 # Investment Appraisal using the Adjusted Present Value (APV)

The Adjusted Present Value approach is a way to determine whether raising debt to undertake a specific project will add value or in other words if it will result in positive cash flows. Raising debt will generally have two effects. The first effect is that the company will pay less tax as the interest charges is a tax allowable expense (the “tax shield”). The second effect is the increased risk of bankruptcy for the company by raising additional debt.

## How can you apply the adjusted present value method?

The application of the adjusted present value is a bit more complicating process when compared with the net present value methodology. The reason for that is that you need to find the cost of raising finance for a company that has no debt (what is called an “ungeared” company”).

You will then calculate the present value of the cash flows and discount them using the discount rate of this hypothetical ungeared company.

The final step is to add the benefit of raising debt which is the tax shield. The tax shield is nothing else from the tax you will save since the interest charges is a tax allowable expense.

To summarize, you should follow these steps to calculate the adjusted present value (APV).

• Calculate the cost of raising finance for an ungeared company
• Calculate the cash flows that the project that is being assessed will bring (including the initial investment)
• Discount the cash flows from the project by using as discount rate the rate derived from step 1 (the cost of equity for the ungeared company)
• The final step is to add the tax shield or the tax saved from the interest accrued.

## An adjusted present value example

The scenario:

Let’s assume that a company is considering investment in a project that will need \$10m initial investment and will bring \$5 annual cash inflows (after tax)  for the next three years.

The company is thinking of raising debt to invest in this project. The debt that will be raised is the \$10m needed for the initial investment and the interest will be 10%.

The company operates in a country where it pays tax at 20%. The risk free rate is 5% and the return on the market is 3%. The company has \$50m debt and \$100m equity contributed by the shareholders. The company has been using the capital asset pricing model to monitor the beta which according to recent calculations is 1.2.

Solution:

Step 1: Calculate the beta of the “ungeared company” and then use the capital asset pricing model to derive the cost of equity for this hypothetical company.

Therefore, using the following formula:

` $Bgeared=Bungeared * (1+ (debt*(1-tax rate)/equity))$`

will give us a beta for an ungeared company equal to 0.86. We will then use capital asset pricing model or $Ke=Rf + Bun * (Rm-Rf)$

which results in a cost of equity equal to 6.7%. This is the rate that we will use to discount

Step 2: Calculate the cash flows for the project and discount them using the cost of equity found from step 1.

T0T1T2T3
Initial Investment(10)555
Discount Rate11/1.0671/1.067^21/1.067^3
Discount Rate10.940.880.82
Discounted Cash flows(10)4.74.44.1
Present Value3.2

Step 3: Calculate and add the tax benefit from the interest charges.We will pay \$10m * 10% interest or \$1m per year. The annuity for the three years 10% rate is 2.487.Therefore, the tax benefit is \$1m * 2.487 or \$2.487m

Step 4: Add the present value from step 2 and the tax shield from step 4 and interpret the results.

The total present value for the project is \$5.7 without taking into account the impact of the loan repayments. The company should accept the project since it has a positive present value.

## One thought on “Investment Appraisal using the Adjusted Present Value (APV)”

1. Alger says:

How would these calculations change if the finance was 60% debt and 40% equity for example?