Question

Your company has recently revamped its health care insurance plan. You now have a choice of one of three plans as shown below:

Plan 1: The monthly cost is $32 and the insurer pays 90% of all expenses after you have paid the first $500 each year ($500 deductible).

Plan 2: The monthly cost is $5 and the insurer pays 90% of all expenses after you have paid the first $1200 each year ($1200 deductible).

Plan 3: The monthly cost is $24 and the insurer pays 70% of all expenses (no deductible).

You have gone back several years and examined past medical expenses and created the following probability distribution.

Annual Medical Expenses ($)	Probability
100	0.15
500	0.30
1500	0.35
5000	0.15
10000	0.05

Required:

a. Prepare a decision table representation of this problem.

b. Prepare a decision tree diagram model of this problem.

c. Calculate the expected annual cost for each of the three plans.

d. Which plan do you recommend from a minimum cost perspective?

Answer 1

Solution:

a. Decision table

	Monthly cost	Expenses	Expected cost with probabilities
Plan 1	$32	$500	$1940 (10%)
Plan 2	$5	$1200	$1940 (10%)
Plan 3	$24	$0	$1940 (30%)

b. Decision tree diagram

c. For the expected annual cost for each of the three plans, we need to first calculate the expected medical expenses

Expected medical expenses = 100*0.15 + 500*0.30 + 1500*0.35 + 5000*0.15 + 10000*0.05

Expected medical expenses = $1,940

Plan 1 = $32 (12) + $500 + (1 - 90%) ($1940) = $1,078

Plan 2 = $5 (12) + $1200 + (1 - 90%) ($1940) = $1,454

Plan 3 = $24 (12) + $0 + (1 - 70%) ($1940) = $870

d. Choose plan 3 since it has the lowest annual cost.