profitability index & NPV

15. Profitability Index versus NPV – Hanmi Group, a consumer electronics conglomerate, is reviewing its annual budget in wireless technology. It is considering investments in three different technologies to develop wireless communication devices. Consider the following cash flows of the three independent projects of Hanmi. Assume the discount rate for Hanmi is 10 percent. Further, the Hanmi Group has only $15 million to invest in new projects this year.

Cash Flows
year	CDMA	G4	Wi-Fi
0	-$5	-$10	-$15
1	13	10	10
2	7	25	20
3	2	20	50

a.   Based on the profitability index decision rule, rank these investment.

b.   Based on the NPV, rank these investment.

c.   Based on your findings in (a) and (b), what would you recommend to the CEO of Hanmi group and why?

Answer:

The profitability index (PI) is the PV of the future cash flows divided by the initial investment. The profitability index (PI) of each project is:

PI_CDMA = ($13,000,000/1.10 + $7,000,000/1.10² + $2,000,000/1.10³) / $5,000,000

PI_CDMA = (11,818,181.82 + 5,785,123.97 + 1,502,629.60) / $5,000,000

PI_CDMA = 3.82

PI_G4 = ($10,000,000/1.10 + $25,000,000/1.10² + $20,000,000/1.10³) / $10,000,000

PI_G4 = (9,090,909.09 + 20,661,157.02 + 15,026,296.02) / $10,000,000

PI_G4 = 4.48

PI_WF = ($10,000,000/1.10 +$20,000,000/1.10² +$50,000,000/1.10³) / $15,000,000

PI_WF = (9,090,909.09 + 16,528,925.62 + 37,565,740.05) / $15,000,000

PI_WF = 4.21

The NPV of each project is:
NPV_CDMA = -$5000,000 + $13,000,000/1.10 + $7,000,000/1.10² + $2,000,000/1.10³ 
NPV_CDMA = $14,105,935.39 

NPV_G4 = -$10,000,000 + $10,000,000/1.10 + $25,000,000/1.10² + $30,000,000/1.10³ 
NPV_G4 = $34,778,362.13 

NPV_WF = -$15,000,000 + $10,000,000/1.10 +$20,000,000/1.10² +$50,000,000/1.10³ 
NPV_WF = $48,185,574.76 


NPV_{CDMA and G4} = $14,105,935.39 + $34,778,362.13 
NPV_{CDMA and G4} = $48,884,297.52

 

Reference: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition. Chapter 5, questions number 15, page 165.