Chapter 9, Problem 7PROB

Summary Introduction

Net Present Value (NPV) of a project is the sum of the present value of all its cash outflows and inflows. When this value is positive, it indicates that the project would add value to the organization and hence should be accepted. On the other hand, if the NPV of the project is negative, the project should be rejected.

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

Here,

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

Required rate of return is “r”

Internal Rate of Return (IRR) of a project is the discount rate at which the present value of all the cash inflows is equal to the present value of cash outflows. IRR is similar to the yield to maturity (YTM) of a bond. A project with IRR greater than the required rate of return cost or the project shall be accepted.

IRR of a project is calculated using a financial calculator. All financial calculators have an inbuild cash flow register, Cash flows in accordance of the timeline and with proper +/- signs should be input, then press the key labelled “IRR”. It will return the internal rate of return of the project.

The project has an initial cost of $75,000 and is expected to generate after tax cash flow of $26,000 per year for four years. Required rate of return is 14%.