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 For example, you may discover outdated plumbing or electrical systems that do not meet building codes.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. Find the expected completion time for each option. Find the expected renovation cost for each option. 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.

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