Question

What is profitability Index? Given the discount rates and the future cash flows of each project, which project should they accept using Profitability Index?

Cash Flows	Project A	Project B	Project C	Project D
Year Zero	- $ 1,500,000	- $ 1,500,000	- $ 2,000,000	- $ 2,000,000
Year One	$ 350,000	$ 400,000	$ 700,000	$ 200,000
Year Two	$ 350,000	$ 400,000	$ 600,000	$ 400,000
Year Three	$ 350,000	$ 400,000	$ 500,000	$ 600,000
Year Four	$ 350,000	$ 400,000	$ 400,000	$ 800,000
Year Five	$ 350,000	$ 400,000	$ 300,000	$ 1,000,000
Discount Rate	4%	8%	13%	18%

Answer 1

• The profitability index is an index that attempts to identify the relationship between the costs and benefits of a proposed project through the use of a ratio calculated as:

  

• If PV> 1, the project is profitable and can be accepted. Conversely, if PV<1, the project may be rejected

• We need to find the present value of benefits and divide by the present value of the costs for each project.

Project A’s PV Benefits = $350,000/1.04 + $350,000/1.04² + $350,000/1.04³ + $350,000/1.04⁴ + $350,000/1.04⁵

Project A’s PV Benefits = $336,538.46 + $323,594.67 + $311,148.73 + $299,181.47 + $287,674.49 = $1,558,137.84

Project A’s PV Costs = $1,500,000

Project A’s PI = $1,558,137.84 / $1,500,000 = 1.0388 and accept project.

Project B’s PV Benefits = $400,000/1.08 + $400,000/1.08² + $400,000/1.08³ + $400,000/1.08⁴ + $400,000/1.08⁵

Project B’s PV Benefits = $370,370.37 + $342,935.53 + $317,532.90 + $294,011.94 + $272,233.28 = $1,597,084.02

Project B’s PV Costs = $1,500,000

Project B’s PI = $1,597,084.02 / $1,500,000 = 1.0647 and accept project.

Project C’s PV Benefits = $700,000/1.13 + $600,000/1.13² + $500,000/1.13³ + $400,000/1.13⁴ + $300,000/1.13⁵

Project C’s PV Benefits = $619,469.03 + $469,888.01 + $346,525.08 + $245,327.49 + $162,827.98 = $1,844,037.59

Project C’s PV Costs = $2,000,000

Project C’s PI = $1,844,037.59 / $2,000,000 = 0.9220 and reject project.

Project D’s PV Benefits = $200,000/1.18 + $400,000/1.18² + $600,000/1.18³ + $800,000/1.18⁴ + $1,000,000/1.18⁵

Project D’s PV Benefits = $169,491.53 + $287,273.77 + $365,178.52 + $412,631.10 + $437,109.22 = $1,671,684.14

Project D’s PV Costs = $2,000,000

Project D’s PI = $1,671,684.14 / $2,000,000 = 0.8358 and reject project.

So, project A and B can be accepted.