5 2016-03-17 Febmat.com

# Adjusted present value (APV)

## Example:

Last updated: 17.03.2016

**Adjusted present value (APV) i****s very similar method to net present value (NPV). It is used for project appraisal mainly if:**

**the existing capital structure will be significantly changed by undertaking the project - compared to traditional NPV technique, the decision based on APV takes into account also the financial effects of specific financing structure of the project****here are frequently assumptions about the project financing structure - it is easy to recalculate APV with different debt parameters (44)**

**The steps for APV calculation are as follows**

**1. Calculate base-case NPV.** It is traditional NPV calculation with one exception - unlevered cost of equity is used as discount rate (not cost of entire capital). This "base case NPV" says which value the project brings in excess of this cost of equity. Unlevered cost of equity is calculated by replacing beta of our company in traditional CAPM with unlevered beta (β_{u} ) of company facing similar business risk operating in the industry where we intend to diversify

**2. Calculate net present value (NPV) of the projects side-financing effects:**

**+** net present value of tax relief on debt interest paid

- net present value of issue costs on equity or debt

+ net present value of tax relief on issue costs above

+/- other possible effects, e.g. subsidies

**3. Add base-case NPV and the present value of side-financing effects.** **If > 0, the project is considered as viable. **(44)

The biggest **disadvantage** is that it does consider the increased financial risk resulting from higher indebtedness. (44)

*The company intends to diversify to the new industry with average beta of 1,25, equity/debt ratio 60:40 and expected market return 14%. Risk-free rate is 5% and the interest rate 9%. The investment value is € 500 (undepreciated, immediately expensed) and annual cash-inflows are € 150, € 200, € 200, € 100 and € 70 respectively. Project equity/debt ratio is 30:70. Income tax rate is 15%.*

*1. Base case NPV:*

*β _{u} = 1,25 / ((1+ (1-0,15) * (40/60)) = 1,25 / 1,57 = 0,8*

*K _{e }= 5% + 0,8 * (14% - 5%) = 12,2% (rounded to 12%)*

__2. NPV of the projects side-financing effects:__

*debt value = 70% * 500 = 350*

*annual interest = 9% * 350 = 31,5*

*tax relief on annual interest = 31,5 * 15% = 4,7*

*PV of tax relief on annual interest = 4,7 * 3,89 (9% annuity factor for 5 years) = 18*

__3. APV__ = 34 + 18 = + 52 ….project is viable