Question

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects:

  

Year	Cash Flow (I)				Cash Flow (II)
0	–$	70,000			–$	17,400
1		31,500				9,400
2		31,500				9,400
3		31,500				9,400

   

a-1	If the required return is 11 percent, what is the profitability index for both projects? (Do not round intermediate calculations. Round your answers to 3 decimal places, e.g., 32.161.)

a-2	If the company applies the profitability index decision rule, which project should the firm accept?
	Project I Project Il

  

b-1	What is the NPV for both projects? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

  

  

b-2	If the company applies the NPV decision rule, which project should it take?
	Project I Project II

Answer 1

Cash flows for project I are:

Year 0:-$70000
Year 1:$31500
Year 2:$31500
Year 3:$31500

Cash flows for project II are:
Year 0:-$17400
Year 1:$9400
Year 2:$9400
Year 3:$9400

Answer a-1:
Given that the required return=11%

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

Present value of future cash flows=Cash flow in year 1/(1+required return)^1+Cash flow in year 2/(1+required return)^2+Cash flow in year 3/(1+required return)^3
For project I:
Present value=31500/(1+11%)^1+31500/(1+11%)^2+31500/(1+11%)^3
=31500/(1.11)^1+31500/(1.11)^2+31500/(1.11)^3
=31500/1.11+31500/1.2321+31500/1.367631
=28378.37838+25566.10665+23032.52851
=76977.01354
Initial cash outflow=$70000

Profitability index=76977.01354/70000=1.099671622

For project II:
Present value=9400/(1+11%)^1+9400/(1+11%)^2+9400/(1+11%)^3
=9400/(1.11)^1+9400/(1.11)^2+9400/(1.11)^3
=9400/1.11+9400/1.2321+9400/1.367631
=8468.468468+7629.250872+6873.198984
=22970.91832
Initial cash outflow=$17400
Profitability index=22970.91832/17400=1.32016772

Answer a-2:
The project with the higher profitability index should be accepted.
So, project II should be accepted.

Answer b-1:

NPV=-Initial cash outflow + Present value of future cash flows
For project I:
Present value of future cash flows=$76977.01354
Initial cash outflow=$70000
NPV=-$70000+$76977.01354=$6977.01354

For project II:
Present value of future cash flows=$22970.91832
Initial cash outflow=$17400
NPV=-$17400+$22970.91832=$5570.91832

Answer b-2:
The project with higher NPV should be accepted.
So, project I should be accepted.