Question

Apple is considering marketing one of two new smartphones for the coming holiday season: iPhone 8 and iPhone X. Estimated profits in total USD under high, medium, and low demand are as follows:

iPhone X	High	Medium	Low
Profit	$3,200,000,000	$2,500,000,000	$1,750,000,000
Probability	0.225	0.5	0.275

There is concern that profitability will be affected by a Google's introduction of the Pixel 2 smartphone viewed as similar to the iPhone 8. Estimated profits in total USD with and without competition are as follows:

With Competition (iPhone 8)	High	Medium	Low
Profit	$1,250,000,000	$800,000,000	$600,000,000
Probability	0.2	0.5	0.3

Without Competition  (iPhone 8)	High	Medium	Low
Profit	$2,000,000,000	$1,250,000,000	$800,000,000
Probability	0.45	0.35	0.2

a. Develop a decision tree for the Apple problem.

b. For planning, Apple believes there is a 0.99 probability that its competitor will produce a new smartphone similar to the iPhone 8. Given this probability of competition, the director of planning in Cupertino recommends spending the ad dollars and heavily marketing the iPhone X smartphone. Using expected value, what is your recommended decision?

c. Show a risk profile for your recommendation.

d. Use sensitivity analysis to determine what the probability of competition for iPhone 8 would have to be for you to change your recommended decision alternative.

Answer 1

(a)

(b)

The expected value of iPhone X is $2,451,250,000 which is the highest. So, the optimal decision is to market iPhone X and not iPhone 8.

(c)

Risk profile

(d)

Using Excel's datatable option,

Probability of competition	Expected payoff (iPhone 8)
0.99	836.675
0.90	896.75
0.81	956.825
0.72	1016.9
0.63	1076.975
0.54	1137.05
0.45	1197.125
0.36	1257.2
0.27	1317.275
0.18	1377.35
0.09	1437.425
0	1497.5

Therefore, it is very clear that for none of the probability values, iPhone 8 will be an optimal option because for all cases the expected values are less than 2451.25.