Barry and Ellinger
costs and b is the rate response to a one-unit
increase in leverage. Substituting i = ifa + b{D!
E) and AIE = DIE + 1 into equation (1),
expanding terms, and deleting the consump-
tion and tax components yields
(5) re = ∖ra(D∕E) + ra - ila(D∕E) - b(D∕E)2}.
If the objective is to maximize re by treating
DIE as the decision variable, then differen-
tiating (5) with respect to DIE, equating the
result to zero, and solving for DIE gives op-
timal leverage of
(6) DIE=r-^⅛.
Optimal leverage then is positively related to
changes in the returns on assets and negatively
related to changes in the base rate and leverage
parameter.
In contrast, the traditional framework in
which no differential pricing based on credit
scoring occurs would maximize (1) subject to
a nonprice constraint imposed by the lender
on the maximum DIE. Without risk consid-
erations or other nonlinearities in returns or
borrowing costs, the maximization of (1) would
push leverage to the limit.
In practice, of course, credit scoring usually
is based on multiple variables whose weights
vary among lenders. The major variables de-
termining credit worthiness generally include
a borrower’s profitability, liquidity, solvency,
collateral position, and repayment ability (e.g.,
Lufburrow, Barry, and Dixon). The exact
weights are an empirical question that may
vary among lenders. However, the character-
istics of loan contracts involving the required
repayment of loan principal and the fixed in-
terest obligation generally suggest that lenders
will emphasize loan safety and repayment more
than the borrower’s expected profitability, be-
cause the lender does not share directly in the
borrower’s profits.
Finally, the tendency for lenders to group
their borrowers into a few discrete classes for
pricing, credit evaluation, and monitoring sug-
gests that the credit score and resulting risk
premium become discrete and ordinally ranked
variables. Thus,
iri if CREDIT SCORE > CSi
∏∖ ∙ = J C if CS2 < CREDIT SCORE < CSi
( ' J h ʌ :
if CSn < CREDIT SCORE < CSn ,
V
where CSn indicates the cut-off score between
the various credit classes.
Loan Pricing and Farm Performance 47
A significant feature of these variables is the
interrelationships that occur over time among
business performance, the credit score, and loan
pricing. In principle, the credit score (and thus
the loan rate) should depend on both the firm’s
current financial position and projected per-
formance. In addition, as time passes, the cred-
it score will change as changes occur in current
and projected performance, some of which are
intended changes while others result from the
effects of unanticipated random factors. How-
ever, modeling such simultaneous and dynam-
ic relationships would yield a highly complex
framework that also would be subject to the
quality of the projections. Moreover, lenders
themselves fall considerably short of this level
of sophistication because most of their credit
evaluations and the credit scoring models in
use are based on data about the borrower’s past
and present financial position rather than long-
term projections of financial performance.
When projections are used, mostly they reflect
anticipated outcomes for a single year or con-
stant levels of farm performance and interest
rates over longer periods of time.
Thus, the temporal relationships among
credit scoring, loan pricing, and business per-
formance can be plausibly modeled in a re-
cursive framework in which the lender’s credit
decisions affecting the borrower’s future fi-
nancing terms are based on the firm’s current
financial position which in turn is determined
by past performance. That is, the lender is as-
sumed to base credit decisions on expected
outcomes in the context of a firm’s current
financial structure which itself is based on past
experiences.
The recursive framework is portrayed by the
flow chart in figure 1. At the start of period 1,
the financial position of the borrower’s firm is
described in terms of its size, tenure position,
and structure of assets, liabilities, and equity
capital, along with various performance mea-
sures reflecting the outcomes of previous op-
erations. The borrower then formulates the
business plans for the coming year including
intended decisions about production and mar-
keting activities, acquisition of operating in-
puts, investment plans and capital transac-
tions, withdrawals for consumption and
taxation, financing needs, and anticipated debt
servicing. The lender responds to the business
plans and financing requests by evaluating the
firm’s credit worthiness using a credit scoring
technique. Based on the credit evaluation, the