
NPV = $1,144
Calculator solution: $1,136.29
Project E, with the highest NPV, is preferred.
b.
RADRE
RADRF
RADRG
c.
Project E:
= .10 + (1.80 x (.15 - .10)) = .19
= .10 + (1.00 x (.15 - .10)) = .15
= -.10 + (0.60 x (.15 - .10)) = .13
$6,000 x (2.639) = $15,834
NPV = $15,834 - $15,000
NPV = $834
Calculator solution: $831.51
15
PV
$3,480
4,536
5,264
6,864
$20,144
Part 3 Long-Term Investment Decisions
Project F:
Same as in a., $1,678 (Calculator solution: $1,673.05)
Project G: Year
PVIF13%,n
$ 4,000
6,000
8,000
12,000
1
2
3
4
CF
.885
.783
.693
.613
PV
$ 3,540
4,698
5,544
7,356
$ 21,138
NPV = $21,138 - $19,000
NPV = $2,138
Calculator solution: $2,142.93
Rank:
1
2
3
Project
G
F
E
d.
After adjusting the discount rate, even though all projects are still acceptable, the
ranking changes. Project G has the highest NPV and should be chosen.
10-8
LG 4: Risk-adjusted Discount rates-Tabular
a.
NPVA = ($7,000 x 3.993) - $20,000
NPVA = $7,951 (Use 8% rate)
Calculator solution: $ 7,948.97
NPVB = ($10,000 x 3.443) - $30,000
NPVB = $4,330 (Use 14% rate)
Calculator solution: $ 4,330.81
Project A, with the higher NPV, should be chosen.
b.
Project A is preferable to Project B, since the net present value of A is greater
than the net present value of B.
10-9
LG 4: Risk-adjusted Rates of Return using CAPM
a.
kX = 7% + 1.2(12% - 7%) = 7% + 6% = 13%
kY = 7% + 1.4(12% - 7%) = 7% + 7% = 14%
NPVX = $30,000(PVIFA13%,4) - $70,000
NPVX = $30,000(2.974) - $70,000
NPVX = $89,220 - $70,000 = $19,220
16
Chapter 10 Risk and Refinements in Capital Budgeting
NPVY $22,000(PVIF14%,1) = + $32,000(PVIF14%,2) + $38,000(PVIF14%3) +
$46,000(PVIF14%,4) - $70,000
NPVY = $22,000(.877) + $32,000(.769) + $38,000(.675) + $46,000(.592) $70,000
NPVY = $19,294 + $24,608 + $25,650 + $27,232 - 70,000 = $26,784
b.
The RADR approach prefers Y over X. The RADR approach combines the risk
adjustment and the time adjustment in a single value. The RADR approach is
most often used in business.
10-10 LG 4: Risk Classes and RADR
a.
Project X: Year
1
2
3
4
5
CF
PVIF22%,n
PV
$80,000
70,000
60,000
60,000
60,000
.820
.672
.551
.451
.370
$65,600
47,040
33,060
27,060
22,200
$194,960
NPV = $194,960 - $180,000
NPV = $14,960
Calculator solution: $14,930.45
Project Y: Year
1
2
3
4
5
CF
PVIF13%,n
PV
$50,000
60,000
70,000
80,000
90,000
.885
.783
.693
.613
.543
$ 44,250
46,980
48,510
49,040
48,870
$237,650
NPV = $237,650 - $235,000
NPV = $2,650
Calculator solution: $2,663.99
Project Z: Year
1
2
3
4
5
CF
PVIFA15%,5
$90,000
$90,000
$90,000
$90,000
$90,000
3.352
NPV = $ 301,680 - $ 310,000
NPV = - $ 8,320
Calculator solution: -$8,306.04
17
PV
$ 301,680
Part 3 Long-Term Investment Decisions
b.
Projects X and Y are acceptable with positive NPV's, while Project Z with a
negative NPV is not. Project X with the highest NPV should be undertaken.
10-11 LG 5: Unequal LivesANPV Approach
a.
Machine A
PVn = PMT x (PVIFA12%,6 yrs.)
PVn = $12,000 x (4.111)
PVn = $49,332
NPV =
NPV =
NPV =
Calculator
PVn - Initial investment
$ 49,332 - $ 92,000
- $ 42,668
solution: - $ 42,663.11
Machine B
Year
1
2
3
4
CF
PVIFA12%,n
PV
.893
.797
.712
.636
$ 8,930
15,940
21,360
25,440
$ 71,670
$10,000
20,000
30,000
40,000
NPV = $71,670 - $65,000
NPV = $6,670
Calculator solution: $6,646.58
Machine C
PVn = PMT x (PVIFA12%,5 yrs.)
PVn = $ 30,000 x 3.605
PVn = $ 108,150
NPV = PVn - Initial investment
NPV = $ 108,150 - $ 100,500
NPV = $ 7,650
Calculator solution: $ 7,643.29
Rank
1
2
3
Project
C
B
A
(Note that A is not acceptable and could be rejected without any additional
analysis.)
18
Chapter 10 Risk and Refinements in Capital Budgeting
b.
Annualized NPV (ANPVj) =
NPVj
PVIFAk%, nj
Machine A:
ANPV = - $ 42,668 4.111 (12%,6 years)
ANPV = - $ 10,378
Machine B:
ANPV = $ 6,670 3.037 (12%,4 years)
ANPV = $ 2,196
Machine C
ANPV = $ 7,650 3.605 (12%,5 years)
ANPV = $ 2,122
Rank
1
2
3
c.
Project
B
C
A
Machine B should be acquired since it offers the highest ANPV. Not considering
the difference in project lives resulted in a different ranking based in part on C's
NPV calculations.
10-12 LG 5: Unequal LivesANPV Approach
a.
Project X
Year
1
2
3
4
CF
PVIF14%,n
$ 17,000
25,000
33,000
41,000
.877
.769
.675
.592
PV
$ 14,909
19,225
22,275
24,272
$ 80,681
NPV = $80,681 - $78,000
NPV = $2,681
Calculator solution: $2,698.32
19
Part 3 Long-Term Investment Decisions
Project Y
Year
1
2
CF
PVIF14%,n
$ 28,000
38,000
.877
.769
$ 24,556
29,222
$ 53,778
NPV = $53,778 - $52,000
NPV = $1,778
Calculator solution: $1,801.17
Project Z
PVn = PMT x (PVIFA14%,8 yrs.)
PVn = $15,000 x 4.639
PVn = $69,585
NPV = PVn - Initial investment
NPV = $69,585 - $66,000
NPV = $3,585
Calculator solution: $3,582.96
Rank
1
2
3
b.
Project
Z
X
Y
Annualized NPV (ANPVj) =
NPVj
PVIFAk%, nj
Project X
ANPV = $2,681 2.914 (14%,4 yrs.)
ANPV = $920.04
Project Y
ANPV = $1,778 1.647 (14%,2 yrs.)
ANPV = $1,079.54
Project Z
ANPV = $3,585 4.639 (14%, 8 yrs.)
ANPV = $772.80
Rank
1
2
3
PV
Project
Y
X
Z
20
Chapter 10 Risk and Refinements in Capital Budgeting
c.
Project Y should be accepted. The results in a and b show the difference in NPV
when differing lives are considered.
10-13 LG 5: Unequal LivesANPV Approach
a.
Sell
Year
CF
PVIF12%,n
1
2
$ 200,000
250,000
.893
.797
PV
$ 178,600
199,250
$ 377,850
NPV = $377,850 - $200,000
NPV = $177,850
Calculator solution: $177,786.90
License
Year
1
2
3
4
5
CF
$ 250,000
100,000
80,000
60,000
40,000
PVIF12%,n
.893
.797
.712
.636
.567
PV
$ 223,250
79,700
56,960
38,160
22,680
$ 420,750
NPV = $420,750 - $200,000
NPV = $220,750
Calculator solution: $220,704.25
Manufacture
Year
CF
1
2
3
4
5
6
$ 200,000
250,000
200,000
200,000
200,000
200,000
PVIF12%,n
.893
.797
.712
.636
.567
.507
$ 178,600
199,250
142,400
127,200
113,400
101,400
$ 862,250
NPV = $862,250 - $450,000
NPV = $412,250
Calculator solution: $412,141.16
Rank
1
2
PV
Alternative
Manufacture
License
21
Part 3 Long-Term Investment Decisions
3
b.
Sell
Annualized NPV (ANPVj) =
NPVj
PVIFAk%, nj
Sell
License
ANPV = $177,850 1.690 (12%,2yrs.) ANPV = $220,750 3.605 (12%,5yrs.)
ANPV = $105,236.69
ANPV = $61,234.40
Manufacture
ANPV = $412,250 4.111 (12%,6 yrs.)
ANPV = $100,279.74
Rank
1
2
3
c.
Alternative
Sell
Manufacture
License
Comparing projects of unequal lives gives an advantage to those projects that
generate cash flows over the longer period. ANPV adjusts for the differences in the
length of the projects and allows selection of the optimal project.
10-14 LG 6: Real Options and the Strategic NPV
a.
Value of real options = value of abandonment + value of expansion + value of
delay
Value of real options = (.25 x $1,200) + (.30 x $3,000) + (.10 x $10,000)
Value of real options = $300 + $900 + $1,000
Value of real options = $2,200
NPVstrategic = NPVtraditional + Value of real options
NPVstrategic = -1,700 + 2,200 = $500
b.
Due to the added value from the options Rene should recommend acceptance of
the capital expenditures for the equipment.
c.
In general this problem illustrates that by recognizing the value of real options a
project that would otherwise be unacceptable (NPV traditional < 0) could be
acceptable (NPVstrategic > 0). It is thus important that management identify and
incorporate real options into the NPV process.
22
Chapter 10 Risk and Refinements in Capital Budgeting
10-15 LG 6: Capital Rationing-IRR and NPV Approaches
a.
Rank by IRR
Project
F
E
G
C
B
A
D
IRR
23%
22
20
19
18
17
16
Initial investment
$ 2,500,000
800,000
1,200,000
Total Investment
$ 2,500,000
3,300,000
4,500,000
Projects F, E, and G require a total investment of $4,500,000 and provide a total
present value of $5,200,000, and therefore a net present value of $700,000.
b.
Rank by NPV (NPV = PV - Initial investment)
Project
F
A
C
B
D
G
E
NPV
$500,000
400,000
300,000
300,000
100,000
100,000
100,000
Initial investment
$2,500,000
5,000,000
2,000,000
800,000
1,500,000
1,200,000
800,000
Project A can be eliminated because, while it has an acceptable NPV, its initial
investment exceeds the capital budget. Projects F and C require a total initial
investment of $4,500,000 and provide a total present value of $5,300,000 and a
net present value of $800,000. However, the best option is to choose Projects B,
F, and G, which also use the entire capital budget and provide an NPV of
$900,000.
c.
The internal rate of return approach uses the entire $4,500,000 capital budget but
provides $200,000 less present value ($5,400,000 - $5,200,000) than the NPV
approach. Since the NPV approach maximizes shareholder wealth, it is the
superior method.
d.
The firm should implement Projects B, F, and G, as explained in part c.
23
Part 3 Long-Term Investment Decisions
10-16 LG 6: Capital Rationing-NPV Approach
a.
Project
A
B
C
D
E
F
G
PV
$ 384,000
210,000
125,000
990,000
570,000
150,000
960,000
b.
The optimal group of projects is Projects C, F, and G, resulting in a total net
present value of $235,000.
24
Chapter 10 Risk and Refinements in Capital Budgeting
Chapter 10 Case
Evaluating Cherone Equipment's Risky Plans for Increasing Its Production
Capacity
a.
(1)
Plan X
Year
1
2
3
4
5
CF
$ 470,000
610,000
950,000
970,000
1,500,000
PVIF12%,n
.893
.797
.712
.636
.567
PV
$ 419,710
486,170
676,400
616,920
850,500
$3,049,700
NPV = $3,049,700 - $2,700,000
NPV = $349,700
Calculator solution: $349,700
Plan Y
Year
1
2
3
4
5
CF
$ 380,000
700,000
800,000
600,000
1,200,000
PVIF12%,n
.893
.797
.712
.636
.567
PV
$ 339,340
557,900
569,600
381,600
680,400
$2,528,840
NPV = $2,528,840 - $2,100,000
NPV = $428,840
Calculator solution: $428,968.70
(2)
Using a financial calculator the IRRs are:
IRRX = 16.22%
IRRY = 18.82%
Both NPV and IRR favor selection of project Y. The NPV is larger by $79,140
($428,840 - $349,700) and the IRR is 2.6% higher.
25
Part 3 Long-Term Investment Decisions
b.
Plan X
Year
1
2
3
4
5
CF
$ 470,000
610,000
950,000
970,000
1,500,000
PVIF13%,n
.885
.783
.693
.613
.543
PV
$ 415,950
477,630
658,350
594,610
814,500
$2,961,040
NPV = $2,961,040 - $2,700,000
NPV = $261,040
Calculator solution: $261,040
Plan Y
Year
1
2
3
4
5
CF
$ 380,000
700,000
800,000
600,000
1,200,000
PVIF15%,n
.870
.756
.658
.572
.497
PV
$ 330,600
529,200
526,400
343,200
596,400
$2,325,800
NPV = $2,325,800 - $2,100,000
NPV = $225,800
Calculator solution: $225,412.37
The RADR NPV favors selection of project X.
Ranking
Plan
X
Y
c.
d.
NPV
2
1
IRR
2
1
RADRs
1
2
Both NPV and IRR achieved the same relative rankings. However, making risk
adjustments through the RADRs caused the ranking to reverse from the non-risk
adjusted results. The final choice would be to select Plan X since it ranks first
using the risk-adjusted method.
Plan X
Value of real options = .25 x $100,000 = $25,000
NPVstrategic = NPVtraditional + Value of real options
NPVstrategic = $261,040 + $25,000 = $286,040
26
Chapter 10 Risk and Refinements in Capital Budgeting
Plan Y
Value of real options = .20 x $500,000 = $100,000
NPVstrategic = NPVtraditional + Value of real options
NPVstrategic = $225,412 + $100,000 = $328,412
e.
The addition of the value added by the existence of real options the ordering of
the projects is reversed. Project Y is now favored over project X using the RADR
NPV for the traditional NPV.
f.
Capital rationing could change the selection of the plan. Since Plan Y requires
only $2,100,000 and Plan X requires $2,700,000, if the firm's capital budget was
less than the amount needed to invest in project X, the firm would be forced to
take Y to maximize shareholders' wealth subject to the budget constraint.
27
Part 3 Long-Term Investment Decisions
INTEGRATIVE CASE
3
LASTING IMPRESSIONS COMPANY
Integrative Case III involves a complete long-term investment decision. The Lasting
Impressions Company is a commercial printer faced with a replacement decision in
which two mutually exclusive projects have been proposed. The data for each press have
been designed to result in conflicting rankings when considering the NPV and IRR
decision techniques. The case tests the students' understanding of the techniques as well
as the qualitative aspects of risk and return decision-making.
a.
(1) Calculation of initial investment for Lasting Impressions Company:
Press A
Press B
Installed cost of new press =
Cost of new press
$830,000
$640,000
+ Installation costs
40,000
20,000
Total cost-new press
$870,000
$660,000
- After-tax proceeds-sale of old asset =
Proceeds from sale of old press
420,000
420,000
+ Tax on sale of old press*
121,600
121,600
Total proceeds-sale of old press
(298,400)
(298,400)
+ Change in net working capital"
90,400
0
Initial investment
$662,000
$361,600
*
Sale price
- Book value
Gain
x Tax rate (40%)
$420,000
116,000
$304,000
121,600
Book value = $ 400,000 = [(.20 +.32 +.19) x $400,000] = $116,000
**Cash
Accounts receivable
Inventory
Increase in current assets
Increase in current liabilities
Increase in net working capital
$ 25,400
120,000
(20,000)
$125,400
( 35,000)
$ 90,400
28
Chapter 10 Risk and Refinements in Capital Budgeting
(2)
Depreciation
Press A
Cost
1
$870,000
2
870,000
3
870,000
4
870,000
5
870,000
6
870,000
Rate
.20
.32
.19
.12
.12
.05
Depreciation
$ 174,000
278,400
165,300
104,400
104,400
43,500
$ 870,000
Press B
1
2
3
4
5
6
Cost
$660,000
660,000
660,000
660,000
660,000
660,000
Rate
.20
.32
.19
.12
.12
.05
Depreciation
$132,000
211,200
125,400
79,200
79,200
33,000
$ 660,000
Existing
Press
1
2
3
4
5
6.,
Cost
$400,000
400,000
400,000
0
0
0
Rate
.12 (Yr. 4)
.12 (Yr. 5)
.05 (Yr. 6)
0
0
0
Depreciation
$ 48,000
48,000
20,000
0
0
0
$116,000
29
Part 3 Long-Term Investment Decisions
Operating Cash Inflows
Existing Earnings Before
Press
Depreciation
Year
and Taxes
Depreciation
1
$ 120,000
$ 48,000
2
120,000
48,000
3
120,000
20,000
4
120,000
0
5
120,000
0
6
0
0
Earnings
Before Taxes
$ 72,000
72,000
100,000
120,000
120,000
0
Earnings
After Taxes
$ 43,200
43,200
60,000
72,000
72,000
0
Press A Earnings Before
Depreciation
Year
and Taxes
Depreciation
1
$ 250,000 $ 174,000
2
270,000
278,400
3
300,000
165,300
4
330,000
104,400
5
370,000
104,400
6
0
43,500
Earnings
Before Taxes
$ 76,000
- 8,400
134,700
225,600
265,600
- 43,500
Earnings
After Taxes
$ 45,600
- 5,040
80,820
135,360
159,360
- 26,100
Cash Flow
$ 219,000
273,360
246,120
239,760
263,760
17,400
Old
Incremental
Cash Flow
Cash Flow
$ 91,200
$ 128,400
91,200
182,160
80,000
166,120
72,000
167,760
72,000
191,760
0
17,400
Press B Earnings Before
Depreciation
Year
and Taxes
Depreciation
1
$ 210,000 $ 132,000
2
210,000
211,200
3
210,000
125,400
4
210,000
79,200
5
210,000
79,200
6
0
33,000
Earnings
Before Taxes
$ 78,000
- 1,200
84,600
130,800
130,800
- 33,000
Earnings
After Taxes
$ 46,800
- 720
50,760
78,480
78,480
- 19,800
Cash Flow
$ 178,800
210,480
176,160
157,680
157,680
13,200
Old
Incremental
Cash Flow
Cash Flow
$ 91,200
$ 87,600
91,200
119,280
80,000
96,160
72,000
85,680
72,000
85,680
0
13,200
30
Cash Flow
$ 91,200
91,200
80,000
72,000
72,000
0
Chapter 10 Risk and Refinements in Capital Budgeting
(3)
Terminal cash flow:
Press A
Press B
After-tax proceeds-sale of new press =
Proceeds on sale of new press
$ 400,000
$ 330,000
Tax on sale of new press*
(142,600)
(118,800)
Total proceeds-new press
$257,400
$211,200
- After-tax proceeds-sale of old press =
Proceeds on sale of old press
(150,000)
(150,000)
+ Tax on sale of old press**
60,000
60,000
Total proceeds-old press
(90,000)
(90,000)
+ Change in net working capital
90,400
0
Terminal cash flow
$257,800
$121,200
*
Press A
Sale price
$400,000
Less: Book value (Yr. 6)
43,500
Gain
$356,500
Tax rate
x.40
Tax
$142,600
Press B
Sale price
Less: Book value (Yr. 6)
Gain
Tax rate
Tax
** Sale price
$150,000
Less: Book value (Yr. 6)
0
Gain
$150,000
Tax rate
x.40
Tax
$ 60,000
Initial Investment
Year
1
2
3
4
5*
*
Press A
Press B
$662,000
$361,600
Cash Inflows
$128,400
$ 87,600
182,160
119,280
166,120
96,160
167,760
85,680
449,560
206,880
Year 5
Operating cash flow
Terminal cash inflow
Total
Press A
$191,760
257,800
$449,560
31
Press B
$ 85,680
121,200
$206,880
$330,000
33,000
$297,000
x .40
$118,800
Part 3 Long-Term Investment Decisions
b.
Press A
|
0
$128,400
|
1
$182,160
|
2
Cash Flows
$166,120
$167,760
|
|
3
4
End of Year
$449,560
|
5
|
6
$119,280
|
2
Cash Flows
$96,160
$85,680
|
|
3
4
End of Year
$206,880
|
5
|
6
Press B
$87,600
|
1
|
0
c
Relevant cash flow
Cumulative Cash Flows
Press A
Press B
$ 128,400
$ 87,600
310,560
206,880
476,680
303,040
644,440
388,720
1,094,000
595,600
Year
1
2
3
4
5
(2)
Press A:
Payback
Payback
4 years + [(662,000 - 644,440) 191,760]
= 4 + (17,560 191,760)
= 4.09 years
Press B:
Payback
Payback
(1)
3 years + [(361,600 - 303,040) 85,680]
=
3 + (58,560 85,680)
=
3.68 years
Press A:
Year
Cash Flow
1
2
3
4
5
$ 128,400
182,160
166,120
167,760
449,560
Net present value = $697,455 - $662,000
Net present value = $35,455
Calculator solution: $35,738.83
32
PVlF14%,t
.877
.769
.675
.592
.519
PV
$ 112,607
140,081
112,131
99,314
233,322
$ 697,455
Chapter 10 Risk and Refinements in Capital Budgeting
Press B:
Year
Cash Flow
1
2
3
4
5
PVlF14%,t
$ 87,600
119,280
96,160
85,680
206,880
.877
.769
.675
.592
.519
PV
$ 76,825
91,726
64,908
50,723
107,371
$391,553
Net present value = $391,553 - $361,600
Net present value = $29,953
Calculator solution: $30,105.89
(3)
Internal rate of return:
Press A:15.8%
Press B:17.1%
d.
Net Present Value Profile
500000
450000
400000
Net Present
Value ($)
350000
300000
NPV - A
250000
NPV - B
200000
150000
100000
50000
0
0
2
4
6
8
10
12
14
Discount Rate (%)
Data for Net
Present Value Profile
Discount rate
Net Present Value
Press A
Press B
0%
$ 432,000
$ 234,000
14%
35,455
29,953
33
16
18
Part 3 Long-Term Investment Decisions
15.8%
17.1%
0
-
0
When the cost of capital is below approximately 15 percent, Press A is preferred
over Press B, while at costs greater than 15 percent, Press B is preferred. Since
the firm's cost of capital is 14 percent, conflicting rankings exist. Press A has a
higher value and is therefore preferred over Press B using NPV, whereas Press B's
IRR of 17.1 percent causes it to be preferred over Press A, whose IRR is 15.8
percent using this measure.
e.
(1)
(2)
If the firm has unlimited funds, Press A is preferred.
If the firm is subject to capital rationing, Press B may be preferred.
f.
The risk would need to be measured by a quantitative technique such as certainty
equivalents or risk-adjusted discount rates. The resultant net present value could
then be compared to Press B and a decision made.
34