Advanced Life Insurance and Annuity Pricing

A product has a benefit pattern, mortality table, interest rate, expense assumptions, tax structure, and profit target, and you must compute the gross level premium.

Set APV(premium income) - APV(commissions and expenses) - APV(taxes) = APV(benefits) + APV(profit). Solve for the premium. Recognize different expense types — first-year (acquisition), renewal, claim. For taxes, model premium taxes and income taxes separately. Verify by plugging the gross premium back into the equation.

APV(P · ä_x) = APV(benefits) + APV(expenses) + APV(profit).

A product with a multi-year cash flow projection is given and you must compute profit per unit issued, IRR, or break-even year.

Project cash flows by year for a model point: premium in, benefits and expenses out, taxes, change in reserve. Compute the after-tax profit signature. Discount at the hurdle rate to get NPV; solve NPV = 0 for the IRR. Identify the break-even year as the first year cumulative discounted profit turns positive.

Profit signature: P - B - E - T - ΔV per year; NPV at hurdle rate.

You must compute embedded value (EV) and value of new business (VNB) given assumptions and projections.

EV = adjusted net worth (ANW) + present value of future profits (PVFP) on in-force business, discounted at the risk discount rate, net of cost of capital. VNB is the same calculation applied to one year of new sales, evaluated at issue. Distinguish between traditional EV and market-consistent EV (MCEV) in their treatment of options and guarantees.

EV = ANW + PVFP - Cost of Capital; VNB = PV of profits on one year of new business.