SUMMARY
1. Capital Budgeting Decisions: Capital budgeting decision refers to the decision in respect of purchase or sale of fixed assets and long term investment.
CAPITAL BUDGETING DECISIONS
On the Basis of Firm Existence
Accept-Reject
You can accept one or more projects
On the Basis of Decision Situation
If you accept one project then you have to reject others Contingent
If you accept one project then you have to accept associated projects also
2. Capital Budgeting: Capital budgeting refers to application of appropriate capital budgeting technique (one or more) to evaluate any capital budgeting proposal and take capital budgeting decision.
3. Importance of Capital Budgeting Decisions: Involvement of Substantial Expenditure Long-Term Effect/Growth
Involvement of High Risk
Irreversibility
Complex Decisions
Traditional Techniques or Non-Cash Discounting or Non-Time Adjusted Technique Accounting Rate of Return or Average Rate of Return (ARR)
BUDGETING TECHNIQUES
Time Adjusted or Discounted Cash Flow (DCF) or Modern Technique
5. Book Profit v. Cash Flow:
Book Profit: It is also known as accounting profit. Cash Flow: It is focused on cash inflow and outflow and ignore all non-cash activities Proforma Book Profit and Cash Flow After Tax
Less: Tax @ 50%(XXX) Profit After Tax (Accounting or Book
Particulars `
Add: Depreciation (Non-Cash Item)(XXX)
Cash Flow After Tax (CFAT)/Cash Receipts After TaxXXX
Cash Flow After Tax (CFAT):
CFAT=PAT + Depreciation
CFAT=Cash Receipt Before Tax (1 - t) + Depreciation × t
CFAT=Cash Receipt Before Tax (1 - t) + Tax Shield on Dep.
CFAT=Cash Receipt Before Tax - Tax on PBT
6. Cash Flow & Discounted Cash Flow (DCF):
Cash Flow: Cash flow without considering time value of money.
Discounted Cash Flow: Cash flow after considering time value of money.
Discounted Cash Flow (Formulae):
Year 1= + 1 C 1k orC1 × PVIF or DF for year 1
Year 2= + 2 2 C (1k) orC2 × PVIF or DF for year 2
Sum of Discounted Cash Flow (In Case of Equal Inflow Formula):
Discounted Cash Flow = Uniform Cash Flow × PVIFA or Sum of DF
Note:
ARR Technique is based on Accounting/Book Profit
Payback Period is based on Cash Flow (Non-Discounted)
Discounted Payback, NPV, PI and IRR Techniques are based on Discounted Cash Flow
MIRR technique if based on Future/Compounded Cash Flow
Discounted Cash Flow is also known as Present Value of Cash Flow
7. Accounting/Average Rate of Return (ARR): ARR is the rate of return in terms of average book profit on investment. It can be calculated by using one of the following three methods:
Formula 1: ARR (Total Investment Basis) = Average Profit p.a. Initial Investment × 100
Formula 2: ARR (Average Investment Basis) = Average Profit p.a. Average Investment × 100
Formula 3: ARR (Annual Basis):
Step 1: Calculate Annual Rate of Return = Profit for the Year
Investment at the Beginning of Concern Year × 100
Step 2: Calculate Average Rate of Return of Annual ARR in Step 1
Note:
Average Investment = ½ × (Initial Investment + Salvage) + Additional Working Capital (If Any) Or
Average Investment = (½ × Depreciable Investment) + Salvage + Additional Working Capital
8. Payback Period (Traditional): It is refers to the period within which entire amount of investment is expected to be recovered in form of Cash.
Situation 1: Uniform Cash Receipts: Payback Period = Initial Investment Annual Cash Inflow
Situation 2: Unequal Cash Receipts:
Step 1: Calculate Cumulative Cash Inflow
Step 2: Calculate Payback Period
9. Discounted Payback Period: It is refers to the period within which entire amount of investment is expected to be recovered in form of Discounted Cash.
Step 1: Calculate Cumulative Discounted Cash Inflow
Step 2: Calculate Discounted Payback Period
10. Net Present Value (NPV): The net present value of a project is the amount, in current value of amount, the investment earns after paying cost of capital in each period.
NPV = PV of Inflow - PV of Outflow/Initial Investment Or
NPV = (PI - 1) × PV of Outflow/Initial Investment
11. Profitability Index (PI)/Desirability Factor (DF)/Present Value Index Method:
PI = PV of Inflow ÷ PV of Outflow/Initial investment Or
PI = 1 + NPV Initial Investment/PV of Outflow
Note: PI technique is useful:
In case of Capital Rationing with indivisible projects
In case of equal NPV under mutually exclusive projects
12. Internal Rate of Return (IRR): Internal rate of return refers to the actual rate of return generated by the project. Internal rate of return for an investment proposal is the discount rate that equates the present value of the expected cash inflows with the initial cash outflow.
INTERNAL RATE OF RETURN (IRR)
One Point Inflow & Outflow
RR = n Inflow Outflow - 1
Unequal Cash Inflow
Step 1: Calculate NPV by using two discount rate
One positive & one negative NPV
Step 2: Calculate IRR
IRR = L + L
Situation 1: One Point Inflow & Outflow:
IRR = n Inflow Outflow - 1
Multiple Point Inflow & Outflow
Equal Cash Inflow
Step 1: Calculate
PVIFA = InitialOutflow AnnualInflow
Step 2: Check PVIFA value in table and select IRR
Note : Student can calculate IRR in same manner as in Unequal Cash Inflow
Situation 2: Multiple Point Inflow (Unequal Cash) & Outflow:
Step 1: Calculate one positive and one negative NPV by using random discount rate
Step 2: Calculate IRR: IRR = L + () L
Where, L = Lower Discount Rate H = Higher Discount Rate
NPVL = NPV at Lower Discount Rate
NPVH = NPV at Higher Discount Rate
Situation 3: Multiple Point Inflow (Equal Cash) & Outflow:
Step 1: Calculate PVIFA at IRR: PVIFAIRR = Initial Investment Annual Cash Inflow
Step 2: Calculate IRR on the basis of PVIFA table: (a) If matched in table : Matched PVIFA rate is IRR
(b) If not matched then have to use interpolation: IRR = L + ()
13. Modified Internal Rate of Return (MIRR): The MIRR is obtained by assuming a single outflow in the zero year and the terminal cash inflow.
Step 1: Calculate cumulative compounded value of intermediate cash inflow by using cost of capital as rate of compounding.
Step 2: Calculate MIRR : MIRR = n Cumulative Compounded Value Initial Investment - 1
14. Replacement Decision: Decision in respect of replacement of an existing working machine with new one having higher production capacity or lower operating cost or both.
Step 1: Calculate Initial Outflow:
Particulars `
Purchase Cost of New MachineXXX
Less: Sale Value of Old Machine(XXX)
Less: Tax Saving on Loss on Sale of Old Machine(XXX)
Add: Tax Payment on Profit on Sale of Old MachineXXX
Add: Increase In Working CapitalXXX
Less: Decrease in Working Capital(XXX) Initial OutflowXXX
Step 2: Calculate Incremental CFAT.
Step 3: Calculate Incremental Terminal Value (net of tax).
Step 4: Calculate Incremental NPV and Take Replacement Decision.
15. Capital Rationing: Capital rationing refers to the process of selection of optimal combination of projects out of many subject to availability of funds.
Situation 1 : Projects are Divisible:
Step 1 : Calculate PI of all the available projects
Step 2 : Give Rank to all projects on the basis of PI
Step 3 : Select Projects on the basis of Rank
Situation 2 : Projects are Indivisible:
Step 1 : Calculate all possible combinations
Step 2 : Select combination of projects having higher combined NPV
16. Unequal Life of Projects: In case of comparison between two projects having different life we can solve the problem by using Equivalent Annualized Criterion:
Step 1 : Calculate NPV of the projects or PV of outflow of the projects.
Step 2 : Calculate Equivalent Annualized NPV or Outflow:
Equivalent Annualised NPV or Outflow = NPV or PV of Outflow PVIFA
Step 3 : Select the proposal having higher annualised NPV or Lower annualised outflow.
Note : Such problems can also be solved by using Common Life/Replacement Chain Method
17. Decision Under Various Techniques
TechniquesYesNo
ARRARR Desired ReturnARR < Desired Return
Traditional PaybackPayback Desired Payback Payback > Desired Payback
Discounted PaybackPayback Desired Payback Payback > Desired Payback
< 0
1PI < 1
IRRIRR Cost of CapitalIRR < Cost of Capital MIRRMIRR Cost of CapitalMIRR < Cost of Capital
18. Special Points:
Sunk Cost and Allocated Overheads are irrelevant in Capital Budgeting.
Opportunity Cost is considered in Capital Budgeting.
Working Capital introduced at the beginning of project (cash outflow) and recover (cash inflow) at the end of the project life.
Running Cost : Always Cash Cost.
Operating Cost : Variable Cost plus Fixed Cost (Including Depreciation) subject to operating cost must be > Depreciation.
Depreciation : Only as per Tax is relevant.
If nothing is specified: Depreciation as per books is assumed to be depreciation as per tax and Losses can be carry forwarded for tax benefit.
THEORY QUESTIONS THEORY
Q1. Distinguish between Net Present Value method and Internal Rate of Return method. (Nov. 2011, Nov. 2015, 4 Marks)
Ans. NPV : NPV or net present value refers to the net balance after subtracting present value of outflows from the present value of inflows. Present value
is calculated by using cost of capital as discount rate. As per NPV technique internal cash inflows are re-invested at cost of capital rate. NPV higher than zero indicates that project will provide return higher than cost of capital, zero NPV indicates that expected cash inflow will provide return equal to cost of capital and negative NPV indicates that project will fail to recover even cost of funds to be invested in proposal. Negative NPV leads to rejection of proposal. NPV is expressed in financial values and fails to provide actual rate of return associated with proposal.
IRR : IRR technique refers to actual rate of return associated with proposal. IRR refers to rate of discount at which present value of inflows and outflows are same or NPV is zero. IRR is expressed in percentage terms. As per IRR technique internal cash inflows are re-invested at IRR rate. IRR rate is compared with desired rate of return. Proposal is accepted when IRR is higher than desired rate of return and rejected when it is lower than desired rate of return.
There may be contradictory results under NPV and IRR techniques in some situations due to size disparity problem, time disparity problem and unequal expected lives.
Q2. What is ‘Internal Rate of Return’? Explain. (Nov. 2014, 2 Marks; Jan. 2021, 4 Marks)
Ans. IRR technique refers to actual rate of return associated with proposal. IRR refers to rate of discount at which present value of inflows and outflows are same or NPV is zero. IRR is expressed in percentage terms. As per IRR technique internal cash inflows are re-invested at IRR rate. IRR rate is compared with desired rate of return. Proposal is accepted when IRR is higher than desired rate of return and rejected when it is lower than desired rate of return.
Q3. Which method of comparing a number of investment proposals is most suited if each proposal involves different amount of cash inflows? Explain and state its limitations. (Nov. 2017, 4 Marks)
Ans. The best technique to compare number of investment proposals involves different amount of cash inflows is Profitability Index or Desirability Factor. In this technique present value of cash inflows is compared with present value of outflow and project is accepted if PI is 1 or above. It is calculated as :
Desirability Factor or Profitability index = PVofInflows PVofOutflows
Limitations of Profitability Index :
(1) This technique cannot be used in case of capital rationing with indivisible projects.
(2) Many times single large project with high NPV is selected and ignored various small projects with higher cumulative NPV than selected single one.
(3) There is a situation where a project with a lower profitability index may generate cash flows in such a way that another project can be also taken after one or two years later, the total NPV in such case will be higher than NPV of another project with highest Profitability Index today.
Q4. Explain the steps while using the equivalent annualized criterion. (Nov. 2019, 3 Marks)
Ans. Following are the steps involved in Equivalent Annualised Criterion :
Step 1 : Calculate NPV of the projects or PV of outflow of the projects.
Step 2 : Calculate Equivalent Annualized NPV or Outflow :
Equivalent Annualised NPV or Outflow = NPV or PV of Outflow PVIFA
Step 3 : Select the proposal having higher annualised NPV or Lower annualised outflow.
Q5. Explain the limitations of Average Rate of Return. (July 2021, 2 Marks)
Ans. Following are the limitations of ARR:
(a) The accounting rate of return technique, like the payback period technique, ignores the time value of money and considers the value of all cash flows to be equal.
(b) The technique uses accounting numbers that are dependent on the organization’s choice of accounting procedures, and different accounting procedures, e.g., depreciation methods, can lead to substantially different amounts for an investment’s net income and book values.
(c) The method uses net income rather than cash flows; while net income is a useful measure of profitability, the net cash flow is a better measure of an investment’s performance.
(d) Furthermore, inclusion of only the book value of the invested asset ignores the fact that a project can require commitments of working capital and other outlays that are not included in the book value of the project.
Q6. Identify the limitations of Internal Rate of Return.
(May 2022, 4 Marks)
Ans. Followings are the limitations of IRR:
(a) The calculation process is tedious if there is more than one cash outflow interspersed between the cash inflows; there can be multiple IRR, the interpretation of which is difficult.
(b) The IRR approach creates a peculiar situation if we compare two projects with different inflow/outflow patterns.
(c) It is assumed that under this method all the future cash inflows of a proposal are reinvested at a rate equal to the IRR. It ignores a firm’s ability to re-invest in portfolio of different rates.
(d) If mutually exclusive projects are considered as investment options which have considerably different cash outlays. A project with a larger fund commitment but lower IRR contributes more in terms of absolute NPV and increases the shareholders’ wealth. In such situation decisions based only on IRR criterion may not be correct.
PRACTICAL PROBLEMS PROBLEMS
NET PRESENT VALUE
Q1. Domestic Services (P) Ltd. is in the business of providing cleaning sewerage line services at homes. There is a proposal before the company to purchase a mechanised sewerage cleaning system for a sum of ` 20 lakhs. The present system of the company is to use manual labour for the job.
You are provided with the following information :
Proposed Machanised System :
Cost of machine ` 20 lakhs
Life of machine10 years
Depreciation (on straight line basis)10%
Cash Operating cost of machanised system ` 5 lakhs per annum
Present System (manual) :
Manual labour200 persons
Cost of manual labour ` 10,000 per person per annum
The company has after tax cost of fund at 10% per annum. The applicable tax rate is 30%.
PV factor for 10 years at 10% are as given below : Years
You are required to find out whether it is advisable to purchase he machine. Give your recommendation with workings.
(June 2015, 8 Marks)
Ans. Net Present Value
YearParticulars ` DF @ 10%PV 0Cost of Machine (20,00,000)1.000(20,00,000)
1 - 10Incremental CFAT 11,10,0006.14468,19,840 NPV48,19,840
Recommendation : Company should purchase the machine having positive NPV.
Working Notes :
Calculation of Incremental CFAT : Particulars `
Saving in labour cost (200 persons @ `10,000 p.a.)20,00,000
Less : Cash Operating cost of mechanized system p.a.(5,00,000)
Less : Depreciation(2,00,000) PBT13,00000
Less : Tax @ 30%(3,90,000) PAT9,10,000
Add : Depreciation (20,00,000 ÷ 10 years)2,00,000 CFAT11,10,000
Q2. PD Ltd. an existing company is planning to introduce a new product with projected life of 8 years. Project cost will be ` 2,40,00,000. At the end of 8 years no residual value will be realized. Working capital of ` 30,00,000 will be needed. The 100% capacity of the project is 2,00,000 units p.a. but the production and sales volume are expected as under : YearUnits 160,000 280,000 3-51,40,000 6-81,20,000
information :
3. Fixed cost p.a. ` 30,00,000.
4. In addition to these advertisement expenditure will have to be incurred as under :
5. Income tax is 25%.
6. Straight line method of depreciation is permissible for tax purpose.
7. Cost of capital is 10%.
8. Assume that loss cannot be carried forward. Present value table
Advise about the project acceptability. (Nov. 2018, 10 Marks) Ans. Net Present Value
0Initial outflows (2,40,00,000 + 30,00,000) (2,70,00,000)1.000 (2,70,00,000)
1CFAT(8,00,000)0.909(7,27,200)
2CFAT38,25,0000.82631,59,450
3 - 5CFAT 1,03,50,0002.0552,12,69,250
6 - 8CFAT89,25,0001.5441,37,80,200
8Working Capital30,00,0000.46714,01,000 NPV1,18,82,700 Company should accept the proposal having positive NPV of the project. Working Notes :
1. Depreciation = OriginalCostlessSalvage LifeofEquipment = 2,40,00,000 8Years = 30,00,000
2.Statement showing CFAT : Particulars123 - 56 - 8 Units sold60,00080,0001,40,0001,20,000 Sales @ ` 200 p.u.1,20,00,0001,60,00,0002,80,00,0002,40,00,000
Particulars123 - 56 - 8
Less : VC @ 40%48,00,00064,00,0001,12,00,00096,00,000
Contribution72,00,00096,00,0001,68,00,0001,44,00,000
Less : Advertisement expenses (50,00,000)(25,00,000)(10,00,000)(5,00,000)
Less : Cash fixed cost (30,00,000)(30,00,000)(30,00,000)(30,00,000)
Less : Depreciation(30,00,000)(30,00,000)(30,00,000)(30,00,000)
PBT(38,00,000)11,00,00098,00,00079,00,000
Less : Tax @ 25%-(2,75,000)(24,50,000)(19,75,000)
PAT(38,00,000)8,25,00073,50,00059,25,000
Add : Depreciation30,00,00030,00,00030,00,00030,00,000 CFAT(8,00,000)38,25,0001,03,50,00089,25,000
Q3. CK Ltd. is planning to buy a new machine. Details of which are as follows : Cost of the machine at the commencement ` 2,50,000 Economic life of the machine8 years
Residual valueNil
Analyse the abovementioned proposal using the
Note : The PV
