CHAPTER 14CHAPTER 14

CAPITAL FINANCING CAPITAL FINANCING AND ALLOCATIONAND ALLOCATION

CAPITAL BUDGETINGCAPITAL BUDGETING

To produce goods and services, To produce goods and services, the first thing an entrepreneurial the first thing an entrepreneurial firm must do is obtain capital firm must do is obtain capital funds from investors and lendersfunds from investors and lenders

CAPITAL ALLOCATIONCAPITAL ALLOCATION

After obtaining funds, the After obtaining funds, the entrepreneurial firm must invest entrepreneurial firm must invest these funds in equipment, tools these funds in equipment, tools and other resourcesand other resources

ADDITIONAL WEALTHADDITIONAL WEALTHRevenues from the engineering Revenues from the engineering and other capital projects must and other capital projects must earn an adequate return on funds earn an adequate return on funds invested in terms of profit for a invested in terms of profit for a firm to achieve economic growth firm to achieve economic growth and be competitive in the futureand be competitive in the future

CAPITAL FINANCING FUNCTIONCAPITAL FINANCING FUNCTION• Determines the amount of new funds needed from Determines the amount of new funds needed from

investors, lenders, and internal sources (I.e., investors, lenders, and internal sources (I.e., depreciation and retained earnings) to support new depreciation and retained earnings) to support new capital projectscapital projects

• Decides on the sources of new externally acquired Decides on the sources of new externally acquired funds (I.e., issuing additional stock, selling bonds, funds (I.e., issuing additional stock, selling bonds, obtaining loans, etc…)obtaining loans, etc…)

• This function also insures that the total amount of This function also insures that the total amount of new funds and the ratio of debt to equity capital is new funds and the ratio of debt to equity capital is commensurate with the financial status of the firm commensurate with the financial status of the firm and balanced with the current and future capital and balanced with the current and future capital investment requirementsinvestment requirements

CAPITAL ALLOCATION FUNCTIONCAPITAL ALLOCATION FUNCTION• Selects engineering projects for Selects engineering projects for

implementation based on constraints of total implementation based on constraints of total capital investment during capital financing capital investment during capital financing considerationsconsiderations

• Capital allocation activities begin in various Capital allocation activities begin in various company organizations --departments, company organizations --departments, operating divisions,operating divisions, research and research and development, etc…development, etc…

• During each capital budgeting cycle, these During each capital budgeting cycle, these organizations plan, evaluate and recommend organizations plan, evaluate and recommend projects for funding and implementationprojects for funding and implementation

COMBINED SCOPE OF CAPITAL COMBINED SCOPE OF CAPITAL FINANCING AND ALLOCATION FINANCING AND ALLOCATION

FUNCTIONSFUNCTIONS1.1. Acquisition of financial resourcesAcquisition of financial resources

2.2. Establishment of minimum economic Establishment of minimum economic acceptability requirementsacceptability requirements

3.3. Identification and evaluation of capital Identification and evaluation of capital ProjectsProjects

4.4. Selection of projects for implementationSelection of projects for implementation

5.5. Postaudit reviews Postaudit reviews

SOURCES OF CAPITALSOURCES OF CAPITALDebt CapitalDebt Capital

• Involves both short and long-term borrowing of fundsInvolves both short and long-term borrowing of funds• Interest must be paid to capital providers and the debt Interest must be paid to capital providers and the debt

must be repaid by a specified timemust be repaid by a specified time• Capital providers do not share in any profits resulting from Capital providers do not share in any profits resulting from

capital usecapital use• Borrower may be required to pledge some type of security Borrower may be required to pledge some type of security

to ensure money will be repaidto ensure money will be repaid• Terms of loan may limit the use of borrowed funds Terms of loan may limit the use of borrowed funds • Terms may also restrict further borrowingTerms may also restrict further borrowing• Loan interest is a tax-deductible expense for the firmLoan interest is a tax-deductible expense for the firm

SOURCES OF CAPITALSOURCES OF CAPITALEquity CapitalEquity Capital

• Supplied and used by owners in expectation of Supplied and used by owners in expectation of profitprofit

• No assurance that profit will be made or that No assurance that profit will be made or that investment capital will be recoveredinvestment capital will be recovered

• No limitations placed on the use of fundsNo limitations placed on the use of funds• No explicit cost for use of such capital; therefore, No explicit cost for use of such capital; therefore,

not tax deductible for firmnot tax deductible for firm• Expected rate-of-return must be high enough, at Expected rate-of-return must be high enough, at

an acceptable risk, to be attractive to potential an acceptable risk, to be attractive to potential investors investors

SOURCES OF CAPITALSOURCES OF CAPITALRetained EarningsRetained Earnings

• Profits that are reinvested in the business instead Profits that are reinvested in the business instead of being paid as dividends to ownersof being paid as dividends to owners

• Retention of some of company’s profits reduces Retention of some of company’s profits reduces the immediate amount of dividends per share, the immediate amount of dividends per share, increases the book value of the stock, and results increases the book value of the stock, and results in greater future dividends and / or market resale in greater future dividends and / or market resale value of the stockvalue of the stock

• While some investors expect more of the profit a While some investors expect more of the profit a company earns, many prefer to have some of the company earns, many prefer to have some of the profits retained and reinvested to help increase profits retained and reinvested to help increase the value of their stock the value of their stock

SOURCES OF CAPITALSOURCES OF CAPITALDepreciation ReservesDepreciation Reserves

• Set aside out of revenue as an allowance Set aside out of revenue as an allowance for the replacement of equipment and other for the replacement of equipment and other depreciable assetsdepreciable assets

• Depreciation funds provide a revolving Depreciation funds provide a revolving investment fund that may be used to the investment fund that may be used to the best possible advantagebest possible advantage

• A source of capital for financing new A source of capital for financing new projects within existing firm, so long as projects within existing firm, so long as required capital is available for replacing required capital is available for replacing essential equipment as requiredessential equipment as required

SOURCES OF CAPITALSOURCES OF CAPITALLeasingLeasing

• A way of acquiring use of an asset without capital A way of acquiring use of an asset without capital expenditure for purchaseexpenditure for purchase

• A form of contract that establishes conditions A form of contract that establishes conditions under which asset owner conveys use, and under which asset owner conveys use, and associated costs,of the asset to the lesseeassociated costs,of the asset to the lessee

• A method of achieving benefits of capital A method of achieving benefits of capital investment witout actually acquiring additional investment witout actually acquiring additional debt ot equity capitaldebt ot equity capital

• Leasing costs are tax deductible from operating Leasing costs are tax deductible from operating incomeincome

COST OF DEBT CAPITALCOST OF DEBT CAPITAL• The debt part of the capital structure The debt part of the capital structure

leverages the equity part by increasing the leverages the equity part by increasing the total funds available for capital projects and total funds available for capital projects and wealth of the firmwealth of the firm

• Proportion of debt capital, however, must be Proportion of debt capital, however, must be maintained below a level which would maintained below a level which would adversely affect the market value of the adversely affect the market value of the firm’s common stockfirm’s common stock– Varies by type of companyVaries by type of company

LOANS (SHORT-TERM DEBT)LOANS (SHORT-TERM DEBT)• Usually for periods less than five years and Usually for periods less than five years and

frequently for less than two yearsfrequently for less than two years• Sources are banks, insurance companies, Sources are banks, insurance companies,

retirement systems, other lending institutionsretirement systems, other lending institutions• Financial instrument – line of credit or short-term Financial instrument – line of credit or short-term

note – defines promise to repay, amount of note – defines promise to repay, amount of borrowed funds, interest , some prearranged borrowed funds, interest , some prearranged repayment schedulerepayment schedule

• Lending institution may require tangible value as Lending institution may require tangible value as security or the certainty that borrowers financial security or the certainty that borrowers financial position presents minimal riskposition presents minimal risk

LOANS (SHORT-TERM DEBT)LOANS (SHORT-TERM DEBT)

Assuming all interest payments and Assuming all interest payments and income taxes paid by firm are paid on income taxes paid by firm are paid on annual basis, after-tax cost of capitalannual basis, after-tax cost of capital

CCLL = = iiLL(1 – (1 – tt))

CCLL = after-tax cost of capital for a loan = after-tax cost of capital for a loan

iiL L == rate of interest per year paid on the loanrate of interest per year paid on the loan

t = effective (marginal) income tax ratet = effective (marginal) income tax rate

BONDS (LONG-TERM DEBT)BONDS (LONG-TERM DEBT)• A long-term note given to the lender by the borrower, A long-term note given to the lender by the borrower,

stipulating the terms of repayment and other conditionsstipulating the terms of repayment and other conditions• In return for the money loaned, the company promises to In return for the money loaned, the company promises to

repay the loan (bond) and interest upon it at a specified repay the loan (bond) and interest upon it at a specified raterate

• As long as interest is paid, bondholder has no voice in As long as interest is paid, bondholder has no voice in affairs of business and is not entitled to a share of profitsaffairs of business and is not entitled to a share of profits

• Face value or par value of a bond is the amount (I.e., Face value or par value of a bond is the amount (I.e., $1,000, $10,000, etc… ) for which bond is issued$1,000, $10,000, etc… ) for which bond is issued

• When face value is repaid, bond is When face value is repaid, bond is retiredretired or or redeemedredeemed• Interest rate quoted on the bond is the Interest rate quoted on the bond is the bond ratebond rate• The periodic interest payment due is computed as the face The periodic interest payment due is computed as the face

value times the bond interest rate per period value times the bond interest rate per period

BONDS (LONG-TERM DEBT)BONDS (LONG-TERM DEBT)Annual After-Tax Cost of CapitalAnnual After-Tax Cost of Capital

[ Zr + (Z –P +S[ Zr + (Z –P +See) / N + A) / N + Aee ] (1- ] (1- tt))

CCBB = = (Z + P – S(Z + P – See) / 2) / 2

Z = face (par) value of bondZ = face (par) value of bond

r = bond rate (nominal interest) per yearr = bond rate (nominal interest) per year

N = Number of years until bond is retired (redeemed)N = Number of years until bond is retired (redeemed)

SSee = initial selling expense associated with the bond = initial selling expense associated with the bond

P = Actual selling price of the bond) [if P<Z, the bond is sold P = Actual selling price of the bond) [if P<Z, the bond is sold at a discount (to par value), and if P>Z, the bond is sold at at a discount (to par value), and if P>Z, the bond is sold at a premium]a premium]

AAee = annual administrative expenses associated with bond = annual administrative expenses associated with bond

tt = effective (marginal) income tax rate = effective (marginal) income tax rate

BONDS (LONG-TERM DEBT)BONDS (LONG-TERM DEBT)

Annual After-Tax Cost of CapitalAnnual After-Tax Cost of Capital

[ Zr + (Z –P +S[ Zr + (Z –P +See) / N + A) / N + Aee ] (1- ] (1- tt))

CCBB = = (Z + P – S(Z + P – See) / 2) / 2Numerator is the Numerator is the after-tax cost of the bondafter-tax cost of the bond based on the based on the

annual interest expenses plus annualized amount (over annual interest expenses plus annualized amount (over the life of the bond) of any discount or premium and the life of the bond) of any discount or premium and initial selling expenses plus the annual administrative initial selling expenses plus the annual administrative expensesexpenses

Denominator is the Denominator is the average investment in the bondaverage investment in the bond over its over its lifelife

BOND RETIREMENTBOND RETIREMENT• A systematic program for repayment of a bond A systematic program for repayment of a bond

issue when it becomes due gives assurance to issue when it becomes due gives assurance to bondholders and makes bonds more attractive to bondholders and makes bonds more attractive to the publicthe public

• To do this a company periodically sets aside To do this a company periodically sets aside definite sums, that with interest, will accumulate to definite sums, that with interest, will accumulate to the amount needed to retire the bonds when they the amount needed to retire the bonds when they are dueare due

• A sinking fund is most typically used for this A sinking fund is most typically used for this procedureprocedure

CORPORATIONCORPORATION

• A corporation is a fictitious being, A corporation is a fictitious being, recognized by law, that can pursue almost recognized by law, that can pursue almost any type business transaction that a real any type business transaction that a real person can .person can .

• It operates under a state-granted charter It operates under a state-granted charter which allow certain rights and privileges, which allow certain rights and privileges, and is subject to certain restrictions.and is subject to certain restrictions.

• Special taxes may be assessed against it.Special taxes may be assessed against it.

COST OF EQUITY CAPITALCOST OF EQUITY CAPITAL• Equity capital for a corporation is acquired through the Equity capital for a corporation is acquired through the

sale of stock.sale of stock.• Purchasers of the stock are part owners, usually called Purchasers of the stock are part owners, usually called

stockholders, of the corporation.stockholders, of the corporation.• Although stockholders are entitled to a share of the profits, Although stockholders are entitled to a share of the profits,

they are typically not liable for the debts of the corporation.they are typically not liable for the debts of the corporation.• Stockholders are never compelled to suffer any loss Stockholders are never compelled to suffer any loss

beyond the value of their stock.beyond the value of their stock.• The continuous or indefinite corporation life is conducive The continuous or indefinite corporation life is conducive

to long-term investments and a degree of certaintyto long-term investments and a degree of certainty• This makes debt capital easier to obtain, and at a lower This makes debt capital easier to obtain, and at a lower

interest cost interest cost

COMMON STOCKCOMMON STOCK

• Primary source of equity capital Primary source of equity capital used to finance a corporation’s used to finance a corporation’s capital projectscapital projects

• The value of common stock must The value of common stock must be a measure of the earnings be a measure of the earnings received and on factors related to received and on factors related to dividends and market pricedividends and market price

DIVIDEND VALUATION MODELDIVIDEND VALUATION MODEL• A simple approach for the valuation of common stock A simple approach for the valuation of common stock

and the estimation of per share rate of return and the estimation of per share rate of return expected by the investorexpected by the investor

• The current value of a share of common stock can be The current value of a share of common stock can be approximated by the PW of future cash receipts approximated by the PW of future cash receipts during an N-year ownership period during an N-year ownership period

DivDiv1 1 DivDiv22 Div DivNN P PNN

P0 P0 ~~ (1 + e (1 + eaa) + (1 + e) + (1 + eaa))22 + … + (1 + e + … + (1 + eaa))NN + (1 +e + (1 +eaa))NN

eeaa = rate of return per year required by common stockholders = rate of return per year required by common stockholders

PP00 = current value of a share of common stock = current value of a share of common stock

PPNN = selling price of a share of common stock at the end of N = selling price of a share of common stock at the end of N

yearsyears

DivDivkk = After-tax value of cash dividends received during year k = After-tax value of cash dividends received during year k

DIVIDEND VALUATION MODELDIVIDEND VALUATION MODEL

• Incorporates two conservative assumptions:Incorporates two conservative assumptions:– dividends are constant over the long termdividends are constant over the long term

– PP00 = P = PNN

• In this case, current price of a share of common In this case, current price of a share of common stock equals PW of an assumed indefinite series stock equals PW of an assumed indefinite series of dividend receipts that remain constantof dividend receipts that remain constant

PP00 = Div (P / A, e = Div (P / A, eaa, , ) = Div / e) = Div / eaa

AFTER-TAX COST OF AFTER-TAX COST OF EQUITY EQUITY

Given: PGiven: P00 = selling price of a share of = selling price of a share of common stockcommon stock

Div = annual dividend for past Div = annual dividend for past yearyear

eeaa = Div / P = Div / P00

If future price of security is expected to If future price of security is expected to grow at a rate of ‘g’ each yeargrow at a rate of ‘g’ each year

eeaa = Div / P = Div / P00 + g + g

PREFERRED STOCKPREFERRED STOCK• Represents ownership with additional privileges and Represents ownership with additional privileges and

restrictions not assigned to a holder of common stockrestrictions not assigned to a holder of common stock• Preferred stockholders guaranteed a dividend on their Preferred stockholders guaranteed a dividend on their

stock, usually a percentage of par value, before common stock, usually a percentage of par value, before common stockholders receive any returnstockholders receive any return

• If corporation is dissolved, assets must be used to satisfy If corporation is dissolved, assets must be used to satisfy claims of preferred stockholders before holders of claims of preferred stockholders before holders of common stockcommon stock

• Preferred stockholders usually have voting rightsPreferred stockholders usually have voting rights• Because the dividend rate is fixed, preferred stock is a Because the dividend rate is fixed, preferred stock is a

more conservative investment than common stock, and more conservative investment than common stock, and has many features of long-term bondshas many features of long-term bonds

PREFERRED STOCKPREFERRED STOCK• Because dividend rate is fixed, market value Because dividend rate is fixed, market value

is les likely to fluctuateis les likely to fluctuate

• After-tax cost of capital for preferred stock After-tax cost of capital for preferred stock (e(epp) can be approximated by dividing ) can be approximated by dividing

guaranteed dividend (Divguaranteed dividend (Divpp -- paid out after -- paid out after

tax earnings) by the original par value of the tax earnings) by the original par value of the stock (Pstock (Ppp))

eepp = Div = Divp p / P/ Ppp

RETAINED EARNINGSRETAINED EARNINGS

• Normally assumed to be the same as Normally assumed to be the same as for common stockfor common stock

• These earnings are equity funds that These earnings are equity funds that are retained and reinvested for future are retained and reinvested for future growth and increasing stockholder growth and increasing stockholder wealthwealth

WEIGHTED-AVERAGE COST OF WEIGHTED-AVERAGE COST OF CAPITALCAPITAL

• A Weighted-Average Cost of Capital (WACC) A Weighted-Average Cost of Capital (WACC) for a firm can be determined once the amount for a firm can be determined once the amount and explicit cost is established for each debt and explicit cost is established for each debt and equity component in the capital structureand equity component in the capital structure

• This includes short-term debt, bond, common This includes short-term debt, bond, common stock, and preferred stock componentsstock, and preferred stock components

• Retained earnings are also included; the cost Retained earnings are also included; the cost of these funds should be the same as cost of of these funds should be the same as cost of common stockcommon stock

WEIGHTED-AVERAGE COST OF WEIGHTED-AVERAGE COST OF CAPITALCAPITAL

• Depreciation funds (reserves), another source Depreciation funds (reserves), another source of internal funds for investment, are not of internal funds for investment, are not included in the weighted average cost of included in the weighted average cost of capital calculation.capital calculation.

• These funds are are assumed to replace the These funds are are assumed to replace the need for additional debt and equity capital in need for additional debt and equity capital in the same proportions as the present capital the same proportions as the present capital structure, and have an opportunity cost equal structure, and have an opportunity cost equal to the weighted average cost of capital.to the weighted average cost of capital.

WACC TO MARR RELATIONSHIPWACC TO MARR RELATIONSHIP• If MARR were assumed less than WACC If MARR were assumed less than WACC

implementing the project would result in implementing the project would result in a decrease in the value of the firm:a decrease in the value of the firm:

• There would be no surplus earned above There would be no surplus earned above the cost of capital invested in the projectthe cost of capital invested in the project– project would impact negatively on wealth of project would impact negatively on wealth of

firmfirm

• WACC should be minimum value used WACC should be minimum value used for MARRfor MARR

WACC TO MARR RELATIONSHIPWACC TO MARR RELATIONSHIP

• If MARR were assumed greater than WACC If MARR were assumed greater than WACC

• Then best economic measure of equivalent Then best economic measure of equivalent current value that would be added to the current value that would be added to the firm by the project remains the PW value firm by the project remains the PW value calculated at i = WACC.calculated at i = WACC.

• Regardless of MARR, WACC is important Regardless of MARR, WACC is important and should be available for decision and should be available for decision making.making.

LEASING AS A SOURCE OF LEASING AS A SOURCE OF CAPITALCAPITAL

• Leasing is a business arrangement that makes assets Leasing is a business arrangement that makes assets available without initial capital investment costs of purchaseavailable without initial capital investment costs of purchase

• Leasing is a source of capital generally regarded as a long-Leasing is a source of capital generally regarded as a long-term liability, similar to a mortgageterm liability, similar to a mortgage

• For corporations, rent paid on leased assets used in For corporations, rent paid on leased assets used in business is generally deductible as a business expensebusiness is generally deductible as a business expense

• Studies have shown no real income tax advantage in leasingStudies have shown no real income tax advantage in leasing• There may or may not be savings in maintenance expenses There may or may not be savings in maintenance expenses

through leasing, but simplifies maintenance problemsthrough leasing, but simplifies maintenance problems• True advantage in leasing is in allowing a firm to obtain True advantage in leasing is in allowing a firm to obtain

modern equipment that is subject to rapid technological modern equipment that is subject to rapid technological change -- a hedge against inflation and obsolescencechange -- a hedge against inflation and obsolescence

COST OF THE LEASE ALTERNATIVECOST OF THE LEASE ALTERNATIVE

IIkk = L = Lkk ( 1 - ( 1 - tt ) )

IIk k = after-tax lease expense during year k= after-tax lease expense during year k

LLk k = before-tax lease expense during year k= before-tax lease expense during year k

t t = effective income-tax rate= effective income-tax rate

If i, the after-tax MARR is known and fixed, If i, the after-tax MARR is known and fixed, PW of the after-tax PW of the after-tax costcost of the lease of the lease during a life of N years isduring a life of N years is

PWPWLeaseLease (i%) = (i%) =k=1k=1NN[L[Lkk (1 - (1 - tt ) / ( 1 + i ) ) / ( 1 + i )kk

Annual lease costs are borne by equipment supplierAnnual lease costs are borne by equipment supplier

COST OF PURCHASE ALTERNATIVECOST OF PURCHASE ALTERNATIVE

• After-tax cost of equipment when After-tax cost of equipment when purchased is a function of purchased is a function of

• expected annual expenses during life expected annual expenses during life of equipmentof equipment

• purchase price purchase price

• book value book value

• and expected market valueand expected market value

COST OF PURCHASE ALTERNATIVECOST OF PURCHASE ALTERNATIVE

MVMVNN( 1 - ( 1 - tt ) + ) + ttBVBV O&MO&Mkk( 1 - ( 1 - tt ) - d ) - dkk((tt))

PWPWBuyBuy(i%) = (i%) = 1-1- ( 1 - I )( 1 - I )NN + + k=1k=1NN ( 1 + i )( 1 + i )kk

I = capital investmentI = capital investment

MV = expected market value at the end of year NMV = expected market value at the end of year N

BVBVNN = book value at the end of year N = book value at the end of year N

i = interest rate per yeari = interest rate per year

N = life of equipment in yearsN = life of equipment in years

O&MO&Mkk = operating and maintenance expense during year k = operating and maintenance expense during year k

tt = effective income tax rate = effective income tax rate

ddkk = depreciation during year k = depreciation during year k

Note that market value, book value and depreciation Note that market value, book value and depreciation amounts are negative because they reduce costsamounts are negative because they reduce costs

LINEAR PROGRAMMING FORMULATIONS OF LINEAR PROGRAMMING FORMULATIONS OF CAPITAL ALLOCATION PROBLEMSCAPITAL ALLOCATION PROBLEMS

• Linear programming is a mathematical procedure for maximizing ( Linear programming is a mathematical procedure for maximizing ( or minimizing) a linear objective function, subject to one or more or minimizing) a linear objective function, subject to one or more linear constraint equationslinear constraint equations

• A useful technique for solving certain multi-period capital A useful technique for solving certain multi-period capital allocation problems when a firm is not able to implement all allocation problems when a firm is not able to implement all projects that may increase PW.projects that may increase PW.

Maximize net PW = Maximize net PW = jj = 1= 1mmBBjj*X*Xjj

BBjj* = net PW of investment opportunity (project) j during the * = net PW of investment opportunity (project) j during the

planning period being consideredplanning period being considered

XXj j = fraction of project j that is implemented during the planning = fraction of project j that is implemented during the planning

period (Note Xperiod (Note Xj j will normally be ‘0’ or ‘1’)will normally be ‘0’ or ‘1’)

m = number of mutually exclusive combinations of projects under m = number of mutually exclusive combinations of projects under considerationconsideration

LINEAR PROGRAMMING FORMULATIONS OF LINEAR PROGRAMMING FORMULATIONS OF CAPITAL ALLOCATION PROBLEMSCAPITAL ALLOCATION PROBLEMS

In computing the net PW of each mutually exclusive In computing the net PW of each mutually exclusive combination of projects, a MARR must be specifiedcombination of projects, a MARR must be specified

Notation used in writing constraints for linear Notation used in writing constraints for linear programmingprogramming

cckjkj = cash outlay (e.g., initial capital investment or = cash outlay (e.g., initial capital investment or

annual operating budget) required for project j in annual operating budget) required for project j in time period ktime period k

CCkk = maximum cash outlay that is permissible in time = maximum cash outlay that is permissible in time

period kperiod k

LINEAR PROGRAMMING FORMULATIONS OF LINEAR PROGRAMMING FORMULATIONS OF CAPITAL ALLOCATION PROBLEMSCAPITAL ALLOCATION PROBLEMS

Two types of constraints in capital budgeting problemsTwo types of constraints in capital budgeting problems

1. Limitations on cash outlays for 1. Limitations on cash outlays for period k of planning horizonperiod k of planning horizon

j=1j=1mm c ckkXXjj << C Ckk

LINEAR PROGRAMMING FORMULATIONS OF LINEAR PROGRAMMING FORMULATIONS OF CAPITAL ALLOCATION PROBLEMSCAPITAL ALLOCATION PROBLEMS

Two types of constraints in capital budgeting problemsTwo types of constraints in capital budgeting problems

2. Interrelationships among projects:2. Interrelationships among projects:

a. If projects p,q and r are mutually exclusivea. If projects p,q and r are mutually exclusive

XXpp + X + Xqq + X + Xrr << 1 1

b. If project r can be undertaken only if project s has already b. If project r can be undertaken only if project s has already been selectedbeen selected

XXrr << X Xss or X or Xrr - X - Xss << 0 0

c. If projects u and v are mutually exclusive and project r is c. If projects u and v are mutually exclusive and project r is dependent (contingent) on acceptance of u and vdependent (contingent) on acceptance of u and v

xxuu + x + xvv << 1 1

andand

xxrr << x xuu + x + xvv

CAPITAL BUDGETING PROCESS CAPITAL BUDGETING PROCESS OVERVIEWOVERVIEW

1.1. Preliminary planning and cost of Preliminary planning and cost of capitalcapital

2.2. Annual capital budget and proposed Annual capital budget and proposed project portfolioproject portfolio

3.3. Capital expenditure policies and Capital expenditure policies and evaluation procedureevaluation procedure

4.4. Project implementation and postaudit Project implementation and postaudit reviewreview

5.5. CommunicationCommunication