Chapter 11 • Gearing, the cost of capital and shareholders’ wealth
The cost of capital of elements of financing at different levels of gearing
We have seen in this chapter that the cost of the various elements of long-term finance
is partially dependent on the level of capital gearing. It is a basic tenet of both the MM
and the traditional models that, as gearing increases, so does the cost of equity. When
we deduce costs of capital using the traditional approach (based on market prices), the
figures that we calculate will be based on a particular level of gearing, and therefore
that level of gearing will affect the deduced costs. If that level of gearing is not the level
that will be relevant to the investment under consideration, the WACC to be used as
the discount rate must reflect this difference in the gearing level.
For example, a business’s equity may have been calculated to have a cost of 10 per
cent p.a. This, however, assumes a particular level of gearing. Say that in this case we
are talking about an all-equity business, that is, zero gearing. Suppose that the business
is to borrow to fund a new project. This means that, all other things being equal, the cost
of equity will increase. If we now want to calculate a WACC at which to discount the
estimated cash flows of the new investment project, we must adjust the cost of equity
from 10 per cent to reflect the level of gearing before we do the weighted averaging.Adjusted net present value
Linked to the previous point is the fact that we have a problem in that undertaking
a positive NPV project changes the level of gearing (unless the business is all-equity
financed) and, therefore, the WACC. The value of a positive NPV project accrues
entirely to the shareholders and increases the value of the equity. This alters the
WACC. This means that the WACC that was used to deduce the NPV was the wrong
one. The problem is that until we have deduced the NPV we do not know what the
gearing ratio and, therefore, the correct WACC, are. Without knowing what the cor-
rect WACC is, we cannot calculate the correct NPV.
The most practical way to deal with this problem is to deduce the NPV in two
stages. First we calculate the NPV assuming that the investment is all-equity financed
and then, when we know the NPV on this basis, we adjust it for the tax effect of the
debt finance. This is very similar (for good reason) to the relationship between the
value of the geared and ungeared business that appears on page 304.
For the business as a whole:VG=VU+TBG
For the investment project:NPVG=NPVU+TBPwhereNPVG=NPV if the project is undertaken by the geared business
NPVU=NPV if the project is undertaken by the all-equity business
T=the corporation tax rate
BP=the value of the debt finance used to finance the project.Eleven per cent of the US businesses surveyed by Graham and Harvey (2001) use
the adjusted NPV approach.