Exercises For Lecture 3

Problem
You want to endow a chair for a female professor of finance at your alma mater. You’d like to attract a prestigious faculty member, so you’d like the endowment to add $100,000 per year to the faculty member’s resources (salary, travel, databases, etc.) If you expect to earn a rate of return of 4% annually on the endowment, how much will you need to donate to fund the chair?
Solution
This is a perpetuity of $100,000 per year. The funding you would need to give is the present value of that perpetuity. From the formula:

You would need to donate $2.5 million to endow the chair.

Problem
Suppose your firm has the following five positive NPV projects to choose from. However, there is not enough manufacturing space in your plant to select all of the projects. Use profitability index to choose among the projects, given that you only have 100,000 square feet of unused space.
Project
NPV
Square feet needed
Project 1
100,000
40,000
Project 2
88,000
30,000
Project 3
80,000
38,000
Project 4
50,000
24,000
Project 5
12,000
1,000
Total
330,000
133,000
Solution
Compute the PI for each project

Project
NPV
Square feet needed
Profitability Index (NPV/Sq. Ft)
Project 1
100,000
40,000
2.5
Project 2
88,000
30,000
2.93
Project 3
80,000
38,000
2.10
Project 4
50,000
24,000
2.08
Project 5
12,000
1,000
12.0
Total
330,000
133,000

Rank order them by PI and see how many projects you can have before you run out of space.
Project
NPV
Square feet needed
Profitability Index (NPV/Sq. Ft)
Cumulative total space used
Project 5
12,000
1,000
2.5
1,000
Project 2
88,000
30,000
2.93
31,000
Project 1
100,000
40,000
2.5
71,000
Project 3
80,000
38,000
2.11

Project 4
50,000
24,000
2.08