1. Adjusted Present Value
Normal NPV calculation:
CF1 CF2 CFN
NPV = −investment + + ++
(1 + WACC) (1 + WACC) 2
(1 + WACC) N
where, in a simple situation:
 equity   debt 
 equity + debt ( cos t of equity ) +  equity + debt ( cos t of debt )(1 − tax rate )
WACC =    
   
Using debt for financing has a tax advantage in that interest payments are tax deductible.
This tax deductibility is a source of value for the firm. In the normal NPV calculation,
this additional value is accounted for in the WACC.
However, in many cases the capital structure of the project may change over time. In
other cases the tax rate faced by the firm may be expected to change over time (as firm
goes from loss to profit, or special tax subsidies expire etc.). In other cases, the firm may
be able to obtain subsidized financing from a government agency for the project. In all of
these circumstances, these types of things mean that the WACC for the project will
change, and may even change each year of the project’s life. Incorporating these types of
factors into an NPV-WACC calculation is possible, but very complicated. The normal
assumption is that the WACC is the same for each cashflow and each year of the project.
These more complicated situations are more easily handled by using Adjusted Present
Value (APV). APV is based on the following:
APV = NPV of project assuming it is all equity financed + NPV of financing effects
Essentially, APV breaks the total value of the project into parts: one part is the value
assuming no debt is used, and then you add on the extra value created from using debt in
the capital structure.

2. Consider an example:
A firm is considering a project that will last 5 years. It will generate cashflows of $9
million annually. The initial investment required in the project is $28 million. Assume
that the cost of equity for the project is 20% if the project is 100% equity financed.1
For the project, the firm will be able to obtain some short term debt financing. The firm
can obtain a loan for $22,500,000 to start the project, at a rate of 10% ($2,250,000 in
interest paid each year, with principal paid in a lump sum at the end of the loan).
However, the lender will only extend the loan for 3 years. The firm’s tax rate is 30%.
The problem with this example is that the capital structure of the project actually changes
in three years when the debt must be paid off. This means that the WACC will actually
change at that time. Calculating the NPV by discounting the cashflows at the WACC can
become complicated. APV approaches the problem this way:
NPV of project if all equity financed =
9,000,000 9,000,000 9,000,000 9,000,000 9,000,000
− 28,000,000 + + + + + = −1,084,490
(1.2) (1.2) 2 (1.2) 3 (1.2) 4 (1.2) 5
Note that if all equity financed, the project is not a good one.
The benefit of debt financing is now calculated as the NPV of the loan. Note that the loan
gives a cash inflow of $22,500,000 today, followed by 3 annual interest payments of
$2,250,000(1-0.3) = $1,575,000 on an after tax basis, and then a cash outflow of
$22,500,000 to pay off the loan. The appropriate rate at which to discount is the loan rate
as this reflects the risk of the loan. The NPV of the loan is therefore:
NPV of financing =
1,575,000 1,575,000 1,575,000 22,500,000
22,500,000 − − − − = $1,678,625
(1.1) (1.1) 2 (1.1) 3 (1.1) 3
So, financing with debt creates an extra $1,678,625 in value because of the tax deduction
associated with the interest (note that if there were no tax you could do the calculation
and the NPV of the loan would always be zero; the source of the value in this case is the
tax shield generated by debt).
In total the value of the project is:
APV = -1,084,490 +1,678,625 = $594,135
1
If this project has the same risk as the overall firm, then you could get this by estimating the firm’s beta
and then de-levering it using the method given on page 120 of the Damadoran text. This will give the asset
beta which is the beta that the firm would have if it had no debt. Then, simply use this asset beta in CAPM
to get an unlevered cost of equity.

3. The project is a worthwhile investment after incorporating the value of the financing
arrangements.
The benefit of APV is that it breaks the problem down into the value of the project itself
(if equity financed) and the value of the financing (whereas the effect of financing is
taken account of in the WACC when calculating regular NPV). This makes APV flexible
enough to cover many different types of real-world financing arrangements such as: tax
rates that change each year, amount of debt increases or decrease each year, government
agency subsidizes your interest payments for a certain number of years, new debt must be
issued at some future time and that will involve flotation costs, etc. In each of these cases
the NPV of the project under 100% equity financing would remain the same, and the
value of the specific financing arrangement would simply be calculated separately, in the
same way as in the simple example above.
Some people believe that APV is preferable from a managerial point of view as it shows
directly the sources of value created by a project (i.e. how much is from running the
actual project, how much is from the financing arrangements, how much value is created
by a government subsidy etc.). However, note that calculating NPV based on an
estimated WACC is still, by far, the most common project valuation approach used by
firms.