Chapter 9, Problem 20PROB

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 like 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.

Discounted payback period is the length of the time it takes for the project’s discounted cash flows to be repaid. In other words, it captures the number of years to recover the investment in the project. A project with lower discounted payback period as compared to the project’s useful life, should be accepted.

Three independent projects have been analysed by three interns with NPV, IRR and discounted payback period of each is provided. Inter A’s project has a project life of 7 years, NPV of $5,300, IRR of 12% and discounted payback period of 6.8 years. Intern J has a project life of 6 years, NPV of -$1,800, IRR of 8% and discounted payback period of 5.8 years whereas, Intern K has project life of 10 years, NPV of $4,500, IRR of 10% and discounted payback period of 9.6 years.