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CBT-NPV,BCR,IRR
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Md. Nehal AhmedAssociate Professor, BIBM
Capital Budgeting Capital Budgeting TechniqueTechnique
Capital Budgeting Process
Capital Budgeting is the process of planning expenditures on assets whose cash flows are expected to extend beyond one year.
Capital budgeting refers to the investment decision involving fixed asset of a firm. The term capital refers to the fixed assets used in production and budget is a plan that details projected inflows and outflows during some future periods.
Thus capital budget in an outline of planned expenditures on fixed assets and capital budgeting is the process of analyzing projects and deciding which are acceptable projects.
Classification of Projects
By project size
By type of benefit
By degree of dependence
By type of cash flow
Steps Involved in Capital Budgeting
Determine the cost of the asset.
Estimate the cash flows expected from the asset. Evaluate the risk of the projected cash flows to
determine the appropriate rate of return.
Compute the PV of the expected cash flows.
Compare the present value of the expected cash inflows with initial investment.
Time Value of Money
Future Value: The amount an investment is worth after one or more periods.
Compounding: The process of accumulating interest on an investment over time
to earn more interest.
Present value:The current value of future cash flows discounted at the appropriate discount rate.
Discount: Calculate the present value of some future amount.
Time Value of Money
Future value of the investment for n periods at a rate i percent per period is
ni1PVFV
The present value of a cash flow due n years if it were on hand today, would grow to equal the future amount.
ni1FVPV
Capital Budgeting Evaluation Techniques
The basic methods we will discuss are:
• Payback period (PBP)• Discounted Payback Period• Net Present Value (NPV)• Benefit Cost Ratio (BCR)• Internal Rate of Return (IRR)
Payback Period
• Payback period is defined as the length of time or expected member of years required to recover the original investment.
• To compute a projects pay back period, simply add up the expected each flows for each year until the commutative value is equal to the total amount initially invested.
Example: Payback Period
The exact period can be found using the following formula:
Year 0 1 2 3 4 Net cash flow -3,000 1,500 1,200 800 300 Cumulative net cash flow -3,000 -1,500 -300 500 800
yearerycovrefullduringflowcashTotalyearerycovrefullofstartattcoseredcovUnre
investmentoriginaloferycovrefullbeforeYears
Payback
years4.28003002Payback,AojectPrFor
years27.315004003Payback,BojectPrFor
Discounted Payback Period
The discounted payback period is the length of time until the sum of discounted cash flows is equal to the initial investment.
Example: Calculate the discounted payback period for projects A with discount rate 10%
Year 0 1 2 3 4 Cash Flow -3,000 1,500 1,200 800 300 Discounted Cash Flow -3,000 1363.64 991.74 601.05 204.90 Cumulative net cash flow (discounted) -3,000 -1636.36 -644.62 -43.57 161.33
years2.390.204
57.433PaybackDiscounted,AojectPrFor
Net Present Value
Net present value (NPV) is a measure of how much value is created or added today by undertaking an investment.
capital budgeting process can be viewed as a search for investments with positive net present values.
NPV relies on discounted cash flow (DCF) techniques, which is the process of valuing an investment by discounting its future cash flows. NPV is computed using the following equation:
0
n
1tt
t0n
n2
21
1 Ik1
CFI
k1CF
k1CF
k1CF
NPV
Example: Net Present Value
Considering project A when k = 10% 0 K = 10% 1 2 3 4
(3,000) 1,500 1,200 800 300
1,363.64
991.74
601.05
204.90
Tk. 161.33
Cash flow
NPVA =
33.161.Tk3000
1.1300
1.1800
1.1200,1
1.1500,1NPV 4321A
Decision Criteria for NPV
If NPV > 0, accept the project.
If NPV < 0, reject the project.
If NPV = 0, the firm would be indifferent to the project.
Benefit Cost Ratio
Profitability index (PI) or benefit cost ratio is defined as the present value of the future cash flows divided by the initial investment.
If a project has a positive NPV, then the present value of the future cash flows must be bigger than the initial investment.
The profitability index would thus be greater than 1 for positive NPV investment and less than 1 for a negative NPV investment.
InvestmentInitialInflowCashofPVPI
Internal Rate of Return (IRR)
The internal rate of return (IRR) is defined as the discount rate that equates the present value of the initial investment outlays to the present value of the future cash inflows.
0I
IRR1CF
)I(InvestmentInitialIRR1
CFIRR1
CFIRR1
CFIRR1
CF
0
n
1tt
t
0nn
33
221
Computational Procedure
Given the cash flow and investment outlay, choose a discount rate at random and calculate the project’s NPV.
If the NPV is positive, choose a higher discount rate and repeat the procedure.
If the NPV is negative, choose a lower discount rate and repeat the procedure.
Find the discount rate, which makes the NPV = 0 is the IRR.
IRR for a Hypothetical Project
When discount rate is 10%
Year Net Cash Flow Discount Factor PV of Cash Flow 1 452 0.909 411 2 500 0.826 413 3 278 0.751 209
PV of Cash Inflow 1033 Less: Initial Investment - 1000
NPV + 33
IRR for a Hypothetical Project
Year Net Cash Flow Discount Factor PV of Cash Flow 1 452 0.877 396 2 500 0.769 385 3 278 0.675 188
PV of Cash Inflow 969 Less: Initial Investment - 1000
NPV - 31
When discount rate is 14%
IRR for a Hypothetical Project
Year Net Cash Flow Discount Factor PV of Cash Flow 1 452 0.893 403 2 500 0.797 399 3 278 0.712 198
PV of Cash Inflow 1000 Less: Initial Investment - 1000
NPV 0
When discount rate is 12%
Alternative method
Choose a discount rate at random which makes the NPV of the project positive. This discount rate is known as lower discount rate (LDR).
Choose a higher discount rate (HDR), which makes the NPV negative.
Solve the following equation
LDRHDRHDR@NPVLDR@NPV
LDR@NPVLDRIRR
Example: IRR
LDR = 10%, HDR = 14%, NPV @ 10% = + 33, NPV @ 14% = - 31
LDRHDRHDR@NPVLDR@NPV
LDR@NPVLDRIRR
%12%)10%14(31)33(
33%10IRR
Decision Criteria for IRR
If IRR>Cost of Capital (k), accept the project.
If IRR<Cost of Capital (k), reject the project.
If IRR = Cost of Capital (k), the firm would be indifferent to the project.
Modified Internal Rate of Return
The IRR assumes that a project’s annual cash flows can be reinvested at the project’s internal rate of return, which should be the project’s cost of capital.
MIRR is the discount rate at which the present value of a project’s cost is equal to the sum of the present value of its future cash inflow, where the cash inflows are reinvested at the firm’s cost of capital. So MIRR is more accurate measure for calculating the firms return.
Problems of IRR
Difficult to calculate - Trial and Error method
Non-conventional cash flow – A double change in the sign of the cash flow gives two solution for IRR, which is known as multiple IRR problem.
Differences in the scale of investment - IRR ignores the size of the investment because the result of the IRR method is expressed as a percentage.
The IRR assumes that a project’s annual cash flows can be reinvested at the project’s internal rate of return, which should be the project’s cost of capital. MIRR is an alternative to address above-mentioned problem.
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