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In: Finance

The Arbors at Los Brisos and Ranch Pointe are being considered for investment. Our initial investment...

The Arbors at Los Brisos and Ranch Pointe are being considered for investment. Our initial investment in the two properties are:

   The Arbors at Los Brisos $2,000,000
   Ranch Pointe $2,750,000


The cost of capital for our firm is 12%


We need to rank the projects according to the profitability index.


The Arbors at Los Brisos Ranch Pointe
   Initial Investment    -$2,000,000 -$2,750,000
Year 1    $450,000 $300,000
Year 2    $600,000 $500,000
Year 3    $750,000 $750,000
Year 4    $700,000 $875,000
Year 5    $700,000 $950,000


Which of the two should be ranked higher based upon profitability index?

The Arbors at Los Brisos

Ranch Pointe

Neither because the profitability is less than 1.0

Not enough information available to determine.

Solutions

Expert Solution

Answer: The Arbors at Los Brisos should be ranked higher based upon profitability index.

Initial investment for "The Arbors at Los Brisos"=$2,000,000
Initial investment for "Ranch Pointe"=$2,750,000

Cash flows for "The Arbors at Los Brisos":
Year 0:$2,000,000
Year 1:$450,000
Year 2:$600,000
Year 3:$750,000
Year 4:$700,000
Year 5:$700,000

Profitability index=(Present value of future cash flows)/(Initial investment)

Present value of future cash flows= (Cash flow in year 1)/(1+cost of capital)^1+(Cash flow in year 2)/(1+cost of capital)^2+(Cash flow in year 3)/(1+cost of capital)^3+(Cash flow in year 4)/(1+cost of capital)^4+(Cash flow in year 5)/(1+cost of capital)^5
Present value of future cash flows=450000/(1+12%)^1+600000/(1+12%)^2+750000/(1+12%)^3+700000/(1+12%)^4+700000/(1+12%)^5
=450000/(1.12)^1+600000/(1.12)^2+750000/(1.12)^3+700000/(1.12)^4+700000/(1.12)^5
=450000/1.12+600000/1.2544+750000/1.404928+700000/1.57351936+700000/1.762341683
=401785.7143+478316.3265+533835.1859+444862.6549+397198.799
=2255998.681
Profitability index for "The Arbors at Los Brisos"=2255998.681/2000000=1.127999341 or 1.23 (Rounded to two decimal places)


Cash flows for "Ranch Pointe":
Year 0:$2,750,000
Year 1:$300,000
Year 2:$500,000
Year 3:$750,000
Year 4:$875,000
Year 5:$950,000
Present value of future cash flows=300000/(1+12%)^1+500000/(1+12%)^2+750000/(1+12%)^3+875000/(1+12%)^4+950000/(1+12%)^5
=300000/(1.12)^1+500000/(1.12)^2+750000/(1.12)^3+875000/(1.12)^4+950000/(1.12)^5
=300000/1.12+500000/1.2544+750000/1.404928+875000/1.57351936+950000/1.762341683
=267857.1429+398596.9388+533835.1859+556078.3186+539055.513
=2295423.099
Profitability index=(Present value of future cash flows)/(Initial investment)
=2295423.099/2750000=0.834699309 or 0.83 (Rounded to two decimal places)

The Arbors at Los Brisos should be ranked higher based on profitability index because its profitability index is 1.23 which is higher than that of Ranch Pointe.

jeff jeffy answered 7 months ago
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