Question

The treasurer of Amaro Canned Fruits, Inc., has projected the cash flows of Projects A, B, and C as follows:

  

Year	Project A			Project B			Project C
0	−$	190,000		−$	355,000		−$	190,000
1		123,000			222,000			133,000
2		123,000			222,000			103,000

  

Suppose the relevant discount rate is 9 percent per year.

  

a.	Compute the profitability index for each of the three projects. (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)

   

b.	Compute the NPV for each of the three projects. (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)

   

c.	Suppose these three projects are independent. Which project(s) should Amaro accept based on the profitability index rule?
	Project A Project B Project C Project A, Project B, Project C Project A, Project B Project A, Project C Project B, Project C

  

d.	Suppose these three projects are mutually exclusive. Which project(s) should Amaro accept based on the profitability index rule?
	Project A Project B Project C Project A, Project B, Project C Project A, Project B Project A, Project C Project B, Project C

  

e.	Suppose Amaro’s budget for these projects is $545,000. The projects are not divisible. Which project(s) should Amaro accept?
	Project A Project B Project C Project A, Project B, Project C Project B, Project C Project B, Project A Project A, Project C

Answer 1

a.

Computation of Profitability index:

Profitability index = Present value of future cash flows/Initial investment

Project A:

Profitability index = [($ 123,000/ (1+0.09) + ($ 123,000/ (1+0.09)²] /$ 190,000

                              = [($ 123,000/ (1.09) + ($ 123,000/ (1.09)²] /$ 190,000

                               = [($ 123,000/ (1.09) + ($ 123,000/1.1881)]/$ 190,000

                               = ($ 112,844.036697248 + $ 103,526.639171787)/ $ 190,000                 

                              = $ 216,370.675869035/$ 190,000 = 1.13879303088966 or 1.14

Project B:

Profitability index = [($ 222,000/ (1+0.09) + ($ 222,000/ (1+0.09)²] /$ 355,000

                              = [($ 222,000/ (1.09) + ($ 222,000/ (1.09)²] /$ 355,000

                               = [($ 222,000/ (1.09) + ($ 222,000/1.1881)]/$ 355,000

                               = ($ 203669.724770642 + $ 186852.958505176)/ $ 355,000                 

                              = $ 390,522.683275818/$ 355,000 = 1.1000638965516 or 1.10

Project C:

Profitability index = [($ 133,000/ (1+0.09) + ($ 103,000/ (1+0.09)²] /$ 190,000

                              = [($ 133,000/ (1.09) + ($ 103,000/ (1.09)²] /$ 190,000

                               = [($ 133,000/ (1.09) + ($ 103,000/1.1881)]/$ 190,000

                               = ($122,018.348623853 + $ 86,693.039306456)/ $ 190,000                 

                              = $ 208,711.387930309/$ 190,000 = 1.09848098910689 or 1.10

b.

Computation of NPV:

NPV = PV of future cash flows – Initial investment

Project A:

NPV = $ 216,370.675869035 - $ 190,000 = $ 26,370.675869035 or $ 26,370.68

Project B:

NPV = $ 390,522.683275818 - $ 355,000 = $ 35,522.683275819 or $ 35,522.68

Project C:

NPV = $ 208,711.387930309 - $ 190,000 = $ 18,711.387930309 or $ 18,711.39

c.

If the projects are independent, all three projects Project A, Project B, Project C are acceptable based on Profitability Index as all these projects have PI of more than 1.

d.

If projects are mutually exclusive, Project A should be accepted based on Profitability Index as Project A has highest PI.

e.

If Amaro’s budget for these projects is $ 545,000, Project B and Project A should be accepted.