Chapter 10, Problem 16PROB

Summary Introduction

Net Present Value (NPV) of a project is useful in understanding if the project would add value to the organization. It is calculated as the sum of the present value of all the cash flows of the project. If the NPV of the project is positive, we should accept the project or else reject it.

NPV of the project is calculated by discounting the cash flows as below:

$\begin{array}{c}NPV=-\widehat{C{F}_0}+\frac{{\widehat{CF}}_1}{{\left(1+r\right)}^1}+\frac{{\widehat{CF}}_2}{{\left(1+r\right)}^2}+\mathrm{.......}+\frac{\widehat{C{F}_n}}{{\left(1+r\right)}^n}\\ ={\displaystyle \sum _{t=0}^n\frac{\widehat{C{F}_t}}{{\left(1+r\right)}^t}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}}\end{array}$

Here,

Expected net cash flow in Period t is “$\widehat{C{F}_t}$”

Required rate of return is “r”

In order to discount the cash flows to is present terms, it is essential to use the appropriate discount rate. The discount rate considers the risk of the project and considers the market risk as one of its components. This discount rate or required rate f return on the project can be calculated using Capital Asset Pricing Model (CAPM).

Required return of a project is calculated using CAPM as below:

$r_{proj}=r_{RF}+\left(r_M-r_{RF}\right){\beta }_{\mathrm{Pr}oj}$

Here,

Required return of the project is “$r_{proj}$”

Risk free rate is “$r_{RF}$”

Market rate of return is “$r_M$”

Market risk or beta of the project is “${\beta }_{\mathrm{Pr}oj}$”

The project has a beta co-efficient of 1.3 with prevailing risk-free rate of 3% and market risk premium of 6%. The company needs to evaluate a project which has an initial investment of $405,000 and after-tax net cash flow of $165,000 for the next three years.