In: Statistics and Probability
You are a real estate developer and are trying to determine the EMV of your net commission from a sales call to a potential purchaser.
Assume that your transportation cost is $1.45 per mile
Assume that the sales call is 70 miles round trip
Assume that your transportation time is 2.25 minutes per mile
Assume that the value of your time for transportation is $55.00 per hour
Assume that it will take 3 hours to meet with the potential purchaser
Assume that the value of your time for the customer meeting is $150.00 per hour
Assume that you will have a 19% chance of a successful sales call (sales call #1)
If sales call #1 is successful,
you will sell a house valued at $275,000 with likelihood = 55%
you will sell a house valued at $300,000 with likelihood = 35%
you will sell a house valued at $425,000 with likelihood = 10%
Assume that your commission will be 2.5% of the value of the house if sales call #1 is successful.
a) What is the expected cost (time and transportation) of sales call #1?
b) Without assuming that the sales call will be successful (that is, it may or may not be a success), what is the expected gross commission of sales call #1 (do not net out the expected costs)?
Suppose you have a second possible sales call (sales call #2). Assume that the expected cost remains the same and that the commission rate remains 2.5%, but that the following information is the different information for sales call #2.
Assume that you will have a 12% chance of a successful sales call (sales call #2) If sales call #2 is successful,
you will sell a house valued at $285,000 with likelihood = 45%
you will sell a house valued at $320,000 with likelihood = 25%
you will sell a house valued at $355,000 with likelihood = 30%
c) Assuming that your sales call is successful, look at the worst possible outcome for each decision and choose the decision that has the best (or least bad) of these.
a) What is the expected cost (time and transportation) of sales call #1?
Expected transportation cost = $1.45 per mile * 70 miles = $101.5
Transportation time = 2.25 minutes per mile = 2.25/60 hour per mile
Total Transportation time = 70 mile * 2.25/60 hour per mile = 2.625 hours
Expected value of your time for transportation = 2.625 hours * $55.00 per hour = $144.375
Expected value of your time for the customer meeting = 3 hours * $150.00 per hour = $450
Expected cost (time and transportation) = $101.5 + $144.375 + $450 = $695.875
b)
Expected value of house sold of a successful sales call = 0.55 * $275,000 + 0.35 * $300,000 + 0.1 * $425,000 = $298750
Expected value of house sold = 0.19 * 298750 + (1-0.19) * 0 = $56762.5
Expected gross commission of sales call #1 = 2.5% * 56762.5 = 0.025 * 56762.5 = $1419.062
c)
Maximin approach -
Expected payoff for Sales call #1 for three outcomes -
When you will sell a house valued at $275,000 = 0.025 * $275,000 - $695.875 = $6179.125
When you will sell a house valued at $300,000 = 0.025 * $300,000 - $695.875 = $6804.125
When you will sell a house valued at $425,000 = 0.025 * $425,000 - $695.875 = $9929.125
The worst payoff for Sales call #1 is $6179.125
Expected payoff for Sales call #2 for three outcomes -
When you will sell a house valued at $285,000 = 0.025 * $285,000 - $695.875 = $6429.125
When you will sell a house valued at $320,000 = 0.025 * $320,000 - $695.875 = $7304.125
When you will sell a house valued at $355,000 = 0.025 * $355,000 - $695.875 = $8179.125
The worst payoff for Sales call #2 is $6429.125
The maximum of worst payoffs is for Sales call #2.
So, sales call #2 is the maximin sales call.