Question

Javier Pena has always been interested in financing artistic projects. He has recently been offered two financing opportunities in the fashion industry: financing a new line of avant-garde youth fashions designed by Jorge Vera, and financing a line of business attire designed by Paolo Ricci. Javier has had a lot of past experience with these two designers, and has observed that 20% of Vera’s fashion lines are “hits” and 80% are “misses”. Furthermore, Ricci’s fashion lines are “hits” 30% of the time, and are “misses” 70% of the time. Javier’s net liquid assets amount to $750,000. As a result he can afford to finance at most one of the two fashion lines. However he does have the option of pre-testing at most one of the fashion lines at the upcoming design show in San Francisco, before deciding which, if any, fashion line he would like to finance for the entire U.S. market for the fall fashion season. The costs and revenue associated with the two fashion lines are given below:

Fashion Line	Jorge Vera(Avant-garde)	Paolo Ricci (business attire)
Net cost of San Fransisco pre-test	$200,000	$75,000
Additional cost of U.S production of line after a San Francisco pre-test	$500,000	$275,000
Cost of U.S production if not pre-tested in San Francisco	$600,000	$325,000
Revenue if fashion line is a "hit"	$4,000,000	$2,000,000
Revenue if fashion line is a "miss"	$300,000	$100,000

Javier has observed, based on previous years, that of the avant-garde fashion lines that were hits nationwide, 80% were hits in the San Francisco pre-test; of the avant-garde fashion lines that were misses nationwide, 40% were hits in the San Francisco pre-test. Of the business attire fashion lines that were hits nationwide, 90% were hits in the San Francisco pre-test; of the business attire fashion lines that were misses nationwide, 60% were hits in the San Francisco pre-test. While Javier may find pre-test results useful, he knows the accuracy of this kind of test is not high enough to compel him in all cases to act in accordance with the pre-test results. In any event, Javier is willing to act on the basis of expected monetary values (i.e. maximize expected profit).

You have just been hired by Javier to help him analyze his problem so that he can decide what actions to take. He expects a relatively short report of your findings! Include:

What should Javier do in all possible situations?

How much money will he make on average?

What is Javier’s potential maximum loss?

Suggestion      -           think before you set up the problem

Answer 1

Calculate posterior probabilities of avant-garde as follows

Calculate posterior probabilities of business attire as follows

Decision tree analysis is as follows

a)

EMV of avant-garde (node B) = (.2*4000000+.8*300000)-600000 = 440,000

EMV of business-attire (node C) = (.3*2000000+.7*100000)-325000 = 345,000

EMV of pre-test avant-garde (node D) = .48*MAX((.3333*4000000+.6667*300000-500000), 0) + .52*MAX((.0769*4000000+.9231*300000-500000), 0) - 200000

= 339,956

EMV of pre-test business attire (node E) = .69*MAX((.3913*2000000+.6087*100000-275000), 0) + .31*MAX((.0968*2000000+.9032*100000-275000), 0) - 75000

= 320,010

EMV of avant-garde is the maximum.

Therefore, Javier should finance avant-garde for US market.

b) Expected money that he will make = EMV = $ 440,000

c) Potential maximum loss is if misses.

Potential maximum loss = 300000 - 600000 = $ - 300,000