profitability index or pipi benefit-cost ratio

Question

Profitability Index or P.I.

P.I. (benefit-cost ratio) = Present value of inflows / Present value of cash outlay

Whether P.I. is greater than 1.0, invest and whereas less than 1.0, reject.

Example

The following information was from XYZ feasibility studies. This has studied two ventures as:

a) Cost 100,000/= and 160,000/= on the starting of the 4^th year and it will create inflows 1-3^rd year 80,000/= and from 4-6^th year 50,000/= per annum.

b) Initial cost 200,000/= and 80,000/= on the starting of the 4^th year and it will create the following inflows:

          1^st - 2^nd year -> Shs.100, 000 per annum

          3rd - 6th year -> Shs.70,000 per annum

Using the cost of finance of 12 percent compute the P.I. of these two ventures, advise the company accordingly.

Solution

a) Outflows: 100,000/1 + 160,000 / (1.12)³ = 100,000 + 113,887 = 213,885

Inflows: 80,000 / (1.12)¹/80,000/ (1.12)² + 80,000 / (1.12)³ + 50,000 / (1.12)⁴ + 50,000 / (1.12)⁵ + 50,000 / (1.12)⁶  =  Shs.277,626

       P.I. = 277,626/213,885                                        

       P.I. = 1.298

b) Outflows: = 200,000 / 1 + 80,000 / (1.12)³   =  256,944

Inflows = 100,000 / (1.12)¹ + 100,000 / (1.12)² +70,000 / (1.12)³+70,000 / (1.12)⁴ +70,000 / (1.12)⁵  +70,000 / (1.12)⁶   

  = Shs.338,501

       P.I.    =  338,501 / 256,944                                                

                =  1.32