Question

Aurora theatrical company is considering taking one of its two musicals, on tour. In order to take a musical on tour, it has to first hire a producer at a cost of $1.8 million. Once a producer is hired it can opt for the well-known musical “Phantom of the Opera It has made the following calculations  The tour would cost $8 million  There is a .75 chance that it will earn $12 million and a .25 chance it will earn $8.5 million. Or alternately it can choose a new musical “Aladdin”. The tour would cost $6million. Since Aladdin is relatively unknown, hiring a PR firm to promote it can increase the probability that it will do well. If the PR firm is hired at a cost of 1.3 million and the musical is promoted the following estimates are made  There is a .60 chance that it will earn $9 million and a .4 chance it will earn $4 million It has made the following estimates if Aladdin is chosen and no promotion is done There is a .3 chance that it will earn $9 million and a .7 chance it will earn $4 million.

a. Draw the decision tree for this problem.

b. Calculate the expected values and determine the best decision for Aurora

Answer 1

(a)

(b)

Here, the idea is to decide which option to select, and this will be done based on which of them can give the maximum profit at the end of the tour.

So, let us take the "Phantom of the Opera" at first.

Initial investment = Cost of tour + Cost of producer = 8+1.8=$9.8 million

Earnings estimate = (Probability x Profit estimate) = 0.75*12+0.25*8.5=$ 11.125 million

Profit estimate = Earnings estimate-Initial investment=11.125-9.8=$ 1.325 million (net profit)

Now, the "Alladin" with PR firm.

Initial investment = Cost of tour + Cost of PR firm= 6+1.3=$7.3 million

Earnings estimate = (Probability x Profit estimate) = 0.6*9+0.4*4=$ 7 million

Profit estimate = Earnings estimate-Initial investment=7-7.3= -$ 0.3 million (net loss)

Finally, the "Alladin" without PR firm.

Initial investment = Cost of tour= $6 million

Earnings estimate = (Probability x Profit estimate) = 0.3*9+0.7*4=$ 5.5 million

Profit estimate = Earnings estimate-Initial investment=5.5-6.0= -$ 0.5 million (net loss)

The best option is The Phantom of the opera