The Angry Bird Corporation is trying to choose between the following two mutually exclusive design projects:
Year  Cash Flow (I)  Cash Flow (II)  
0  –$  68,000  –$  17,600  
1  31,000  9,500  
2  31,000  9,500  
3  31,000  9,500  
a1 
If the required return is 12 percent, what is the profitability index for both projects? (Round your answers to 3 decimal places. (e.g., 32.161))

Profitability Index  
Project I  
Project II  
a2 
If the company applies the profitability index decision rule, which project should the firm accept?

Project Il 
b1 
What is the NPV for both projects? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))

NPV  
Project I  $  
Project II  $  
b2 
If the company applies the NPV decision rule, which project should it take?

Project I 
rev: 12_03_2012
Explanation:a.
The
profitability index is the PV of the future cash flows divided by the
initial investment. The cash flows for both projects are an annuity, so:

PI_{I} = $31,000(PVIFA_{12%,3}) / $68,000 = 1.095 
PI_{II} = $9,500(PVIFA_{12%,3}) / $17,600 = 1.296 
The profitability index decision rule implies that we accept project II, since PI_{II} is greater than the PI_{I}. 
b.
The NPV of each project is: 
NPV_{I} = –$68,000 + $31,000(PVIFA_{12%,3}) = $6,456.77 
NPV_{II} = –$17,600 + $9,500(PVIFA_{12%,3}) = $5,217.40 
The NPV decision rule implies accepting Project I, since the NPV_{I} is greater than the NPV_{II}. 
Calculator Solution: 
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. 
Project I  
CFo
 $0 
CFo
 –$68,000  
C01
 $31,000 
C01
 $31,000  
F01
 3 
F01
 3  
I = 12%  I = 12%  
NPV CPT  NPV CPT  
$64,849.44  $6,456.77 
PI = $64,849.44 / $68,000 = 1.095 
Project II  
CFo
 $0 
CFo
 –$17,600  
C01
 $9,500 
C01
 $9,500  
F01
 3 
F01
 3  
I = 12%  I = 12%  
NPV CPT  NPV CPT  
$22,817.40  $5,217.40 
PI = $22,817.40 / $17,600 = 1.296 