Question

5 for the new r 10 discount rate Mall rest 315,580 50,500 t value of each 3. How do the two sites rank in terms of NPV and the profitability index? Next > here to search

Answer 1

Answer:

1)

Mall Resturant

initial Investment P=$766,500

Annual cashflow 1-20 years A=$81,000

n=20 years

interest rate r=8%

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

NPV=81000*(1-(1+8%)^-20)/8% - 766500=$28769.94 EQ1

For Down town Restaurant

Since down town restaurant has only 10 years of life cycle where as mall restaurant has 20 years. So we need to make equal life cycle for both. So we will repeat the cashflow for downtown restaurant for one more time with from 10-20 years to make life cycle equal.

So new cash flow for downtown restaurant

Initial Investment P=$315,500

Annual cashflow 1-9 years A=$50,500

Cashflow for 10th year B=$50,500-$315500=-$265,000(negative sign implies cash outflow)

Annual cashflow 11-20 years C=$50,500

interest rate r=8%

NPV=A*(1-(1+r)^-9)/r -B/(1+r)^10+C*(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 EQ2

From Equation 1 and 2 it is clear that NPV is higher for Downtown restaurant.

2)

Profitability Index=Pv of Future cash flow/Initial Investment

For Mall Restaurant

Profitability Index= {81000*(1-(1+8%)^-20)/8%}/766500= 1.038 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

3)

From Equation 1 and 2 it is clear that NPV is higher for Downtown restaurant.

From Equation 3 and 4 it is clear that Profitability index is higher for Downtown restaurant.

	NPV	Profitability index
Mall Restaurant	2	2
Down town Restaurant	1	1