figURe 1: model Assumptions
a the company sells all of its widgets on Jan. 1.
b all expenses are paid on Jan. 1.
c the company provides a six-month warranty.
d all customers buy a new product annually.
e Uniform breakdown occurs over the yearlong useful life, which means that he incidents of breakdown are spread evenly throughout the year.
f Warranty goodwill occurs only during the last six months of useful product life.
g obsolescence and depreciation are ignored.
h no pipeline claims exist; that is, claims that have occurred but are not known at year-end.
i occurrence, report, and payments of in-warranty claims are on June 30 and on Dec. 31 for warranty goodwill claims.
j the true value of in-warranty costs (labor + parts) is known on June 30 of each year, and all in-warranty costs are paid on June 30.
k expenses and expected losses are identical each year; i.e., inflation is ignored.
l
as in Panning’s article (see Page 70), surplus is the same for all future years.
all profits are immediately paid as dividends to its shareholders. if a loss is
incurred for a given year, it immediately raises equity to restore its surplus
to the initial amount.
m taxes are not considered.
n term structure of interest rates is flat; i.e., risk premiums are ignored.
o insolvency risk is ignored.
p outside effects on customer retention, other than goodwill and product price, are ignored.
q customer base change reacts to price change immediately at time zero.
r recoverables from salvaged parts are ignored.
s fixed costs are fixed into perpetuity.
the number of customers at a given price
and also is dependent on the amount of
warranty goodwill provided. To solve the
equation we must perform an iterative
procedure, shown in the Appendix.
The other inputs for our example,
such as in-warranty and out-of-warranty losses, the cost of manufacturing
the product, discount rate, equity, fixed
costs, and the target return on equity, are
shown in Figure 2.
The results are shown in Figure 3
(note that it wasn’t possible to achieve
the required ROE with warranty goodwill greater than $4 per product).
Figure 3 shows the amount that
would need to be charged per product for
various amounts of warranty goodwill. In
other words, to achieve a 15 percent ROE
for $1 of goodwill per product, we must
charge $56.76 per product and sell 12,159
widgets per year. To provide $2 of goodwill per product, the price would need to
be increased to $58.25 with sales of 11,164
widgets per year.
The Model
Perhaps the simplest way to understand
a new concept is through an example.
Further detail is included in the appendix, including the relevant formulae.
Before going through the example,
please keep in mind that, as with any
other model, all assumptions of the
model should be understood fully before considering its usefulness. Figure
1 details the assumptions of the model,
as discussed in Panning’s working paper. Not all these assumptions would
hold in the real world and may need to
be modified for practical use. With that
out of the way, let’s get to the good stuff.
In this example, we sell widgets on
Jan. 1 of each year. Each year half of the
products sold will fail— 25 percent in
warranty in the first six months of the
year, and 25 percent out of warranty in
the last six months. Each year, every
consumer will buy a new widget. An ex-
hibit in the appendix defines the other
variables used in the model.
current economic value
Now that we have defined a price for
each amount of warranty goodwill, we
can begin to calculate the firm value. The
first component of the total firm value is
the current economic value (or book value), which is simply the value of current
assets less current liabilities. (See Equation 3 in the Appendix.)
As you can see in Figure 4, the current
economic value is constant, regardless of
the amount of warranty goodwill provided, price, etc. This is proven in Equation
4 (see Appendix). If the first component
of firm value is constant, we must maximize the second component.
franchise value
The second component of firm value is
franchise value. The franchise value is
future assets less future liabilities (note
the similarity in concept to the current
economic value).
