Question

Jumbo city must decide where to allocate $3 million, which is available for immediate investment. It has four EV projects from which to choose (all cash flows in millions) and has decided to use the net present value and profitability index approaches when deciding how to allocate these funds. Disregard the difference in project lives. The cost of capital is 10%.

Year              Model 1 Model 2 Model 3 Model 4

  0                       –$1                              –$2                             –$3                          –$1.5

  1                        $1                               $1                               $4                            $0.9

  2                        $1                               $1                                –                              $0.9

  3                           –                                $1                               –                              $0.9

Required:

1. What is the net present value for each project and which projects are acceptable?
2. What is the profitability index for each project and which projects are acceptable?
3. Given the capital constraint, which project or projects do you select and why?
4. How much value does Tesla add to itself by undertaking this project or projects? How does this differ if there was no capital constraint?

Answer 1

NPV of model 1 = -1+1/1.1+ 1/1.1^2 = $0.7355 million

NPV of model 2 = -2+1/1.1+ 1/1.1^2+1/1.1^3 = $0.4868 million

NPV of model 3 = -3+4/1.1 = $0.6364 million

NPV of model 4 = -1.5+0.9/1.1+ 0.9/1.1^2+0.9/1.1^3 = $0.7382 million

All the projects are acceptable as the NPV of all projects are positive

PI of model 1 = (PV of all cashinflows)/Initial investment = 1.7355/1 = 1.7355

PI of model 2 = 2.4868/2 = 1.2434

PI of model 3 = 3.6364/3 = 1.2121

PI of model 4 = 2.2382/1.5 = 1.4921

Again, all projects are acceptable as PI is more than 1

The first project to be selected is project 1 as it has the highest PI, followed by Project 4, then if capital is available project 2 and then project 3

Project 1 and Project 4 entails total $2.5 million investment , $0.5 milion remains which cannot be invested anywhere else. So it must be tried whether NPV can be increased by replacing Project 4 with project 2. As this is not possible

Project 1 and Project 4 must be selected as these increases the NPV the maximum.

By undergoing these projects , value added = NPV of project 1 + NPV of project 4

=$0.7355 million +$0.7382 million

=$1.4737 million

If there was no capital constraint, all the NPV positive projects can be undertaken

Value Added in that case = 0.7355 +0.4869+0.6364+0.7382 = $2.5969 million