Chapter 10: The Basics of Capital Budgeting: Evaluating
Cash Flows
1. Answer Questions 10-1 thru 10-6 on pp. 412-413.
2. Answer Problems 10-1 thru 10-12 on pp. 414-415.
Discussion
Questions (DQs)
10.1: Answers
a) Capital Budgeting; Regular Payback Period;
Discounted Payback Period
Capital Budgeting: Capital Budgeting is a process used by
companies to evaluate and decide which projects or investments are better to
choose. In other words, it is a profit-maximization tool that many companies
use it to make the better decision from available alternatives. However,
capital budgeting decisions depend on an analysis of the cash flows generated
by the projects or investments and costs. It usually involves the calculation
of each project's future accounting profit by period, the cash flow by period,
the present value of the cash flows after considering the time value of money,
the number of years it takes for a project's cash flow to pay back the initial
cash investment, an assessment of risk, and other factors.
Regular Payback Period: Regular payback period refers to the length
of time required to recover the initial costs of investment. A company may have
a target payback period, with any project taking longer than the target period
being rejected. However, it does not consider the time value of project and
targeting length of time is also quite difficult to set.
Discounted Payback Period: The discounted payback period can be defined
as the length of time it takes the discounted net cash revenue or cost savings
of a project to recover the initial investment. Its calculation takes into
account the time value of money by discounting each cash flow before the
cumulative cash flow is calculated, and determine the time at which the net
present value becomes positive.
b) Independent Projects; Mutually Exclusive
Projects
Independent Projects: The projects whose cash flows have no impact
on the acceptance or rejection of other projects are called independent
projects. In these kinds of projects, choosing one projects does not affect
another so that we can accept any projects if they seem profitable to us.
Mutually Exclusive Projects: The projects whose cash flows have potential
impact on the acceptance or rejection of other projects are called mutually
exclusive projects. In these projects, choosing one project may affect the
choosing of another so that projects should be analyzed properly to accept any
project from several alternatives.
c) DCF techniques; Net Present Value (NPV)
Method; Internal Rate of Return (IRR) Method; Profitability Index (PI)
DCF Techniques: Discounted cash flow (DCF) technique is a
method of evaluating a project, company, or asset using the concepts of the
time value of money. All future cash flows are estimated and discounted by
using cost of capital to give their present values (PVs). The sum of all future
cash flows, both inflows and outflows, is the net present value (NPV), which is
taken as the value or price of the cash flows in any projects.
Net Present Value (NPV) Method: Net present value (NPV) of a project is the
potential change in an investor's wealth caused by that project while time
value of money is being accounted for. It equals the present value of net cash
inflows generated by a project less the initial investment on the project. It
is one of the most reliable measures used in capital budgeting because it
accounts for time value of money by using discounted cash flows in the
calculation. It can be calculated in the following two conditions:
NPV = R × [1 - (1 + i)-n /i] - Initial Investment (When cash
inflows are even)
NPV =R1 /(1 + i)1+R2 /(1 + i)2 +R3 /(1 + i)3+
...-Initial Investment (When cash flows are uneven)
Internal Rate of Return (IRR) Method: Internal Rate of Return, often simply
referred to as the IRR, is the discount rate that causes the net present value
of future cash flows from an investment is equal to zero. When multiple
investments are being considered, IRR should not be used as the primary
appraisal tool because NPV analysis provides a better measure of the impact of
different projects on the shareholder wealth. IRR should still be used,
however, as a risk assessment tool to measure the sensitivity of different
investment options towards the cost of capital.
Profitability Index (PI): Profitability index is an investment
appraisal technique calculated by dividing the present value of future cash
flows of a project by the initial investment required for the project. It can
be written as:
Profitability Index = Present Value of Future Cash Flows / Initial
Investment Required
Profitability index is actually a modification of the net present value
method. While present value is an absolute measure (i.e. it gives as the total
dollar figure for a project), the profitability index is a relative measure
(i.e. it gives as the figure as a ratio).
d) Modified Internal rate of Return (MIRR)
Method: It is a
rating tool, which helps in making investment decisions. The modified internal
rate of return (MIRR) method is a modification of the internal rate of return
method, also known as the IRR method.
e) NPV Profile; Crossover rate
NPV Profile: It represents an NPV profile charts the net
present value of a business activity as a function of the cost of capital. This
comparison allows decision-makers to determine the profitability of a project
or initiative in different potential financing scenarios, enabling more
effective cost-benefit planning.
Crossover Rate: It is the cost of capital at which the net
present values of two projects are equal. It is the point at which the net
present value profile of one project crosses over (intersects) the net present
value profile of the other project.
f) Nominal cash flow projects, normal cash
flow projects, multiple IRRs
Non-normal cash flow Projects: It is
a project with pattern of cash flows in which the direction of cash flows
changes more than once. It is also termed as unconventional cash flow.
Normal cash flow Projects: It is a project with pattern of cash flow
stream that comprises of initial investment outlay and then positive net cash
flow throughout the project life. It is also called conventional cash flow
stream.
Internal rate of return (IRR): It is a rate of return used in capital
budgeting to measure and compare the profitability of investments.
g) Reinvestment rate Assumption: It is the amount of interest that can be
earned when money is taken out of one fixed-income investment and put into
another. The reinvestment rate is of particular interest to people holding
short-term investments. In other words it is invested that are again
reinvesting in another field where the return can be achieved and thus that
result to increase the investment amount.
h) Replacement Chain; Economic life; Capital
Rationing; Equivalent Annual Annuity
Replacement
Chain: The Replacement
Chain Method is a capital budgeting decision model that is used to compare two
or more mutually exclusive capital proposals with unequal lives. In Replacement
Chain Analysis, the Net Present Value (NPV) is determined for each proposal.
Economic Life: Economic life is an amount of time, as
determined by the IRS, that an asset is expected to be used. The economic life of
an asset could be different than the actual physical life of the asset.
Capital rationing: Capital rationing is the process of
selecting the most valuable projects to invest available funds. This is
accomplished by imposing a higher cost of capital for investment consideration
or by setting a ceiling on the specific sections of the budget.
Equivalent Annual Annuity: Equivalent annual annuity (EAA) is an
approach used in capital budgeting to choose between mutually exclusive
projects with unequal useful lives. The project with higher equivalent annual
annuity is preferred.
10. 2 Answer:
Capital budgeting can be used for planning process in order to determine
whether an organization's long term investments are worthwhile funding of cash
through the firm's capitalization structure or not. So the projects with high
risk need to be projected with greater accuracy applying the data analysis
techniques with more detailed analysis whereas projects with low risk need to
be projected with lower accuracy applying the data analysis techniques with
less detailed analysis (Brigham & Ehrhardt, 2011). In addition to that,
those projects whose exchange of current funds are for future benefits, whose
funds are invested in long-term assets and whose benefits will occur to the
firm over a series of years in the capital budgeting require the most detail
analysis and vice-versa.
10.3 Answer
NPV assumes that
project’s cash flows are discounted in companies cost of capital. Long-term
projects are more sensitive to change in cost of capital than short-term
projects. It is because higher the term to maturity lesser the discounted cash
flow of the project. For example, Project X has maturity period 5 years and
Project Y has maturity period of 10 years, both have 10% of cost of capital,
and both have $500 cash flow every year. Then,
Cash flow for Project X = (454.54 + 413.22 + 375.65)
Cash flow for Project Y = (454.54 + 413.22 + 375.65 + 341.53 + 310.37)
Now, when cost of capital increase from 10% to 12%
Cash flow for Project X = (446.42 + 398.72 + 355.87)
Cash flow for Project Y = (446.42 + 398.72 + 355.87+ 318.97 + 284.09)
As it can be seen in the
example, the value of cash flow of $500 is getting lower and lower year after
year. Again when cost of capital
increases from 10% to 12% the value of discounted cash flow of $500 is lower
more. As it can be noticed, when cost of capital rises from 10% to 12% the
discounted cash flow for the short term project also reduce but not as lower as
for long term project and since they have short-term maturity the effect will
be lower. Therefore, long-term projects higher percentages of cash flows are
expected and more sensitive to change in interest rate.
10.4 Answer:
Mutually
exclusive projects are those on which it is necessary to choose either project
one or project two, or reject both project, but both project cannot be accepted
at a time. Long-term projects are more sensitive to changes in the
cost of capital than short- term project. Therefore short-term project might
have higher rank under the NPV criterion if the cost of capital is high. While
if cost of capital is lower, a project with long term maturity will be ranked
better as total sum of cash flows of long term project will be higher than
short term project.
Yes
the change in the capital does cause a change in the IRR ranking of two such
projects. For that capital should be change for two of those projects. If
capital change for only short term or only long term project then IRR ranking
may not change (Brigham
& Ehrhardt, 2011).
10.5 Answer:
NPV, IRR, and MIRR are rate of return that
enables firm or project to identify whether to accept or not. It is certainly
true that all of these techniques have different assumption but their objective
is the same. Out of all these three, I would say NPV is the best. NPV is based
on discounted cash flow technique. Firm’s cost of capital is assumed
reinvestment rate of NPV. IRR is the discount rate that makes NPV equal to
zero. IRR assumed the cash flows are reinvested at project’s rate of return. Modified
Internal Rate of Return assumes that firm’s inflows are compounded at firm’s
cost of capital and then determine the discounted rate that makes present value
of the terminal value equal to the present value of outflows (Brigham &
Ehrhardt, 2011).
10-6 Answer:
It is true that bias exists in NPV analysis
against one of the projects, if firm is considering two mutually exclusive
projects and a firm fails to employ replacement chain analysis. Let examine a
project that has life of 10 years has more cash flows coming in later years and
the project which has a life of 5 years has more cash flow coming in early
years so that it seems that NPV analysis favors the project with maturity
period of 5 years but in reality a project that has maturity period of 10 years
could be better. Therefore, if firm is analyzing two mutually exclusive
projects with different maturity period then they have to employ replacement
chain analysis to see the true picture of NPV of both the project.
It is, therefore, obvious that the failure to
employ some type of replacement chain analysis bias an NPV analysis against one
of the projects because it gets no credit for profits beyond its initial life,
even though it could provide additional NPV. Thus they have to employ
replacement chain analysis to see the true picture of NPV of both the project.
References
C.
Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi:
New Age International Publishers.
Brigham,
E. F., & Ehrhardt, M. C.(2011). Financial management: theory and
practice (11th ed.). Mason, Ohio: South-Western
Cengage Learning.
10-1. Solution:
Here given,
Initial cost = $52,125
Expected net cash inflows = $12,000
Cost of capital = 12%
Life of project = 8 years
Project NPV=?
Here,
NPV = -Initial cost + Cash inflows (PVIFA k, n)
= -$52,125 + $12,000
(PVIFA 12, 8)
= -$52,125 + $12,000 *
4.9676
=$7,486.20
Therefore, the project's NPV is $7486.2 and we should accept the
project.
10-2.Solution:
Here we have,
As we know,
Factor = Cash outflow or NCO / Average cash inflow = $52125 / $12000 =
4.3437
The factor 4.3437 lies very nearly at 16% years in a present value of an
annuity table.
Trying at IRR = 16%
We know, at IRR, NPV = 0,
Thus, - $52,125 + $12,000 (PVIFA, 16%, 8) = 0
Or, - $52,125 + $12,000 *
4.3436 = 0
Or, - $52,125 + $52,123.2 =
0
Or,
($1.8) = 0
IRR = 16%
Therefore, the IRR of this project is 16% which is more than cost of
capital (12%) so we should accept this project.
10-3. Solution:
Here we have,
Future values of the cash inflows = cash
inflows * FVIFA K, n
= $12,000 * FVIFA 12%, 8
=$12,000 * 12.300
=$147,600
Then, Present Value of NCO * (1 + MIRR) n = Future values of the cash
inflows
Or, $52,125 * (1 + MIRR) 8 = $147,600
Or, MIRR = ($147,600 / $ 52,125)1/8 – 1
= 13.89%
Therefore, we should accept this project because the MIRR of this
project is 13.89% which is greater than cost of capital (12 %).
10-4. Solution:
Here we have,
Profitability index
(PI) = PV of future cash flows i.e. TPV / Initial cost i.e. NCO
= $12,000 (PVIFA 12, 8) / Initial cost
= $12,000 * 4.9676 / $52,125
= $59,611.20 / $52,125
= 1.14
Therefore, the profitability Index of the project is 1.14 so this
project should be accepted.
10-5. Solution:
We have,
Payback
Period = Net cash outflow i.e. NCO / Net cash inflows per year
=$52,125/$12,000
= 4.34 years
Therefore, Payback period of the project is 4.34 years.
10-6. Solution:
For the discounted payback period,
The project’s discounted payback period is calculated as follows:
Year Annual CF Discounted CF Cumulative
(@12%) Discounted
CF
0 ($52,125) - ($52,125)
1 12,000 $10,714.29 (41,410.71)
2 12,000 9,566.33 (31,844.39)
3 12,000 8,541.36 (23,303.02)
4 12,000 7,626.22 (15,676.81)
5 12,000 6,809.12 (8,867.69)
6 12,000 6,079.57 (2,788.11)
7 12,000 5,428.19 2,640.08
8 12,000 4,846.60 7,486.68
Therefore, the project’s discounted payback period is 6 years +
[$2,788.11/ $5,428.19] = 6.51 years (approximately).
10-7. Solution:
Here given,
a) Calculation of NPV at the different cost of capital, k= 5%, 10% and
15%
For Project A:
Year Cash flows (In Millions)
PVIF @ 5% PV@ 5% (M) PV @ 10%(M) PV @ 15%(M)
1 $5 0.9524
$4.76 $4.55 $4.35
2 10 0.9070 9.07 8.26 7.56
3 20 0.8638 17.23 15.03 13.15
Total Present value (TPV) 31.06 27.84 25.06
Less: NCO -15 -15 -15
NPV $16.06 $12.84 $10.06
Here, Project A has NPV of $16.06 Million at k=5%, $12.84 Million at
k=10% and $10.06 Million at k=15%.
This shows that the value of NPV decreases with the increment in the
cost of capital.
For Project B:
Year Cash
flows (In Millions) PVIF @ 5% PV@ 5% (In Millions) PV @ 10%(In Millions) PV
@ 15%(In Millions)
1 $20 0.9524 $19.05 $18.18 $17.39
2 10 0.9070 9.07 8.26 7.56
3 6 0.8638 5.18 4.51 3.94
Total Present value (TPV) 33.3 30.95 28.89
Less: NCO -15 -15 -15
NPV $18.3 $15.95 $13.89
Here, Project B has NPV of $18.3 Million at k=5%, $15.95 Million at
k=10% and $13.89 Million at k=15%.
This shows that the value of NPV decreases with the increment in the
cost of capital.
b) Calculation of IRRs for both the projects at the given costs of
capital:
For Project A:
We try taking any one of the costs of capital i.e. at 10% discount rate
to calculate the IRR as follows:
Calculating NPV (a) at different IRRs, 30%, 35% and so on until NPV is
negative.
Year Cash flow (In Millions) PV@30% (M)PV@35% (M) PV@40% (M) PV@45% (M)
0 ($15) ($15)
($15) ($15) ($15)
1 5 3.85
3.70 3.57 3.45
2 10 5.92
5.5 5.10 4.75
3 20 9.10
8.13 7.29 6.56
NPV 3.87 2.33 0.96 (0.24)
Through Interpolation
IRR = 40% + [{0.96 / {0.96 + 0.24}] (45% -
40%) = 44%
For Project B:
We try taking any one of the costs of capital i.e. at 10% discount rate
to calculate the IRR as follows:
Calculating NPVa at different IRRs, 25%, 30% and so on until NPV is
negative.
Year Cash flow (In Millions) PV@70% (Millions) PV@75% (Millions) PV@80% (Millions) PV@85%
(Millions)
0 ($15) ($15) ($15) ($15) ($15)
1 20 11.76 11.43 11.11 10.8
2 10 3.46 3.26 3.1 2.92
3 6 1.22 1.12 1.03 0.95
NPV 1.44 0.81 0.24 (0.33)
Through Interpolation
IRR = 80% + [{0.24 / {0.24 + 0.33}] (85% - 80%) = 82.11%
Therefore, Internal Rate of Return is 82.11%
10.8. Solution:
For Truck:
NPV:
Initial cost (NCO) = $17,100
After tax cash flows (CFAT) = $5,100
Life (n) = 5 years
Cost of capital (k) = 14%
NPV = TPV - NCO
= CFAT x PVIFA, k, n - NCO
= $5,100 (PVIFA 14, 5) - $17,100
= $5,100x 3.4331 - $17,100
=$408.81
Since the project’s NPV is $408.81. Since NPV
is positive, accept the decision.
For IRR:
Step 1: Factor = NCO / Annual CFAT = $17100 /
$5100 = 3.3530
Step 2: Referring the PVIFA table at 5 years
row, the factor 3.3530 lies between 14% (3.4331) and 15% (3.3522)
Step 3: Through Interpolation, IRR = LR + [(FLR – Factual) / (FLR – FHR)] (HR
– LR)
=
14% + [(3.4331 – 3.3530) / (3.4331 – 3.3522)] (15% - 14%)
= 14.990%
Since IRR is greater than the given cost of
capital, so it is acceptable.
For MIRR:
Here, Future values of the cash inflows =
cash inflows * FVIFA K, n
=
$5100 * FVIFA 14%, 5
=$5100 * 6.6101
=$33711.51
Then, Present Value of NCO * (1 + MIRR) n =
Future values of the cash inflows
Or, $17100 * (1 + MIRR) 5 = $33711.51
Or, MIRR = ($33711.51 / $ 17100)1/5 – 1 =
14.54%
MIRR = 14.54%
Since MIRR is greater than cost of capital
because it has 14.54% and thus it is greater and therefore, the decision is
accepted.
For Pulley:
We have given in question:
Initial cost (NCO) = $22,430
After tax cash flows (CFAT) = $7,500
Life (n) = 5 years
Cost of capital (k) = 14%
Then,
NPV =
TPV - NCO
= CFAT x PVIFA, k, n - NCO
= $7500 (PVIFA 14, 5) - $22,430
= $7500x 3.4331 - $22,430
=$3318.25
Since the NPV is positive, which is dollar
3318 positive, thus, the decision is accepted.
For IRR:
Step 1: Factor = NCO / Annual CFAT = $22430 /
$7500 = 2.9906
Step 2: Referring the PVIFA table at 5 years
row, the factor 2.9906 is exactly equal to 20%
Therefore, try at IRR = 20%
We know, at IRR, NPV = 0,
Thus, - $22430 + $7500 (PVIFA, 20%, 5) = 0
Or,
- $ 22430 + $7500* 2.9906 = 0
Or, 0= 0
Here, the project’s IRR is 20%.
Since IRR is greater than the given cost of
capital, so it is acceptable.
MIRR:
Here, Future values of the cash inflows =
cash inflows * FVIFA K, n
=
$7500 * FVIFA 14%, 5
=$7500 * 6.6101
=$49575.75
Then, Present Value of NCO * (1 + MIRR) n =
Future values of the cash inflows
Or, $22430 * (1 + MIRR) 5 = $49575.75
Or, MIRR = ($49575.75 / $22430)1/5 – 1
= 17.19%
Since MIRR is greater than the required cost
of capital. So the decision is acceptable.
10-9. Solution:
Here given:
For Mutually exclusive investment
We have,
The required rate of return, k = 12%
Gas Electric
Cash outflows (cost), NCO: $17,500 $22,000
Net cash inflows for 1-6: $5000 $6290
Life of trucks: 6 years 6 years
1. Calculation of NPV and IRR for Gas-powered
forklift truck:
NPV:
NPVG = TPV - NCO
= $5000 (PVIFA 12, 6) - $17500
= $5000 x 4.1114 - $17500
=$3057
IRR:
Factor=$17500 / $5000 = 3.5
The factor 3.5 lies nearly at 18% for 6 years
in PV of an annuity table. Thus, try at IRRG = 18%
-$17500 (PVIF 18%, o year) + $5000(PVIFA 18%,
6 years) = 0
-$17500 x (1) + $5000 x (3.4976) = 0
$12=0
IRRG = 18%
2. Calculation of NPV and IRR for
Electric-powered forklift truck:
NPV:
NPVE = TPV - NCO
= $6290 (PVIFA 12, 6) - $22000
= $6290 x 4.1114 - $22000
=$3861
IRR:
Factor=$22000 / $6290 = 3.4976
The factor 3.4976 lies exactly at 18% for 6
years in PV of an annuity table. IRRE = 18%
Decision:
Although, IRR of both types of truck have
same percent the NPV of electric powered forklift truck is higher than NPV of
Gas powered truck, thus electric powered forklift truck should be purchase.
10-10. Solution:
Herr given:
For Mutually exclusive investment project(S
and L)
The required rate of return, k = 12%
Project S Project L
Cash outflows (cost), NCO: $10,000 $25,000
Net cash inflows for 1-5: $3,000 $7,400
Life of trucks: 5 years 5 years
1. Calculation of NPV, IRR, MIRR and PI for
Project S:
NPV:
NPVS= TPV - NCO
= $3000 (PVIFA 12, 5) - $10000
= $3000 x 3.6048 - $10000
=$814.4
IRR:
Factor=$10000 / $3000 = 3.3333
The factor 3.3333 lies between 15% (3.3522)
and 16% (3.2743) for 5 years in PV of an annuity table.
Thus by interpolation: IRR = LR + [(FLR –
Factual) / (FLR – FHR)] (HR – LR)
= 15% + [(3.3522 – 3.3333) / (3.3522 – 3.2743)] (16% - 15%)
= 15.24%.
MIRR:
Here, Future values of the cash inflows =
cash inflows * FVIFA K, n
=
$3000 * FVIFA 12%, 5
=$3000 * 6.3528
=$19058.4
Then, Present Value of NCO * (1 + MIRRS) n =
Future values of the cash inflows
Or, $10000 * (1 + MIRRS) 5 = $19058.4
Or, MIRRS = ($19058.4 / $10000)1/5 – 1
= 17.19%
PI:
PIS =
PV of future cash flows i.e. TPV / Initial cost i.e. NCO
= $3000 (PVIFA 12, 5) / Initial cost
=
$3000 * 3.6048 / $10000
=
1.081
2. Calculation of NPV, IRR, MIRR and PI for
Project L:
NPV:
NPVL= TPV - NCO
= $7400(PVIFA 12, 5) - $25000
= $7400 x 3.6048 - $25000
=$1675.52
IRR:
Factor=$25000 / $7400 = 3.3784
The factor 3.3784 lie between 14% (3.4331)
and 15% (3.3522) for 5 years in PV of an annuity table.
Thus by interpolation: IRRL = LR + [(FLR –
Factual) / (FLR – FHR)] (HR – LR)
= 14% + [(3.4331 – 3.3784) / (3.4331 – 3.3522)] (15% - 14%)
= 14.67%.
MIRR:
Here, Future values of the cash inflows =
cash inflows * FVIFA K, n
=
$7400 * FVIFA 12%, 5
=$7400 * 6.3528
=$47010.72
Then, Present Value of NCO * (1 + MIRRL)n =
Future values of the cash inflows
Or, $25000 * (1 + MIRRL) 5 = $47010.72
Or, MIRRL = ($47010.72 / $25000)1/5 – 1
= 13.46%
Again,
PI:
PIL = PV of future cash flows i.e. TPV /
Initial cost i.e. NCO
= $7400 (PVIFA 12, 5) / Initial cost
= $7400 * 3.6048 / $25000
= 1.067
For
Decision:
Since, NPVL> NPVS, and IRRS> IRRL,
MIRRS> MIRRL, and PIS> PIL. However, NPV is higher in Project L, and thus
L should be chosen. Because we choose to prefer the NPV having positive value
with higher amount and thus it is project L.
10-11. Solution
Here given,
Here, K=12%, mutually exclusive projects, n=4
years
For Project X
MIRR:
Here, Future values of the cash inflows
= $100 x FVIF 12%, 3 +$ 300 x FVIF 12%,
2 + $400 x FVIF 12%, 1 + $700 x FVIF 12%, 0
= 100 x 1.4049 + 300 x 1.2544 + 400 x 1.1200
+ 700 x 1
= $1664.81
Then, Present Value of NCO * (1 + MIRRL)n =
Future values of the cash inflows
Or, $1000 * (1 + MIRRL) 4 = $1664.81
Or, MIRRX = ($1664.81 / $1000) 1/5 – 1
= 13.59%
For Project Y
MIRR:
Here, Future values of the cash inflows
= $1000 x FVIF 12%, 3 +$100 x FVIF 12%,
2 + $50 x FVIF 12%, 1 + $50 x FVIF 12%, 0
= 1000 x 1.4049 + 100 x 1.2544 + 50 x 1.1200
+ 50 x 1
= $1636.34
Then, Present Value of NCO * (1 + MIRRL)n =
Future values of the cash inflows
Or, $1000 * (1 + MIRRY) 4 = $1636.34
Or, MIRRY = ($1636.34 / $1000) 1/5 – 1
= 13.10%
Decision:
Since MIRR project X > MIRR project Y,
Thus Project X should be chosen.
10-12. Solution:
a. Given:
Purchase price $ 900,000
Installation Cost $165,000
Initial outlay (NCO) $1,065,000
Estimated cash flows for 1-5 years = $350,000
Cost of Capital (K) = 14%
NPV= TPV - NCO
= $350000 (PVIFA 14, 5) - $1065000
= $350000 x 3.4331 - $1065000
=$136,578
IRR:
Factor=$1065000 / $350000 = 3.043
The factor 3.043 lie between 19% (3.0576) and
20% (2.9906) for 5 years in PV of an annuity table.
Thus by interpolation: IRR= LR + [(FLR –
Factual) / (FLR – FHR)] (HR – LR)
=
19% + [(3.0576 – 3.043) / (3.0576 – 2.9906)] (20% - 19%)
= 19.22%
b. The project should be undertaken because its NPV is positive and its
IRR is greater than the firm's cost of capital which is a good sign of
investment.
c. Environmental effects should be considered as estimating penalties
which might be imposed on the firm to help return the land to its previous
state. These outflows could be so large as to cause the project to have a
negative NPV in case of decision of part b.
References
C.
Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi:
New Age International Publishers.
Brigham, E. F., & Ehrhardt, M. C.(2011). Financial
management: theory and practice (11th ed.). Mason, Ohio: South-Western
Cengage Learning.
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