Chapter 14
CAPITAL FINANCING
AND ALLOCATION
Learning Objectives
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Capital financing and allocation functions
Differences between sources of capital
Cost of debt capital
Cost of equity capital
Weighted average cost of capital
Leasing as a source of capital
Capital allocation
Capital Budgeting
• First thing must do is to obtain capital
funds from investors and lenders
• Revenues from the engineering and other
capital projects must earn an adequate
return to achieve economic growth
• Involves the expenditure of the current
capital funds to obtain future economic
benefits
Capital Financing Function
• Determines the amount of new funds
needed from investors, lenders, and internal
sources to support new capital projects
• Decides on the sources of new externally
acquired funds
• These amounts as well as the ratio of debt
to equity capital must be commensurate with
the financial status of the firm
Capital Allocation Function
• Selects engineering projects for
implementation based on constraints of total
capital investment
• Capital allocation activities begin in various
company organizations
• Organizations plan, evaluate and
recommend projects for funding and
implementation
• Engineering economy studies are performed
to develop much of the information required
Various Sources of Capital
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Methods by which the capital is obtained
will impact the MARR
• Obtained from either internal sources,
external sources, or both
• Various sources of capital are
1. Debt capital
2. Equity capital
3. Retained earnings
4. Depreciation reserves
5. Leasing
Debt Capital
• Involves both short and long-term
• Interest must be paid to capital providers
and by a specified time
• Lenders do not share in profits
• Borrower may be required to pledge some
type of security
• Terms may limit the use of borrowed funds
• Terms may also restrict further borrowing
• Loan interest is a tax-deductible expense for
the firm
Equity Capital
• Supplied and used by owners in expectation of
profit
• No assurance that profit will be made or that
investment capital will be recovered
• No limitations placed on the use of funds
• No explicit cost for use of such capital;
therefore, not tax deductible for firm
• Expected rate-of-return must be high enough,
at an acceptable risk, to be attractive to
potential investors
Retained Earnings
• Profits that are reinvested in the business
instead of being paid as dividends to
owners
• Keeping some portion of the company’s
profit
– Reduces the immediate amount of dividends
per share
– Increases the book value of the stock
– Results in greater future dividends and / or
market resale value of the stock
Depreciation Reserves
• Set aside out of revenue as an allowance
for the replacement of equipment and other
assets
• Provide a revolving investment fund that
may be used to the best possible
advantage
• An important source of capital for financing
new projects within existing firm
– Required capital is available for replacing
essential equipment when the time for
replacement arrives
Leasing
• A way of acquiring use of an asset without
capital expenditure for purchase
• A form of contract that establishes
conditions under which asset owner
conveys the use and associated costs to
the lessee
• A method of achieving benefits of capital
investment without actually acquiring
additional debt
• Leasing cost are tax deductible
Cost of Debt Capital
• Proportion of debt capital must be
maintained below a level which would
adversely affect the market value of the
firm’s common stock
• Vary by type of company
• Components of debt capital are short-term
loans and long-term bonds
• Discussed in the following slide
Loans (Short-term Debt)
• Usually for periods less than five years and
frequently for less than two years
• Sources are banks, insurance companies,
retirement systems, other lending institutions
• Used a note to define promise to repay,
amount of borrowed funds, interest, etc.
• Lending institution may require tangible value
as security
Loans (Short-term Debt)
• Assuming all interest payments and
income taxes paid by firm are paid on
annual basis, after-tax cost of capital
CL = iL(1 – t)
– CL = after-tax cost of capital for a loan
– iL = rate of interest per year paid on the loan
– t = effective (marginal) income tax
Bonds (Long-term Debt)
• A long-term note given to the lender by the
borrower
• Bondholder has no voice in affairs of business and
is not entitled to a share of profits
• Face value or par value of a bond is the amount
(I.e., $1,000, $10,000, etc… ) for which bond is
issued
• When face value is repaid, bond is retired or
redeemed
• Interest rate quoted on the bond is the bond rate
– The periodic interest payment due is computed as the
face value times the bond interest rate per period
Bonds (Long-term Debt)
• Annual after-tax cost of capital for a bond
[ Zr + (Z –P +Se) / N + Ae ] (1- t)
CB =---------------------------------------------------(Z + P – Se) / 2
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Z = face (par) value of bond;
r = bond rate (nominal interest) per year;
N = Number of years until bond is retired (redeemed);
Se = initial selling expense associated with the bond;
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 a premium];
– Ae = annual administrative expenses associated with
bond;
– t = effective (marginal) income tax rate
Example
• Assume the initial selling expenses of the bond
issue is 1.17% of the par (face) value; the
annual administrative expense of servicing the
bond issue is 3.1% of the annual interests costs;
and the corporation’s marginal (effective)
income-tax rate is 39.6%. Based on this
additional information, what is the after-tax cost
of capital to the corporation of the bond issue?
Cost of Equity Capital
• Acquired through the sale of stock.
• Purchasers of the stock are part owners usually
called stockholders
• Stockholders are entitled to a share of the
profits
• Are not liable for the debts of the corporation
• Because the life of a corporation is continuous,
long-term investments can be made
• Makes debt capital easier to obtain, and at a
lower interest cost
Types of Stocks
• Many types of stocks
• Common stock
– represents ordinary ownership without special
guarantees of return on investment
• Preferred stock
– has certain privileges over common stock
– Dividends on common stock are not paid until
the fixed percentage return on preferred stock
has been paid
Dividend Valuation Model
• Value of a share of common stock can be
approximated by the PW of future cash receipts
– P0 = selling price of a share of stock
– Div = annual dividend for past year
• Current price of a share of common stock equals
PW of an assumed indefinite series of dividend
receipts
P0 = Div (P / A, ea,  ) = Div / ea
• After-tax cost of equity (common stock)
ea = Div / P0
• If future price of security is expected to grow at a
rate of ‘g’ each year
ea = Div / P0 + g
Example
• The Yog Manufacturing Company’s common
stock is presently selling for $32 per share, and
annual dividends have been constant at $2.40 per
share. If an investor believes that the price of a
share of common stock will grow at 5% per year
into the foreseeable future, what is the
approximate cost of common stock equity to Yog?
What assumptions did you make?
Retained Earnings
• Normally assumed to be the same as for
common stock
• Retained and reinvested for future growth
and increasing stockholder wealth
Weighted-Average Cost of Capital
• Determined once the amount and explicit
cost is established
• Includes short-term debt, bond, retained
earnings common stock, and preferred stock
components
Leasing as a Source of Capital
• Leasing is a business arrangement that
makes assets available
• Leasing is a source of capital generally
regarded as a long-term liability
• For corporations, rent paid is generally
deductible as a business expense
• Studies have shown no real income tax
advantage in leasing
Leasing as a Source of CapitalCont.
• May or may not be savings in
maintenance expenses, but simplifies
maintenance problems
• True advantage is in allowing a firm to
obtain modern equipment
• Provides a hedge against inflation and
obsolescence
Cost of the Lease Alternative
• After-tax cost of a lease
Ik = Lk ( 1 - t )
– Ik = after-tax lease expense during year k
– Lk = before-tax lease expense during year k
– t = effective income-tax rate
• If i is known and fixed, PW of the after-tax
cost
PWLease (i%) =Sk=1N[Lk (1 - t ) / ( 1 + i )k
• Noted that the annual maintenance expenses are
not included
Cost of Purchase Alternative
• After-tax cost of equipment is a function of expected
annual expenses, purchase price, book value, and
expected market value
• PW of after-tax cost of purchased equipme
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I = capital investment
MV = expected market value at the end of year N
BVN = book value at the end of year N
i = interest rate per year
N = life of equipment in years
O&Mk = operating and maintenance expense during year k
t = effective income tax rate
dk = depreciation during year k
• Note that market value, book value and depreciation
amounts are negative because they reduce costs
Example
• An existing piece of equipment has been performing poorly
and needs replacing. More modern equipment can be
purchased or it can be leased. If purchased, the equipment
will cost $20,000 and have a depreciable life of 5 years with
no market value. For simplicity, assume straight-line
depreciation is used by the firm. Because of improved
operating characteristics of the equipment, raw materials
savings of $5,000 per year are expected to result relative to
continued use of the present equipment. However, annual
labor expenses for the new equipment will most likely
increase by $2,000 and annual maintenance will go up by
$1,000.
Capital Allocation
• Allocate the obtained capital through
activities that transform various types of
resources into goods and services
• Process of the capital-expenditure
decision-masking is referred to capital
allocation
– Involves planning, evaluation, and
management of capital projects
Linear Programming Formulations of Capital
Allocation Problems
• Linear programming is a mathematical procedure for
maximizing ( or minimizing) a linear objective function,
subject to one or more linear constraint equations
• A useful technique for solving certain multi-period
capital allocation problems
• Objective function of the capital allocation problem
– Bj* = net PW of investment opportunity
– Xj = fraction of project j that is implemented during the
planning period
• Note Xj will normally be ‘0’ or ‘1’
– m = number of mutually exclusive combinations of projects
Linear Programming Formulations of
Capital Allocation Problems
• Notation used linear programming model
– ckj = cash outlay (e.g., initial capital investment
or annual operating budget) required for project
j in time period k
– Ck = maximum cash outlay that is permissible
in time period k
LP Formulations
• Two types of constraints
1. Limitations on cash outlays for period k of
planning horizon
Sj=1m ckXj < Ck
2. Interrelationships among projects:
1. If projects p, q, and r are mutually exclusive
Xp + Xq + Xr < 1
2. If project r can be undertaken only if project s has
already been selected
Xr < Xs or Xr - Xs < 0
3. If projects u and v are mutually exclusive and project r
is dependent (contingent) on acceptance of u and v
xu + xv < 1 and xr < xu + xv
Example
• Three alternatives are being considered for an
engineering project. Their cash flow estimates are
shown in the accompanying table. A and B are
mutually exclusive, and C is an optional add-on
feature to alternative A. Investment funds are
limited to $5,000,000. Another constraint on this
project is the engineering personnel needed to
design and implement the solution. No more than
10,000 person-hours of engineering time can be
committed to the project. Setup a linear integer
programming formulation of this resource
allocation problem
Example-Cont.
Alternative
A
B
C
Initial investment
($106)
4.0
4.5
1.0
Personal
requirement
(hours)
7,000
9,000
3,000
1.3
2.2
0.9
0.12
2.47
1.85
After-tax annual
savings, year one
through four
($106)
PW at 10% per
Year ($106)