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Part II: Quantitative Analysis You are a homeowner that has accepted a new job. The new job requires a commute that is undesirably long, but
Part II: Quantitative Analysis
You are a homeowner that has accepted a new job. The new job requires a commute that is undesirably long, but not impossible. You would like to sell your home and move into a new one nearer your job. Your discount rate for the funds received from the sale is annualized Potential buyers will come, view and inspect the home, and negotiate a price offer. Your decision is to set in your mind the lowest such offer you are willing to accept. For simplicity, we will assume your decision must be an increment of K ieKKK etc.
We will not go into the details of the negotiating process, and just assume that the eventual price offers come from a random process described below.
ForSalebyOwner. If you sell on your own, you will generate price offers that are uniformly distributed between KK USD, and will attract one offer every months. However, as commission, the buyers agent will get of the sale price you will get the other
a To maximize the expected present value of the sales proceeds, what is the lowest price you should be willing to accept again restricting attention to increments of $K
b Using your solution to part a what is the expected present value of the sales proceeds?
c Using your solution to a what is the expected value of the sale price?
d Comment on how the expected sale price is not a sufficient metric for the value of setting any particular lowestacceptableprice.
Because time value of money.
Hiring an Agent. If you hire an agent, you will pay of the sale price in total commissions to buyer agent, to your agent, and you will get the other
a If nothing else changes, how do your answers to Question change? So if your agent provides no benefit other than the convenience of handling the transaction, what do you pay in expected present value terms for this convenience?
b Suppose selleragents have different skill levels: or More skilled agents help position the house more attractively, generating offers at higher prices and greater frequency. An agent of skill level L will generate offers that are uniformly distributed between KKLK USD, and will attract L offers every months. What is the minimum skill level required for an agent to be worth the commission in your case assuming you do not value the convenience aspect at all
The Agents NPV Suppose you hire a seller agent of the type you identified in Question b The agent must split the commission with the buyers agent, and with the agents parent firm. So your agent takes home only of the sales price. The agent discounts future payments at the same but also incurs costs associated with the marketing of your home eg targeted online ads, open houses, the opportunity cost of the agents timeeffort that come out to $ per month.
a What is the minimum acceptable price offer that maximizes the selleragents expected net present value taking into account the commission and the operating costs from your listing?
b It is often argued that agents know the local market better than sellers. Suppose that you are unsure if the price range for your house is as described above, or with every number shifted down by as much as $K ie on your own, prices between KK; with an Lagent prices between KKLK If your agent attempts to maximize as described in part a what would the agent want you to believe about the price range for your home holding fixed that the true price range is as described in Question b
c Why are the incentives of the seller and the selleragent not perfectly aligned? Can you propose a different way to structure the agents compensation so that their optimal decisions are closer to one anothers
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