Session 3
RWJ, Chapter 17
The tax benefit of debt implies that if a firm chooses to finance itself using debt, it shields part of
its income from taxes. In this session we study the consequent increase in value of the firm. We
focus on two approaches, Adjusted Present Value and Weighted Average Cost of Capital. As
both these approaches have the same logical foundation, they produce identical estimates of the
increase in value of a firm due to the tax benefit of debt.
Adjusted Present Value Approach
The Adjusted-Present-Value (APV) for a project with debt financing is:
APV = NPV
U
+ NPVF.
NPV
U
is the net present value of the project to an all-equity firm:
NPVF is the net present value of financial side effects, which primarily are tax subsidy to debt
and the costs of financial distress arising from the use of debt.
APV has the conceptual advantage of separating the value of the unlevered investment from the
value of financing side-effects.
An Example of APV and the Tax Subsidy to Debt:
Since you are now familiar with the Modigliani-Miller assumptions, the example takes
advantage of the simplicity in the MM world. Suppose PMM, Inc. has an investment that costs
$10,000,000 with expected EBIT (cash flows from operations) of $3,030,303 per year forever.
The investment can be financed either with $10,000,000 in equity or with $5,000,000 of 10%
debt and $5,000,000 of internally generated (equity) cash flows. The discount rate on an
all-equity-financed project in this risk class is 20%. The firm's marginal tax rate is 34%.
1. All equity value
Annual after tax cash flows to unlevered equity are (EBIT)(1- t
c
) = ($3,030,303)(1.34) =
$2,000,000. The net present value of the project if financed with internal equity is
therefore:
NPV = ($2,000,000 / .2) – $10,000,000 = $0
Since NPV = $0, the all-equity firm should be indifferent to accepting or rejecting the project.
2. Financing side-effect: Tax Subsidy
Note that in the MM world, all cash flows are perpetual and even debt does not have a maturity
date. In the real world, the interest expense on debt is tax deductible but repayment of principal
is not.
In our example, the annual interest payment is R
B
B = (.10)($5,000,000) = $500,000.
The
annual tax subsidy is t
C
× R
B
× B
= (.34)(.10)($5,000,000) = $170,000, and the
present
value of this financing side-effect
discounted at 10% (the market cost of debt) is:
NPVF
=$170,000/(0.10) = $1,700,000.