Ronald Roth started his new job as controller with Aerosystems today. Carole, th
ID: 446241 • Letter: R
Question
Ronald Roth started his new job as controller with Aerosystems today. Carole, the employee benefits clerk, gave Ronald a packet that contains information on the company’s health insurance options. Aerosystems offers its employees the choice between a private insurance company plan (Blue Cross/Blue Shield), an HMO, and a PPO. Ronald needs to review the packet and make a decision on which health care program fits his needs. The following is an overview of that information.
Blue Cross/Blue Shield plan: The monthly premium cost to Ronald will be $54.63. For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 25 percent and the insurance company will cover 75 percent of covered charges. The annual deductible is $700.
The HMO is provided to employees free of charge. The copayment for doctors’ office visits and major medical charges is $20. Prescription copayments are $15. The HMO pays 100 percent after Ronald’s copayment. No annual deductible.
The POS requires that the employee pay $36.82 per month to supplement the cost of the program with the company’s payment. If Ron uses health care providers within the plan, he pays the copayments as described above for the HMO. He can also choose to use a health care provider out of the network and pay 25 percent of all charges after he pays a $700 deductible. The POS will pay for 75 percent of those covered visits. No annual deductible.
Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician five times during the year at a cost of $140 for each visit. He also spent $77 and $101 on prescriptions during the year. Assume Ron visited a physician outside of the network plan but had his prescriptions filled at a network-approved pharmacy.
If Ronald selects the POS plan, what would his annual medical costs be?
a.Blue Cross/Blue Shield plan: The monthly premium cost to Ronald will be $54.63. For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 25 percent and the insurance company will cover 75 percent of covered charges. The annual deductible is $700.
b.The HMO is provided to employees free of charge. The copayment for doctors’ office visits and major medical charges is $20. Prescription copayments are $15. The HMO pays 100 percent after Ronald’s copayment. No annual deductible.
c.The POS requires that the employee pay $36.82 per month to supplement the cost of the program with the company’s payment. If Ron uses health care providers within the plan, he pays the copayments as described above for the HMO. He can also choose to use a health care provider out of the network and pay 25 percent of all charges after he pays a $700 deductible. The POS will pay for 75 percent of those covered visits. No annual deductible.
Explanation / Answer
The payoff from the call option is $17 if the stock price rises and $12 if the stock price falls. From the binomial pricing model we can create a replicating portfolio with the following two equations:
$17 = ($47 × x) + (1.05 × y)
$12 = ($42 × x) + (1.05 × y)
x = 1 share of stock
y = –28.57 of risk free bonds
The value of the option is the value of the replicating portfolio:
(1 × $45) + (–28.57) = $16.43
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