The PI of the plant expansion project is ???

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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​Integrative: Conflicting Rankings   
The​ High-Flying Growth Company​ (HFGC) has been expanding very rapidly in recent​ years, making its shareholders rich in the process. The average annual rate of return on the stock in the past few years has been 22​%, and HFGC managers believe that 22​% is a reasonable figure for the​ firm's cost of capital. To sustain a high growth​ rate, HFGC's CEO argues that the company must continue to invest in projects that offer the highest rate of return possible. Two projects are currently under review. The first is an expansion of the​ firm's production​ capacity, and the second project involves introducing one of the​ firm's products into a new market. Cash flows from each project appear in the following​ table:
 
Year  Plant expansion Product introduction
   0         -4,000,000          -500,000
   1          2,000,000            375,000
   2          2,000,000            350,000
   3          3,000,000            400,000
   4          3,000,000            400,000
a. Calculate the NPV for both projects. Rank the projects based on their NPVs.
b. Calculate the IRR for both projects. Rank the projects based on their IRRs.
c. Calculate the PI for both projects. Rank the projects based on their PIs.
d. The firm can undertake only one investment. What do you think the firm should​ do?
 
a) NVP of the planet expansion = $1,989,387
     NVP of the product introduction = $443,371
     According to the NVP method, which project should the firm choose? 
      - Plant expansion
 
b) IRR of the plant expansion = 44.9%
    IRR of the product introduction = 64.8%
    According to the IRR method, which project should the firm choose? 
     - Product introduction
 
c) The PI of the plant expansion project is ???
(please help me figure this out. I do not know how to get the calculations to get the answer.)
Expert Solution
Step 1: Introduction

As per instruction, question c will be solved. 

To determine PI (Profitability Index) we need to use the formula below:

P I space equals space fraction numerator P V thin space o f space c a s h space i n f l o w s over denominator I n i t i a l space i n v e s t m e n t end fraction

PI is used to evaluate the attractiveness of an investment or project. It is a ratio that measures the relationship between the present value of cash inflows and the present value of cash outflows over a specified period of time.

The Profitability Index provides a numerical value that helps in assessing whether an investment is viable. If the PI is greater than 1, it suggests that the project is expected to generate positive returns. The higher the PI, the more attractive the investment.

Since you have already computed the NPV of the projects, we can determine the PV of cash inflows using the formula below:

P V space o f space c a s h space i n f l o w s space equals space N P V thin space plus space i n i t i a l space i n v e s t m e n t

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