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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