TOPIC 2 Capital Budgeting 3

8/8/2019 TOPIC 2 Capital Budgeting 3

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FN312: ADVANCED FINANCIALMANAGEMENT TOPICS


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LECTURE SERIES 2

2 Capital budgeting under risk and uncertaintyj An overview of capital budgeting techniques

j Evaluating projects with unequal lives

j Capital budgeting under risk and uncertainty


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An overview of capital budgetingtechniques

Fundamentals of capital budgeting

Capital budgeting refers to the process, which firmsfollow to make capital investment (long-term) decisions.

Capital investment decisions are decisions that involveexpenditure on assets that are expected to generatebenefits over a period of time greater than a year.

Long-term implications of investment decisions:

affect a firms future profitability, cost of capital, hencecompetitive position, Decisions are not easily reversible


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Capital budgeting techniques

The overall aim is to maximize the value of thefirm

An approach to meet the above aim should consider the following:

The time value of money/time preferences

Risk and return

Identification of all costs and benefits


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Capital budgeting techniques (cont.)

Pay back Method

Accounting Rate of Return (Book rate of return)Internal Rate of Return

Net Present Value

Profitability Index


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P ay Back Method .

Is the time required for the cumulative expected cash flows from an investment project to equal theinitial cash outflow .

E qual weights are given to all flows .

The payback method does not measure profitability but rather how quickly the original investments canbe recouped .

Decision rule:

Compare the calculated payback period (PBP) witha predetermined cut off period; Accept project withcalculated PBP < predetermined cut off period .


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Pay Back Method (cont.)

S hort Falls of the P BP :

It ignores time value of money by assigning

equal weights to all the cash flows,Cash flows received after the payback period are not evaluated .

It neglects risk and returns

S olution: To improve the applicability of PB, usediscounted PB .


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The Accounting rate of Return (ARR)

Benchmark "! ValueBook Avg.Income NetAvg.

ReturnAccountingAvg.

Decision rule:S elect projects with ARR > yard stick (standard) rate of return;

S ome deficiencies(a)Does not consider time value of money (b) It is based on the familiar accrual accounting . This do not

reflect the economic cash flows which are relevant .

(c) Since it uses the accounting data, it is sensitive to accounting valuation methods .

(d) It does not assess risk and returns


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Internal Rate of Return

The IRR is the discounting rate that equates the sumof the present value of future cash flows to the initial cash outflow . At this rate NPV = 0 .

It is based on the assumption that the future cashflow are reinvested at the IRR .

The decision rule is that accept projects whose IRRsare greater than the minimum acceptable rate (i .e . opportunity cost of capital) that considers the time

value of money, risk etc .

0)1( 01

!!

I R

F n

t t

t


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Internal Rate of Return (cont.) Advantages

Considers all cash flows Considers time value of money Assesses risk and returns

L imitations of IRR Complicated when the cash flows are non-conventional . More than one IRR when net benefits are non-conventional,

thus, difficult to decide which one to use . Contradicts with the NPV decision rule when evaluating mutually

exclusive projects with different scales . The assumption that the future cash flow are reinvested at the

IRR seems invalid . S olution: Application of modified IRR


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Modified internal rate of return (MIRR)

MIRR According to the literature, the are different

approaches to calculate MIRR . The differencebetween them is based on how -ve cash-flows that appear after the +ve are treated .

Process of calculations Compound the value of all +ve net CF to the last

period of project life (terminal value), discount thevalue of all -ve net CF to the first period (year 0) at agiven discount rate .

Then find the rate of return that sets the present value of FTV equal to the initial investment amount .


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Modified internal rate of return (MIRR)(cont r=5%)

Y r P roject A P roject BNCF ($) Discout

ed -

NCF ($)

Compau nded +

NCF ($)0 - 1000 -1000 1 200 232 2 400 441

3 500 525 4 -200 -165

-1165 1198

!

!!

n

t n

t nn

t

t

t

t

M I

k C I

k COF

0

0

1

1

1

1165 = 1198 [1/(1+MIIR)4 ]


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Net present value (NPV)N PV is the difference between the sum of the present values of

net future benefits (i.e. benefits costs) and the initial outlay.

!!

N

t t

t

R

CF NPV

0 1

Decision rule: accept projects with positive N PV

Advantages Consistent with the maximisation of the shareholders wealth

Consider time value of moneyAssess risk and returnsAll cashflows are considered in the evaluations

Disadvantages Difficult to explain to non-finance people as the calculated figure is

in dollars, not percentage rates of return, May lead to inappropriate decision when evaluating projects with

different lives .


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Profitability Index (PI)

P I is t he ratio of the

P resent

V alue of a projects futurenet cash flows to the projects initial cash flow

0

1 )1( I

k

F n

t t

t !

Decision rule: accept projects with P I > 1.

Advantages Method is closely similar to NPV . E asy to understand and communicate . [Ratio gives the return

(added value) in the present terms per unit invested]

Can be used to rank projects (instead of using NPV) when availablefunds are limited .

S elected in the order of ranking up to the point where thebudget is exhausted.

Disadvantage

May lead to incorrect decision when comparing mutually exclusive projects


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The equivalent annual annuity method

Approach

Calculate the NPV for each project The NPV is converted into annuity (i .e . an equivalent amount

received at fixed intervals, e .g . annually) .

NPV = Annuity [ 7 t 1/(1+r) t ] Annuity = NPV/ [ 7 t 1/(1+r) t ] Accept the project with the highest annuity .

U se the e .g .. to calculate the annuity

Project A: NPV = 2255, n = 3. Project B: NPV = 2988, n = 5, r is 5%.

Find out which project should be accepted?


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The replacement chain approach

Approach Find the a common life span of the project under

consideration, assuming that the projects will berenewed indefinitely (in our eg. The common lifespan for project A and B is 15).

Then, calculate N PV for each project. S elect the one with the highest N PV . Apply the this method to the previous eg.The method is cumbersome when the evaluation

consists of multiple projects. Thus, the equivalent annual annuity method is preferable.


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Seminar question 1

Project X: initial investment: Tshs 40 million;

Cash flows: Y ears 1 to 6: Tshs 8m, 14m, 13m, 12m,11m, 10m respectively .

Project Y : initial investment: Tshs 20 million;Cash flows: Y ears 1 to 3: Tshs 7m, 13m, 12mrespectively .

If the Opportunity Cost of Capital = 12% and the projects are mutually exclusive which one should beselected? (Show how the two methods you have learnt will be applied)


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Seminar question 2

Y ear Investment A ($) Investment B ($)

0 -100 -100

1 50 20

2 40 -40

3 40 50

4 -30 60

If the required rate of return = 10%, use the MIRR to evaluate the abovemutually exclusive investments and suggest which one should beselected


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LECTURE SERIES 2

2 Capital budgeting under risk and uncertainty

j An overview of capital budgeting techniques

j Evaluating projects with unequal lives

j Capital budgeting under risk and uncertainty

Basics of risk and uncertainty

Approaches used to estimate risk


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Basics of risk and uncertainty

Risk and profitability are closely related

Any investor needs to assess the risk associatedwith alternative investments before makingdecision. If an investment project will make a firm to be more

riskier, investors may not favour it. An increase in risk will lead to a fall in market price of a share

(and the value of a firm) . Thus, the need to incorporate risk in capitalbudgeting


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Basics of risk and uncertainty (cont.)Among the steps under capital budgeting process is the estimationof future cash flows associated with the project to be evaluated.Estimates are just estimates based on some assumptions: Expected sales (PxQ), expected costs, effectiveness of

advertisement campaign, efficiency of the operations. The estimates will depend on the future external factors:

The market environment: purchasing power of people, size of the market, and competition .

Political environment: Policy changes, peace/conflict .

Other economic factors: inflation, state of the economy ingeneral (boom or recession) etc .

Any change in external factors may lead to changes in expectedsales, costs, and returns.

Thus, the actual cash flows will not precisely equal the estimatesdone before the execution of the project, THU S RISK .


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Basics of risk and uncertainty(cont.)

RISK is the variation of the actual returns(monetary value) from the estimates.

There are three capital budgeting decisionsituations related to risk analysis: Risk situation Uncertain situation Certain situation

There is a slight difference between risk anduncertainty (for our level, they will be usedinterchangeably).


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Approaches used to estimate risk

S ensitivity analysisS tandard deviation

Coefficient of variation


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Sensitivity analysis

This offers information on to how sensitive theestimated project parameters (cash flows,discount rate, project life, etc.) are to estimationerrors.The errors arise because the future is uncertain.

S ensitivity analysis is based on what if analysis. Eg. What if the operating cost increases by 10%

What if the actual sales turn out to be less by 5%S everal NPVs are estimated based on what if analysis, then look on their variabilities.


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Sensitivity analysis (cont.)

S ensitivity analysis can further bestructured into scenario analysis, whichcategorises cash flow estimates based onthree assumptions: The worst scenario (the most pessimistic), The expected/average (the most likely), The best scenario (the optimistic).


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Sensitivity analysis (cont. eg.)

P roject X P roject Y Initial cash outlay Rs 40,000 Rs 40,000 Cashflow

estimates (t=1-15

Worst Rs 6,000 Rs 0

Most likely Rs 8,000 Rs 8,000

Best Rs 10,000 Rs 16,000 If the required rate of return for both projects = 10%, both

have economic life = 15 years, E stimate the NPV for each project under different scenario .


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Sensitivity analysis (cont.)

The decision regarding the project to undertake willdepend on the attitude of decision-makers toward risk: Risk aversers will go for project X, while risk takers will go for Y.

Advantage of the sensitivity analysis: It gives additional information on the variability of expected

returns (NPV) given expected changes in environmental factors.Disadvantage: It does not disclose the chances of occurrence of the cash flows

under different scenarios

S olution: S ensitivity analysis, adjusted for probabilities


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Sensitivity analysis adjusted for probabilities (cont.)

Assign probabilities on the forecasted net

cash flows for each year (or NPV under different scenario)

Estimate the expected return (or NPV),which is the same as the weightedaverage return (or NPV).


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Sensitivity analysis (cont. eg.)

N PV for P roject X N PV for P roject Y Rs Rs

Worst 5,636 -40,000

Most likely 20,848 20,848

Best 36,060 81,696

At 10% and period of 15 years, the PVIFA = 7 .606


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Sensitivity analysis adjusted for probabilities (cont.e.g. project X)

N PV for P roject X

Probabilities of the NPV

occurrenceNPV x

Probabilities

Rs Rs

Worst 5,636 0 .25 1,409

Most likely 20,848 0 .50 10,424

Best 36,060 0 .25 9,015

1 .00

E xpected NPV (weighted average NPV) 20,848


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Sensitivity analysis adjusted for probabilities (cont.eg. project Y)

N PV for P roject Y

Probabilities of the NPV

occurrenceNPV x

Probabilities

Rs Rs

Worst -40,000 0 .25 -10,000

Most likely 20,848 0 .50 10,424

Best 81,696 0 .25 20,424

1 .00

E xpected NPV (weighted average) 20,848


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Sensitivity analysis adjusted for probabilities(contEg. Assume the discounting rate = 10%)Y

ear 1Y

ear 2 Y

ear 3

CF prob value CF prob value CF prob value

3000 0.25 750 3000 0.5 1500 3000 0.25 750

6000 0.50 3000 6000 0.25 1500 6000 0.25 1500

8000 0.25 2000 8000 0.25 2000 8000 0.50 4000

Expected CF 5750 5000 6250 PV DF 0.909 0.825 0.751

P resent V of expected CF

5227 4130 4694 14051


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Assignment 3: Assume the discounting rate = 10% and the initialinvestment is Rs 12,000; evaluate the project below and give

suggestion on whether the project should be undertaken

Y ear 1 Y ear 2 Y ear 3

CF

(Rs)

prob value CF

(Rs)

P rob value CF

(Rs)

prob

1500 0.20 2000 4000 0.15

4000 0.50 6500 0.15 9000 0.60

5000 0.30 9000 0.65 2000


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Sensitivity analysis adjusted for probabilities (cont.)

Major limitation: The sensitivity analysis adjusted for

probabilities only gives the expected return(i.e. expected monetary value) but does notgive a concrete value indicative of variability,i.e. Risk.

Thus, the need to apply other measures of risk (i.e. standard deviation and coefficient of variation).


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Standard deviation and coefficient of variation

Both measures are used to estimate thevariability associated with expected cashflows.S tandard deviation is used when theprojects involve the same outlay (i.e. initialinvestment),

Coefficient of variation is applied when theprojects to be compared have differentcash outlays.


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Standard deviation

S tandard deviation is an absolute measure of risk

It is defined as the square root of the mean of squareddeviation

Deviation is the difference between the outcome and theexpected mean value of outcomes.

n

= (CF i - CF) 2

n

WW 7 7 i=1

n


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Standard deviation (cont.)

Given probabilities, the expected meanvalue of outcomes is the weighted averagevalue of outcomes and the standarddeviation is calculated as follows

= (CF i - CF) 2 P (CF i )WW 7 7 i=1

n


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Standard deviation (cont.) (eg. project X)

CF i CF CF i -CF (CF i CF) 2 P (CF i ) P (CF i ) (CF i CF) 2

($) ($) ($) ($) ($)

5636 20848 -15,212 231404944 0.25 57851236

20848 20848 0 0 0.5 0

36060 20848 15,212 231404944 0.25 57851236

115702472

10756.5 =WW 115702472 =

CF = 77i=1

n

CF i P (CF i )


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Standard deviation (cont.) (e.g.. project Y)


($) ($) ($) ($) ($)

-40,000 0.25

20848 0.5

81696 0.25

=WW =

CF = 77i=1

n

CF i P (CF i )


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Standard deviation (cont.) (eg. project Y)


($) ($) ($) ($) ($)

-40,000 20848 -60,848 3702479104 0.25 925619776

20848 20848 0 0 0.5 0

81696 20848 60,848 3702479104 0.25 925619776

1851239552

43026,03=WW 1851239552 =


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Standard deviation (cont.)

Project Xs S td deviation = 10756.5

Project Ys std deviation = 43026.03

Both projects have equal weighted NPV (i.e. $20,848) but project Y is more riskier than projectX.

Decision rule: S elect project X.

Limitation of Std deviation : Unable to evaluateprojects with unequal cash outlays. S olution: Use the coefficient of variation method


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Coefficient of variation (CV)

CV is a relative measure of risk

CV for project X = ( 10756.5)/ 20848 = 0.515 W hat is the C V for project Y?

The higher the CV the higher the riskS ince the CV adjusts for the size of the project,then it is a better measure of risk than the S tddeviation.

CV =S tandard Deviation

Expected cash flow

Or WW

CF


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Risk-Adjusted Discount Rate Approach(RAD) (cont..)

Once the risk is measure usingthe CV (or Beta), it need to beincorporated in capitalbudgeting decision throughRAD approach.

Under RAD, the risk isincorporated in the discountrate used to estimate thepresent value of cash flows.

The projects with relativelyhigh risk will have relativelyhigh discount rates, and thereverse hold for relatively lowrisky projects.

C and RAD

. . .6

C

R A D ( )

RAD


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Further application of probabilitydistribution to capital budgeting

Application of the probability distribution inanalysing risk depends on the behaviour of cashflow.

The behaviour of cash flows (CFs) can beviewed as: Independent

Future cash flows are not affected by the cash flows in the

preceding or following years . Dependent

Cash flow in one period depend upon the cash flow in the previous period


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Probability distribution, capital budgetingunder independence of cash flows

Procedures:1. Estimate the expected CF (weighted average

cash flow) for each period

In the above formula, j stands for the probable outcomes (1,2,3i) in a givenperiod (a year)

2. Estimate the NPV for the project for theentire life.

CF = 77 j=1

m

CF j P (CF j )

NPV = 77t=1

n

CF t

(1+k)t


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Previous E.g. under Sensitivity analysis adjusted for probabilities(contEg. Assume the discounting rate = 10%)


CF prob value CF prob value CF prob value

3000 0.25 750 3000 0.5 1500 3000 0.25 750

6000 0.50 3000 6000 0.25 1500 6000 0.25 1500

8000 0.25 2000 8000 0.25 2000 8000 0.50 4000

Expected CF 5750 5000 6250

PV DF 0.909 0.825 0.751


5227 4130 4694 14051


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Probability distribution, capital budgetingunder independence of cash flows (cont.)

3. Estimate theS

td Deviation of the probability distributionof NPV HOW?

Calculate the standard deviation of the distribution of cash flow for each year

Estimate the overallS

td deviation on the NPV

= (CF j - CF) 2 P (CF j )WWXX 77 j=1

m

=WW 77t=1

n WWXX(1+k)2t


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Standard deviation for year 1


($) ($) ($) ($) ($)

3000 5750 -2750 75 2500 0.25 1890 25

6000 5750 250 2500 0.50 31250

8000 5750 2250 50 2500 0.25 12 5 25

3187500

1785.35 =WW 3187500 =


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($) ($) ($) ($) ($)

3000 5000 -2000 4000000 0.5 2000000

6000 5000 1000 1000000 0.25 250000

8000 5000 3000 9000000 0.25 2250000

4500000

2121.32 =WW 4500000 =


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($) ($) ($) ($) ($)

3000 6250 -3250 105 2500 0.25 2 40 25

6000 6250 -250 2500 0.25 15 25

8000 6250 1750 30 2500 0.50 1531250

4187500

2046.33=WW 4187500 =


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3. Estimate theS

td Deviation of the probability distributionof NPV HOW?

Calculate the standard deviation of the distribution of cash flow for each year

Estimate the overallS

td deviation on the NPV

= (CF j - CF) 2 P (CF j )WWXX 77 j=1

m

=WW 77t=1

n WWXX(1+k)2t


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Estimate the overall S td deviation on the NPV

=WW 3187500 +(1+0.1) 2

4500000 +

(1+0.1) 4

3187500

(1+0.1)


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Assignment 4: Assume the discounting rate = 10% and the initialinvestment is Rs 12,000; Assume the cash flows are independent,

estimate the risk associated with this project


CF

(Rs)

prob value CF

(Rs)

P rob value CF

(Rs)

prob

1500 0.20 2000 4000 0.15

4000 0.50 6500 0.15 9000 0.60

5000 0.30 9000 0.65 2000


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Further application of probabilitydistribution to capital budgeting (cont.)

After estimating the standard deviation and theweighted average NPV, it is possible to use theprobability distribution to find our the probability

of having diffent levels/values of NPV. E.g.: probability of NPV being greater or equal to zero. probability of NPV being lower than zero. Probability of NPV = Probability of NPV falling between --- and ----

The assumption here is that the probabilitydistribution of NPVs is normal.


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Further application of probabilitydistribution to capital budgeting (cont.)

The assumption here is that the probabilitydistribution of NPVs is normal.

8.2%

X WWWW

d l d d f b b l


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Previous E.g. under Sensitivity analysis adjusted for probabilities(contEg. Assume the discounting rate = 10%; Initial investment

is $12,000)


CF ($) prob V alue($)



3000 0.25 750 3000 0.5 1500 3000 0.25 750

6000 0.50 3000 6000 0.25 1500 6000 0.25 1500

8000 0.25 2000 8000 0.25 2000 8000 0.50 4000

Expected CF 5750 5000 6250

PV DF 0.909 0.825 0.751


5227 4130 4694 14051


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What is the expected (i.e. weighted average)NPV of the project? (assume that the probabilitydistribution are independent)What is the standard deviation related to theexpected?Find the probability that the NPV will be ZEROor LESS ?

What is the probability that the NPV will begreater than ZERO?What is the probability that the NPV will bebetween $ 2000 and $7,000?

Previous E.g. cont.


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What is the expected (i.e. weighted average) NPV of the project?(assume that the probability distribution are independent)

NPV = $14,051 - $12,000 = $2,051What is the standard deviation related to the expected?

= $ 2740

Previous E.g. cont.

NPV = 77

t=1

nP resent value of CF t initial investment

=WW 3187500 +

(1+0.1) 2

4500000 +

(1+0.1) 4

3187500

(1+0.1)


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Find the probability that the NPV will be ZERO or LE SS ? Calculate the Z-value

Previous E.g. cont.

Z = 0 - X WW

Z = 0 - N PV WW

Z = 0 - $2,051

$ 2740= -0.74

The probability that the NPV will be ZERO = 0.5- 0.2704 = 0.229 (i.e. around 30 %) In this case, the lower the probability, the lower the risk the

project is


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Decision Tree (DT) Approach

Useful in a situation whereby Decision at one point in time affect a decision at the

later point,

Project requires decisions to be taken in sequentialmanner.

The DT indicates the probabilities, magnetudeand dependence (inter-relationship) betweenoutcomes.

It shows the sequential cashflows and NPV of the proposed project under differentcircumstances.


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Decision Tree (DT) Approach

Useful in a situation whereby Decision at one point in time affect a decision at the

later point,

Project requires decisions to be taken in sequentialmanner.

The DT indicates the probabilities, magnitudeand dependence (inter-relationship) betweenoutcomes.

It shows the sequential cash flows and NPV of the proposed project under differentcircumstances.


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Decision Tree (DT) Approach (cont..)

CF 1=$1 00

CF1=$2000

CF1=$2400

CF1=$800

CF1=$1000

CF1=$1500

t=1

CF 1=$1300

CF 1=$1500

CF 1=$1 00

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88.5

1 8.2

CF 1=$400

CF1=$1000

CF1=$1500

t=2 NPV$

-9 .8

-488-

-90.1

14.7

933.5

1252.3

CF 0=$2000

t=0

K =12%


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CF0 CF1 PVDF

PV of CF

1 CF2 PVDF2

PV of CF

2 NPV

JointProbabilit

y (JP)

JP*NP

V2000 800 0.893 714.4 400 0.797 318.8 -9 .8 0.0 -58.008

2000 800 0.893 714.4 1000 0.797 797 -488. 0.18 -87.948

2000 800 0.893 714.4 1500 0.797 1195.5 -90.1 0.0 -5.40

2000 1000 0.893 893 1300 0.797 103 .1 -70.9 0.12 -8.508

2000 1000 0.893 893 1500 0.797 1195.5 88.5 0.1 14.1

2000 1000 0.893 893 1 00 0.797 1275.2 1 8.2 0.12 20.184

2000 1500 0.893 1339.5 1 00 0.797 1275.2 14.7 0.03 18.441

2000 1500 0.893 1339.5 2000 0.797 1594 933.5 0.24 224.04

2000 1500 0.893 1339.5 2400 0.797 1912.8 1252.3 0.03 37.5 9

1

Expected/WA-NPV 154.5


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Assignment 5

Do the following questions for discussionin seminars:

Q .13; Q .15Do others with tick for increasing your knowledge.

TOPIC 2 Capital Budgeting 3

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