tejas.gaikwad.1044
Tejas Gaikwad
Adjusted Present Value (APV) is a business valuation method. APV is the net present value of a project if financed solely by ownership equity plus the present value of all the benefits of financing. It was first studied by Stewart Myers, a professor at the MIT Sloan School of Management and later theorized by Lorenzo Peccati, professor at the Bocconi University, in 1973.
The method is to calculate the NPV of the project as if it is all-equity financed (so called base case). Then the base-case NPV is adjusted for the benefits of financing. Usually, the main benefit is a tax shield resulted from tax deductibility of interest payments. Another benefit can be a subsidized borrowing at sub-market rates. The APV method is especially effective when a leveraged buyout case is considered since the company is loaded with an extreme amount of debt, so the tax shield is substantial.
Technically, an APV valuation model looks similar to a standard DCF model. However, instead of WACC, cash flows would be discounted at the unlevered cost of equity, and tax shields at either the cost of debt (Myers) or following later academics also with the unlevered cost of equity. APV and the standard DCF approaches should give the identical result if the capital structure remains stable.
The adjusted present value ("APV") analysis is similar to the DCF analysis, except that the APV does not attempt to capture taxes and other financing effects in a WACC or adjusted discount rate. Recall from our discussion of DCF that the WACC used in the DCF analysis is calculated as a blend of the cost of debt and the cost of equity, thereby capturing the effects of taxes and financing. APV, on the other hand, seeks to value these effects separately.
APV formula:-
APV = Unlevered NPV of Free Cash Flows and assumed Terminal Value + NPV of Interest Tax Shield and assumed Terminal Value.
The discount rate used in the first part is the return on assets or return on equity if unlevered. The discount rate used in the second part is the cost of debt financing by period.
Adjusted Present Value is a slight variation of the NPV approach for valuation. NPV approach has an inherent assumption that the project/business is financed solely through equity while the APV approach considers the impact of debt such as the tax shield that it provides.
It adds to the NPV, the PV of the tax shield that would be obtained by the debt financing. In this approach the NPV is calculated by discounting at the Cost of equity while the financing benefit is discounted at the cost of debt.
In detaill:-
EBIT
- Taxes on EBIT
=Net Operating Profit After Tax (NOPAT)
+ Non cash items in EBIT
- Working Capital changes
- Capital Expenditures and Other Operating Investments
=Free Cash Flows
Take Present Value (PV) of FCFs discounted by Return on Assets % (also Return on Unlevered Equity %)
+ PV of terminal value
=Value of Unlevered Assets
+ Excess cash and other assets
=Value of Unlevered Firm (i.e. firm value without financing effects or benefit of interest tax shield)
+ Present Value of Debt's Periodic Interest Tax Shield discounted by Cost of Debt Financing %
=Value of Levered Firm
- Value of Debt
=Value of Levered Equity or APV
The value from the interest tax shield assumes the company is profitable enough to deduct the interest expense. If not, adjust this part for when the interest can be deducted for tax purposes.
Example 1:-
Consider a project with perpetual cash flows
Investment = Rs. 200,000
Cash flow each year = Rs. 19,000
Cost of Equity = 10%
Cost of Debt = 5%
Interest on Debt = 5%
Tax Rate = 40%
NPV = -200,000 + (19,000/10%) = -10,000
Tax Shield = (0.05*200000*0.4) = 4,000
PV of tax shield = 4000/5% = 80,000
APV = -10,000 + 80,000 = Rs. 70,000
Example 2:-
A project costing $50 million is expected to generate after tax cash flows of $10 million a year forever. Risk free rate is 3%, asset beta is 1.5, required return on market is 12%, cost of debt is 8%, annual interest costs related to project are $2 million and tax rate is 40%. Calculate the adjusted present value of the project.
Solution:-
Adjusted Present Value = Present Value of Cash Flows + Present Value of Tax Savings
We need to find ungeared cost of equity which is 3% + 1.5*(12% − 3%) = 16.5%. Using this rate the present value of cash flows = $10 million/0.165 = $60.61 million. Initial investment is $50 million no net present value of future cash flows using ungeared cost of equity is $10.61 million ($60.61 million-$50 million).
Present value of tax savings = $2 million × 0.4 / 0.08 = $10 million
Adjusted present value = present value of cash flows + present value of tax savings = $10.61 million + $10 million = $20.61 million.
The method is to calculate the NPV of the project as if it is all-equity financed (so called base case). Then the base-case NPV is adjusted for the benefits of financing. Usually, the main benefit is a tax shield resulted from tax deductibility of interest payments. Another benefit can be a subsidized borrowing at sub-market rates. The APV method is especially effective when a leveraged buyout case is considered since the company is loaded with an extreme amount of debt, so the tax shield is substantial.
Technically, an APV valuation model looks similar to a standard DCF model. However, instead of WACC, cash flows would be discounted at the unlevered cost of equity, and tax shields at either the cost of debt (Myers) or following later academics also with the unlevered cost of equity. APV and the standard DCF approaches should give the identical result if the capital structure remains stable.
The adjusted present value ("APV") analysis is similar to the DCF analysis, except that the APV does not attempt to capture taxes and other financing effects in a WACC or adjusted discount rate. Recall from our discussion of DCF that the WACC used in the DCF analysis is calculated as a blend of the cost of debt and the cost of equity, thereby capturing the effects of taxes and financing. APV, on the other hand, seeks to value these effects separately.
APV formula:-
APV = Unlevered NPV of Free Cash Flows and assumed Terminal Value + NPV of Interest Tax Shield and assumed Terminal Value.
The discount rate used in the first part is the return on assets or return on equity if unlevered. The discount rate used in the second part is the cost of debt financing by period.
Adjusted Present Value is a slight variation of the NPV approach for valuation. NPV approach has an inherent assumption that the project/business is financed solely through equity while the APV approach considers the impact of debt such as the tax shield that it provides.
It adds to the NPV, the PV of the tax shield that would be obtained by the debt financing. In this approach the NPV is calculated by discounting at the Cost of equity while the financing benefit is discounted at the cost of debt.
In detaill:-
EBIT
- Taxes on EBIT
=Net Operating Profit After Tax (NOPAT)
+ Non cash items in EBIT
- Working Capital changes
- Capital Expenditures and Other Operating Investments
=Free Cash Flows
Take Present Value (PV) of FCFs discounted by Return on Assets % (also Return on Unlevered Equity %)
+ PV of terminal value
=Value of Unlevered Assets
+ Excess cash and other assets
=Value of Unlevered Firm (i.e. firm value without financing effects or benefit of interest tax shield)
+ Present Value of Debt's Periodic Interest Tax Shield discounted by Cost of Debt Financing %
=Value of Levered Firm
- Value of Debt
=Value of Levered Equity or APV
The value from the interest tax shield assumes the company is profitable enough to deduct the interest expense. If not, adjust this part for when the interest can be deducted for tax purposes.
Example 1:-
Consider a project with perpetual cash flows
Investment = Rs. 200,000
Cash flow each year = Rs. 19,000
Cost of Equity = 10%
Cost of Debt = 5%
Interest on Debt = 5%
Tax Rate = 40%
NPV = -200,000 + (19,000/10%) = -10,000
Tax Shield = (0.05*200000*0.4) = 4,000
PV of tax shield = 4000/5% = 80,000
APV = -10,000 + 80,000 = Rs. 70,000
Example 2:-
A project costing $50 million is expected to generate after tax cash flows of $10 million a year forever. Risk free rate is 3%, asset beta is 1.5, required return on market is 12%, cost of debt is 8%, annual interest costs related to project are $2 million and tax rate is 40%. Calculate the adjusted present value of the project.
Solution:-
Adjusted Present Value = Present Value of Cash Flows + Present Value of Tax Savings
We need to find ungeared cost of equity which is 3% + 1.5*(12% − 3%) = 16.5%. Using this rate the present value of cash flows = $10 million/0.165 = $60.61 million. Initial investment is $50 million no net present value of future cash flows using ungeared cost of equity is $10.61 million ($60.61 million-$50 million).
Present value of tax savings = $2 million × 0.4 / 0.08 = $10 million
Adjusted present value = present value of cash flows + present value of tax savings = $10.61 million + $10 million = $20.61 million.