A. Calculate the annual premium for a competitive firm with no expenses other than claims. That is, calculate the premium that sets the present value of total claims equal to the present value of total premiums. Try to do this calculation in Excel using a formula or the NPV function rather than Goal Seek or Solver. (I will sketch out a suggested approach in class.)

B. Calculate the reserves for each year two different ways on two different rows.   First, use the present value definition I mentioned above. Second, set time 0 reserves equal to the full amount of premiums received immediately. Then set reserves for each later year at the previous year’s reserves plus current inflows (premiums and investment income) minus current outflows. For this firm that earns no economic profits, these two methods should generate equal answers.

C. For each year, calculate the loss ratio, the net benefits, and the net benefit ratio. Graph the loss ratio and net benefit ratio over time.

Consider a disability insurer that issues 1,000 policies today. Suppose that each year (starting 1 year from now), 10 policies result in new claims and 10 other policies are not renewed. Assume that premiums are paid at the start of each year, with the first premiums collected immediately and the last 9 years from now. Once an individual files a claim, assume that the individual receives payments of $30,000 each year (in contrast with a feature of many plans that indexes benefits for inflation) and that the claim continues through the 10^th year.   Individuals with claims continue to pay premiums. For example, exactly nine years from now premiums are collected on 910 policies, and 90*$30,000=$2,700,000 is paid out in benefits.    The final benefits are paid 10 years from now and are for 100 claims. The insurer earns 5% per year on its investments. In particular, whatever cash the insurer has each year is invested at 5%. So all of today’s premiums are invested. The accumulation from this first year of investing should then be added to year 1 net cash from policyholders (premiums minus claims), with that new total then being invested the following year. This continues each year.

Each year, the insurer records reserves equal to the present value (as of that date) of all claims to be paid after (not including) that date minus all premiums to be received after that date. Use the 5% return as a discount rate. Each dollar amount must be discounted an appropriate number of years.

Produce a worksheet that addresses the following requests. Use columns for the years 0 (today) through 10.