capital budgeting
TRANSCRIPT
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CAPITAL BUDGETING
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What is Capital Budgeting ? Capital budgeting is the process of evaluating and
selecting long term investments that are consistentwith the goal of shareholders wealth maximistioncriterion.
Capital Budgeting is employed to evaluate expendituredecisions which involve current outlays but are likelyto produce benefits over a period of time longer thanone year. These benefits may be in the form ofincreased revenue or decreased cost.
Capital Exp Mgt. therefore addition, disposition,modification and replacement of FA.
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Basic Features of Capital Budgeting Potentially large anticipated benefits
A relatively high degree of risk
Long gestation period
Importance of Capital Budgeting Such decisions effect profitability of firm
They have an effect on competitive position of the firm as they relate to FAand they enable firms to generate finished goods and thus profit
They are strategic investment decisions as against tactical which involverelatively smaller amounts, thus a major departure may be a possibilityleading to a significant impact on companies' expected profits.
Has effect over a long time span & thus effects companies future cost structure.
CExp Dec once made are not easily reversible without much financial loss
Involves huge cost and thus prudent and thoughtful use becomes important.
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Difficulties Benefits from investments are received in some future
period. Future is uncertain, therefore an element ofrisk is involved.
Secondly: costs incurred and benefits received fromthe capital budgeting decisions occur in different timeperiods . They are not logically comparable because oftime value of money.
Thirdly, it is not often possible to calculate in strictquantitative terms all the benefits of the costs relatingto a particular investment decision.
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The rationale underlying the capital budgetingdecision is efficiency. Thus replacement of obsolete orworn out P&M; acquiring of FA for current and newproducts are among the main objective of CBDecisions.
Capital budgeting decisions can be of two types: Decisions affecting revenues
Decisions affecting costs
Rationale:
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Types of Investment Decision:
There are many ways to classify investment decisions; one suchway is as follows:
Expansion of Existing Business
Expansion of New Business
Replacement and Modernisation
Expansion and Diversification: To increase plant capacity is anexample of expansion and to venture into a completely new area isdiversification.
Replacement and Modernaisation: The main objective of R&Mdecisions is to improve operating efficiency and reduce costs.
Another way of classification is as follows: Mutually exclusive investments
Independent investments
Contingent investments.
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Investment Evaluation Criteria:
Three steps are involved in the evaluation of an investment: Estimation of Cash flows Estimation of the required rate of return (the opportunity cost of
capital) Application of a decision rule for making the choice
Investment decision rule: A sound appraisal techniqueshould be used to measure the economic worth of aninvestment project. The ultimate objective is to maximisethe shareholder’s wealth. The following characteristicsshould be possessed by a sound investment evaluationcriterion:
It should consider all cash flows to determine the true profitability ofthe project
It should provide for an objective and an unambiguous way ofseparating good projects from bad projects
It should help ranking of projects according to their true profitability
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It should recognize the fact that bigger and earlier cash flows arepreferable to smaller and delayed ones respectively.
It should help to choose among mutually exclusive projects whichmaximizes shareholder’s wealth.
It should be a criterion which is applicable to any conceivableinvestment project independent of others.
The cash flow approach for measuring benefits is theoretically superiorto the accounting profit approach because:
Avoids the ambiguity of the accounting profits concept
Measures the total benefit
Takes into account the time value of money.
Accounting Profit Vs Cash
Flow Approach
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Investment Evaluation Criteria
The methods of appraising capital expenditure
proposals can be classified into two broad
categories:
1) Traditional (Non-Discounted Cash Flow Criteria)
a) Average Rate of Return (ARR)
b) Pay back period (PB)
2) Time adjusted (Discounted Cash Flow Criteria – DCF)
a) Net Present Value Method
b) Internal Rate of Return method
c) Net Terminal Value Method
d) Profitability Index (PI)
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TRADITIONAL TECHNIQUES
This is also known as accounting rate of return method. It isbased on accounting information rather than cash flows.There are a no. of methods for calculating ARR:
ARR= (Av Annual PAT / Av Inv over the life of the proj.)X 100
Av PAT = AfTx Pr expected for each yr / No of years
Av Inv = Net Inv /2
The averaging process also assumes that the firm is using straight line method ofdepreciation. Book value of the asset declines at a constant rate from its purchase price tozero at the end of its depreciable life. This means that on an average firms will have ½ oftheir initial purchase price in the books.
And if the machine has a salvage value then only the depreciable cost of the machine shouldbe divided by 2 in order to ascertain the average net investment… as the salvage money willbe recovered only at the end.
Average investment = NWC + Salvage Val + ½ (initial cost of machine – salvage val)
1.Average rate of return: (ARR)
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Eg:
Mch A Mch B
Cost 56,125 56,125
An Estimated inc (aft D & T)
Yr. 1 3375 11375
Yr. 2 5375 9375
Yr. 3 7375 7375
Yr. 4 9375 5375
Yr. 5 11375 3375
36875 36875
Estimated Life 5yrs 5yrs
Estimated Salvage Val 3000 3000
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ARR = (Av Inc / Av Inv) X 100Av Inc of Mch. A & B 36875 /5 = 7375Av Inv = Salvage Val + ½ (Cost of Mch. – Salvage Val)Rs. 3000 + ½ (Rs. 56,125 – Rs 3000) = Rs. 29, 562.50ARR for Mch. A& B = Rs. (7375/ 29562.50) X 100= 24.9%
ACCEPT REJECT RULE
ARR would be compared with a predetermined or aminimum required rate of return or cut off rate. Aproject would qualify to be accepted if the actualARR is higher than that desired ARR. Alternativelythe ranking method could be used.
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Evaluation of the ARR:
Favorable Attributes :Figures are easily availableEasy to understand
Drawbacks:Uses the Accounting income instead of Cash flows.Does not take into a/c time value of money Does not take into a/c size of investment required for each project.Competing investment proposals may have the same ARR but mayrequire different av. investmentsMethod does not take into consideration any benefits which can accrueto the firm from the sale or abandonment of equipment which isreplaced by the new investment. (The new inv From the pt of view of correctfinancial decision making should be measured in terms of incremental cash outflows due tonew investment i.e. new inv – sale proceeds of existing equipment +/- tax adjustment)
Machines Av An Earnings
Average Inv
ARR %
A Rs 6000 Rs. 30,000 20
B 2000 10,000 20
C 4000 20,000 20
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2. PAY BACK PERIOD
This method answers the question: how many yearswill it take for the cash benefits to pay the original costof an investment? (normally, disregarding salvagevalue)
The pay back method measures the number of yearsrequired for the CFAT to pay back the original outlayrequired in an investment proposal.
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There are two ways of calculating PBP
1) When cash flow is in the nature of an annuity:PB=(Inv/Const. annual Cash Flows)Eg: Inv of Rs. 40,000 in a mch is expected to produce a CFAT of Rs.8000. PB = 40000/8000 = 5 yrs.
2) When cash flows are not uniform: (Mixed Stream)PB,here is determined by cumulating cash flows till thetime when cumulative cash flows become equal tooriginal investment outlay.
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Annual CFAT Cumulative CFAT
Yr. Mch.A Mch.B Mch.A Mch.B
1 14000 22000 14000 22000
2 16000 20000 30000 42000
3 18000 18000 48000 60000
4 20000 16000 68000 76000
5 25000 17000 93000 93000
CFAT in the 5th yr includes Rs.3000 salvage val.
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Initial Inv of Rs.56,125 on Mch.A will be recovered between 3rd & the 4th yr.
56,125-48,000 = 8,125/20,000 = 0.406
(CFAT) = 3.406 yrs.
Similarly the other one is 2.785 yrs.
ACCEPT REJECT CRITERION:Compare actual with predetermined if actual PB is < Predetermined PB the project will be accepted & vice-versa. Alternatively a ranking method can be used in case of mutually exclusive projects.
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MERITS / DEMERITS
MERITS:1) Easy to Calculate & Simple to Understand
2) It is based on cash flow rather than Accounting Profits
DEMERITS:1) Completely ignores cash flows after the pay back period
2) It does not measure correctly even the cash flows expected to bereceived within the pay back period as it does not differentiatebetween projects in terms of the timing or magnitude of cash flows. Itconsiders only the recovery period as a whole. (it ignores the timevalue of money)
3) It does not take into consideration the entire life of the projectduring which cash flows are generated. As a result project with largecash inflows will be in the later part of their lives may be rejected infavour of less profitable projects.
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1. Net present Value Method It is a DCF Technique that explicitly recognizes the
time value of money.
NPV may be described as the summation of PresentValues of Cash Proceeds (CFAT) in each year minusthe summation of the present values of the net cashoutflows in each yr.
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It is described as the summation of the present values of cash proceeds (CFAT) in each year minus the summation of present values of the net cash outflows in each year.
NPV = CFt + Sn + Wn - CO0
t=1 (1+K)t (1+K)n
0
1
NPV = (1 + )
nt
tt
CC
k
K = Discount Rate
CFt = Cash Inflows at different time periods
Sn, Wn = (salvage val & Wkg Cap adjustments)
CO0 = initial cash outlay
COt
(1+K)tC= Cash Flows
K= Opportunity
cost of capital
C0 = initial cost of
inv.
n= expected life
of investment
Summation of Pr.Val of Cash proceeds in each
yr – Summation of Pr Val of Cash outflows in
each yr.
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Mch-A 56,125 Mch-B 56,125
Yr CFAT PV Factor (0.10)
(rate of disc 10%)
PV CFAT PV Factor
(0.10)
PV
1 14000 0.909 12726 22000 0.909 19998
2 16000 0.826 13216 20000 0.826 16520
3 18000 0.751 13518 18000 0.751 13518
4 20000 0.683 14660 16000 0.683 10928
5 25000 0.621 15525 17000 0.621 10557
69,645 71,521
Rs. Rs.
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The decision rule for a project under NPV is to acceptthe project if the NPV is positive and reject if it isnegative.
IF NPV>0 Accept & if NPV<0 Reject & a firm withNPV=0 is also practically rejected.
Evaluation: The method has several MERITS:
1. It recognizes time value of money. (For e.g. the total cash
inflows (CFAT) of both machines are equal, but the PV as well as
the NPV are different. (This is because of the difference in pattern
of cash flows – magnitude of cash fl. CFAT for machine A is lower
than B in the initial years.
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2) It also fulfills the second attribute of a sound method of appraisal as itconsiders the total benefit arising out of the proposals over its life.
3) A changing discount rate can be built into the NPV calculations by alteringthe denominator. (This feature becomes important as this rate normallychanges – because the longer the time span, the lower is the value of moneyand the higher is the discount rate.)
4) The Present Value method is logically consistent with the goal ofmaximizing share holder’s wealth. (If NPV = O, the ROI just equals theexpected or required rate by investors… but if PV exceeds the outlay of NPVthe return would be higher than expected and as such lead to an increase inshare prices)
DEMERITS:1) It is difficult to compute and understand as compared to the PB or the ARR
method.
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2) It involves the calculation of the required rate of return to discountcash flows. The discount rate is very important as different disc.Rates will give different PVs. (The cost of capital k is generally thebasis of the discount rate.)
3) It is an absolute measure (The method favours projects with higherPV / NPV)… but some projects may involve a large initial outlay. SoNPV method is not suitable where projects involve different outlays.The result is not very dependable.
4) Also this method is not suitable in case of projects having differenteffective lives. (Projects with shorter economic life would bepreferable.) But Projects having a high PV may also have a largereconomic life and the funds will remain invested for a longer timewhile the alternative proposal may have a shorter time period but alower PV too.
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2. IRR - Method
• It is defined as the discount rate (r) which equates the
aggregate present value of the net cash inflows (CFAT)
with the aggregate PV of cash outflows of a project.
• It is the rate that equates the investment outlay with the
PV of cash inflows received after 1 period.
n
0 = CFt + Sn + Wn - CO0
t=1 (1+r)t (1+r)n
n
0 = CFt + Sn + Wn - COt
t=1 (1+r)t (1+r)n t=0 (1+r)t
For Conventional
Cash flows
For Un-conventional Cash flows
R = internal rate of returnCFt = Cash Inflow at different Time periodsSn = Salvage ValueWn = Working Capital AdjCot = Cash Outlay at Different time periodsCo0 = Initial Outlay
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In case of NPV the discount rate is the required rate of returnand being a predetermined rate usually the cost of capital, itsdeterminants are external to the proposal under consideration.The IRR on the other hand are based on facts which are internalto the proposal.
In other words while arriving at the required rate of return forfinding out present value: the cash flows - inflows as well asoutflows are not considered. But the IRR depends entirely onthe initial outlay and the cash proceeds of the project which isbeing evaluated for acceptance or rejection. Therefore it is calledinternal rate of return.
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Point of difference between NPV & IRR (k) Here is not calculated on the basis of cash inflow and cash outflow but
rather on initial outlay and cash proceeds of the project under consideration.
The basis of discounting factor is different in both cases: in NPV the disc rate isthe required rate of return and is predetermined. (on the basis of factorsexternal to the proposal)
Computation
• The calculation procedure depends on whether the cash flow is in
the nature of an annuity or mixed stream
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Calculation in case of an annuity
STEPS REQUIRED
1. Determine the pay back period of the proposed investment
2. From the present value table of an annuity look for the pay back period that is equal to or closest to the life of the project
3. In the year row find two PV values or discount factors closest to PB period but one bigger and the other smaller than it
4. From the table note the corresponding PV values
5. Determine actual IRR by interpolation.
PB - DFr
IRR = r - -----------------------------------
DFrL – DFrH
PB = Pay Back Period
DFr= Discount Factor for Interest rate r
DFrL = Discount Factor for lower interest rate
DFrH = Discount Factor for higher interest rate
r = either of the 2 interest rates used in the formula.
PVco – PVCFAT
IRR = r - ----------------------------------- X ▲ r
PV
PVco = Present Value of Cash Outlay
PVCFAT = Present Value of Cash Inflows (DFr X Annuity)
r = either of the 2 interest rates used in the formula.
▲ r = Difference in interest rates
PV = Difference in calculated PV of inflows.
OR
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A project cost Rs. 36,000 and is expected to generate cash inflows of Rs. 11,200 annually for 5 years. Calculate the IRR of the project.
Step I: Determine the Pay Back PeriodRs.36,000/Rs.11,200 = 3.214
Step II: Refer to PV table for annuity
Disc factor closest to 3.214 for 5 yrs are 3.274(16%)
and 3.199 at (17%)
Step III: Now determine the actual ARR lying between the two values.
IRR = r- [ (PB – DFr) / (DFrl - DFrh) ]
= 16 + [ (3.274 -3.214)/ (3.274-3.199)] = 16.8%
alternatively,
17 – [(3.214 – 3.199)/(3.274-3.199)] = 16.8%
Can also use the interpolation formula:
PV CFAT = (0.16) = Rs. 11,200 X 3.274 = Rs. 36,668.8
PV CFAT = (0.17) = Rs. 11,200 X 3.199 = Rs. 35,828.8
IRR = 16+ [(36,668.8 – 36,000)/ (36,668.8-35,828.8)]X 1 = 16.8%
IRR = 17- [(36,000 – 35,828.8)/ (36,668.8-35,828.8)]X 1 = 16.8%
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For a Mixed Stream of Cash Flows: STEPS1) Calculate the average annual cash inflow to get a fake annuity
2) Determine ‘fake PB period’ dividing the initial outlay by the average annual CFATdetermined in step 1
3) Look for the factor in the annuity table closest to the fake PB value in the samemanner as in the case of annuity. The result will be a rough approximation of theIRR, based on the assumption that the mixed stream is an annuity (fake annuity)
4) Adjust subjectively the IRR obtained in step 3 by comparing the pattern ofaverage annual cash inflows as per step 1 to the actual mixed stream of cashflows. If the actual cash flow stream happens to be higher in the initial years ofthe project’s life than the average stream, adjust the IRR a few % point upwards.(Reason: the greater recovery of funds in the earlier years are likely to give ahigher yield rate.
5) Find out the PV of the mixed cash flows using the PV table taking the IRR as thediscount rate as estimated in step 4
6) Calculate the PV using the discount rate. If the PV of CFAT equals the initialoutlay, i.e. NPV=0, it is the IRR, otherwise repeat step 5. Stop as soon as the twoconsecutive discount rates that causes the NPV to be +ve & -ve is arrived at.Whichever of these two rates causes the NPV to be closest to 0 is the IRR to thenearest 1%
7) The actual value can be ascertained by the method of interpolation as in the caseof an annuity.
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The same example taken
earlier: Mch A Mch B
Cost 56,125 56,125
An Estimated inc (aft D & T)
Yr. 1 3375 11375
Yr. 2 5375 9375
Yr. 3 7375 7375
Yr. 4 9375 5375
Yr. 5 11375 3375
36875 36875
Estimated Life 5yrs 5yrs
Estimated Salvage Val 3000 3000
Annual CFAT Cumulative CFAT
Yr. Mch.A Mch.B Mch.A Mch.B
1 14000 22000 14000 22000
2 16000 20000 30000 42000
3 18000 18000 48000 60000
4 20000 16000 68000 76000
5 25000 17000 93000 93000
CFAT in the 5th yr includes Rs.3000 salvage val.
Cash Flows
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1) The sum of cash inflows of both machines is Rs. 93,000 ÷ 5yrs (ec. life) = 18,600 fake annuity
2) Fake av. PB period: 56,125 (initial outlay) ÷ 18,600 = 3.017yrs.
3) From the PV table of Annuity the factor closest to 3.017 for 5yrs is 2.991 for a rate of 20%
4) Since the actual cash flows in the earlier years are greaterthan the average cash flows of Rs. 18,600 in machinery B asubjective increase of say 1% is made. This makes anestimated IRR of 21% for machinery B. In case of machineryA since cash inflows in the initial years are smaller than theaverage cash flows, a subjective decrease of say 2% is made.This makes the estimated IRR for machinery A at 18%
Sol. using IRR:
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5) Using the PV factor of 21% for M-B and 18% for M-A, the PVs are calculated as follows by referring to the PV table.
Mch-A 56,125 Mch-B 56,125
Yr CFAT PV Factor (0.18) Total PV CFAT PV Factor (0.21) Total PV
1 14000 0.847 11,858 22000 0.826 18,172
2 16000 0.718 11,488 20000 0.683 13,660
3 18000 0.609 10.962 18000 0.564 10,152
4 20000 0.516 10,320 16000 0.467 7,472
5 25000 0.437 10,925 17000 0.386 6,562
Total PV 55,553 56,018
Less Initial Inv: 56,125 56,125
NPV -572 -107
Rs. Rs.
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6) Since NPV is negative for both the machines the discount rate shouldsubsequently be lowered. In case of machinery A the difference is Rs.572 whereas in machinery B the difference is Rs. 107. Therefore in theformer case the discount rate is lowered by 1% in both the cases. Thenew disc rate is : 17% for A and 20% for B.
7) Now do fresh calculations at the above rates:
Mch-A 56,125 Mch-B 56,125
Yr CFAT PV Factor (0.17) Total PV CFAT PV Factor (0.20) Total PV
1 14000 0.855 11,970 22000 0.833 18,326
2 16000 0.731 11,696 20000 0.694 13.880
3 18000 0.624 10,232 18000 0.579 10,422
4 20000 0.534 10,680 16000 0.484 7,712
5 25000 0.456 11.400 17000 0.442 6,834
Total PV 56,978 57,174
Less Initial Inv: 56,125 56,125
NPV 853 1,049
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8) For M-A, 17 & 18% discount rates consecutively gives +ve &-ve NPVs. Applying method of interpolation we get:
M-A : IRR = 17+ [(56978-56125)/56978-55553)]X 1= 17.6%
M-B : IRR = 20+ [(57174-56125)/57174-56018)] X 1 = 20.9%
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Evaluation of IRR:
Merits:
It considers the time value of money
It takes into a/c total cash inflows and outflows
It is easier to understand for lay people as they may have difficulties inunderstanding NPV
It also is consistent with shareholders objective
Demerits:
First it involves tedious calculations
Next it produces multiple rates which is confusing
Thirdly in evaluating mutually exclusive proposals the project with the highestIRR would be picked up to the exclusion of all others. But practically it may notbe so..
Finally under the IRR it is assumed that all intermediate cash flows arereinvested at the IRR . In the example above we saw M-A & M-B has an IRR of17.6 and 20.9 % rsp. and as such can be reinvested at these rates, which isridiculous that the same firm has the ability to reinvest the cash flows atdifferent rates. There is no difference in quality of cash received from project A & B. Moreover, it is not that
all cash may be reinvested, they may be retained back or distributed as dividends.
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3. TERMINAL VALUE METHOD
The terminal value approach even more distinctlyseparates the timing of cash inflows and outflows. Theassumption behind the TV approach is that each cashinflow is reinvested in another asset at a certain rate ofreturn from the moment it is received until thetermination of the project.
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Accept/Reject Rule: The decision rule is that the PV of the sum total of the compounded
reinvested cash inflows (PVTS) is greater than the PV of the outflows(PVO)
PVTS>PVO = Accept
PVTS<PVO = Reject
Advantage:
1) It explicitly incorporates the assumption about how the cash inflows are reinvested once they are received and avoid any influence of cost of capital on cash inflow stream itself.
2) It is mathematically easier
3) Is easier to understand
4) it is better suited to cash budgeting requirements
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4. Profitability Index Method
Yet another time adjusted Capital budgeting technique is the PIor the Benefit Cost Ratio (B/C) method. It is similar to NPVapproach.
It measures the PV of returns per rupee invested, while the NPVis based on the PV of future cash inflows and PV of future cashoutflows.
A major shortcoming of the NPV method is that being anabsolute measure it is not a reliable method to evaluate projectsrequiring different initial investments. The PI method provides asolution to this kind of a problem. PI= (PV of Cash Infl/PV ofCash Outfl) Numerator measures benefit and denominatorCosts. Therefore B/C method.
Accept Reject Rule: PI >1 accept otherwise reject
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Capital Budgeting Practices in India
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Example 1:
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Example 2:
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Capital Rationing: Capital Rationing refers to the choice of investment proposals
under financial constraints in terms of a given size of capitalexpenditure budget. The objective to select the combination ofprojects would be the maximisation of total NPV. Project selectionunder capital rationing involves 2 stages: (1) identification of theacceptable projects (2) Selection of the combination of projects.The acceptability of projects can be based either on PI or IRR. Themethod of selecting investment projects under capital rationingsituation will depend upon whether the projects are indivisible ordivisible. In case the project is to be accepted or rejected in itsentirety, it is called an indivisible project ; a divisible project on theother hand can be accepted/rejected in part.
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Exercises on capital rationing
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iiheh
Q3
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