# Adjusted Present Value

Adjusted present value is an investment appraisal technique similar to net present value method. However, instead of using weighted average cost of capital as the discount rate, ungeared cost of equity is used to discount the cash flows from a project and there is an adjustment for the tax shield provided by related debt capital.

## Formula

Adjusted Present Value = |

PV of Cash Flows using Ungeared Cost of Equity |

+ Present Value of Tax Shield |

Where PV stands for 'present value' and **ungeared cost of equity** is the required rate of return for a firm that is financed by equity. It is calculated using the following formula:

Ungeared Cost of Equity = |

Risk Free Rate |

+ Asset beta × (Market Return − Risk Free Return) |

Since interest cost is allowable as tax deduction therefore, when calculating taxable income it provides tax savings (also called tax shield).

Tax Savings = Tax Rate × Interest Expense Related to the Project |

Tax savings are discounted using gross cost of debt.

## Example

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.

## Decision Rule

The decision rule for adjusted present value is the same as net present value: accept positive APV projects and reject negative APV projects. The project discussed in the example has an APV of $20.61 which is positive hence the company should undertake the project.

Written by Obaidullah Jan, ACA, CFA <--- Hire me on Upwork