Question

. Build a new r discount rate Investment 315,580 3. How do the two sites rank in terms of NPV and the profitability index?

Answer 1

Answer:

Given

Cash flow for Mall restaurant

Year 0 P=766500

Year 1-20 A=81000

r=8%

n=20 years

NPV=A*(1-(1+r)^-n)/r -P

NPV=81000*(1-(1+8%)^-20)/8% - 766500= $28769.94 Eq 1

Since Down town restaurant cashflow is given for 10 years but mall restaurant has cash flow for 20 years so we need to make equal life cycle for both projects.So we need to increase the life cycle of downtown restaurant by repeating downtown cashflow of 0-10 years to 10-20 years.

New cash flow for down restaurant

Year 0 P=315,500

Year 1-9 A=50500

Year 10 Q=50500-315500=-265000 (negative sign implies cash out flow)

year 11-20 S=50500

r=8%

n=20 years

NPV=A*(1-(1+r)^-9)/r -Q/(1+r)^10 +S*(1-(1+r)^-10)/{r*(1+r)^10} -P

NPV=50500*(1-(1+8%)^-9)/8% - 265000/(1+8%)^10+50500*(1-(1+8%)^-10)/{8%*(1+8%)^10}-315500=$34178.89 Eq 2

From Eq 1 and Eq2 it is clear that NPV for downtown restaurant is higher.

Profitability index= PV of future cashflow/ initial Investment

For mall restaurant profitability index = {81000*(1-(1+8%)^-20)/8%}/766500=1.037 Eq 3

For downtown restaurant profitability index = {50500*(1-(1+8%)^-9)/8% - 265000/(1+8%)^10+50500*(1-(1+8%)^-10)/{8%*(1+8%)^10}}/315500=1.108 Eq 4

From Eq 3 and Eq 4 it is clear that profitability index for downtown restaurant is higher.

Ranking

	NPV	Profitability index
Mall Restuarant	2	2
Downtown restuarant	1	1