Suppose you are interested in purchasing a home and have the opportunity to eith

Question

Suppose you are interested in purchasing a home and have the opportunity to either purchase a new home or a fixer-upper. A new home in your desired location will cost $450,000, but an older home costs $250,000 and will require renovations. You know the cost of each home purchase with certainty, but the cost of renovations can vary significantly due to the age of the house. For example, you may discover outdated plumbing or electrical systems that do not meet building codes. These conditions will drive the cost of renovations up. After evaluation, you determine that there is a 25% chance the cost of renovations will be $100,000 and a 75% chance that the cost will be $250,000. Using the expected value method, determine if you purchase a new home or buy the fixer-upper and complete the renovations. Suppose you chose to purchase the fixer-upper and then were faced with the decision to hire a contractor or manage the renovation project yourself. If you hire a contractor, then the probability of successfully completing the renovation in 5 months with a cost of $200,000 is 80%, and a 20% chance it will cost $250,000 and take 6 months. If you manage the renovation project yourself, then the probability of successfully completing the renovation in 7 months with cost $125,000 is 75%, and a 25% chance it will cost $200,000 and take 8 months. a) Find the expected completion time for each option. b) Find the expected renovation cost for each option. c) What option should you choose? Justify your answer.

Explanation / Answer

Question 1:

Cost of new home = $450, 000

Expected cost of an fixed-upper post renovations = 250,000 + expected cost of renovations.

Now expected cost of renovations = 0.25*100,000 + 0.75*250,000 because there is a 25% chance that the cost of renovations would be 100,000 and a 75% chance that the cost of renovations would be 250,000

Therefore expected cost of renovations = 0.25*100,000 + 0.75*250,000 = 25,000 + 187,500 = 212,500

Therefore total expected cost of the fixed upper including renovations cost = 250,000 + 212,500 = $462,500

Therefore from the above analysis we get that the cost of a new house is $450,000 and the expected cost of the fixed upper including the expected cost of the renovations would be $462,500 > $450,000 Therefore we should buy a new home.

Question 2:

a) For option 1 where we are hiring a contractor, the expected time of completion would be 5* probability of completion in 5 months + 6* probability of completion in 6 months = 5*0.8 + 6*0.2 = 4+1.2 = 5.6 months.

For option 2 where we doing it ourselves, the expected time of completion would be 7* probability of completion in 7 months + 8* probability of completion in 8 months = 7*0.75 + 8*0.25 = 5.25 + 2= 7.25 months.

b) For option 1 where we are hiring a contractor, the expected renovation cost would be 200,000* probability of expected cost to be 200,000 + 250,000* probability of expected cost to be 250,000 = 200,000*0.8 + 250,000*0.2 = 160,000+50,000 = $210,000

For option 2 where we are doing it ourselves, the expected renovation cost would be 125,000* probability of expected cost to be 125,000 + 200,000* probability of expected cost to be 200,000 = 125,000*0.75 + 200,000*0.25 = 93,750+50,000 = $143,750

c) The option we choose depends on our priority whether we want the work to be finished early or whether in lesser cost. There is clearly a huge cost difference between teh 2 expected costs. If we want to save on costs then we should clearly go for option 2 where we are doing it ourselves. If want to finish it up as early as possible we should go for option-1 where we are giving the worl to the contractor to do the job for us.

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