EV Calculation for Life Insurance Co

Question 1

Definition of embedded value (3)

Answer 1

1. A calculation of the value of a block of business, based on the present value of surplus distributable to shareholders
2. Is based on current in-force business only (not new business)
3. Equals the value of in force business plus the value of free capital. Free capital is the capital in excess of regulatory capital requirements (locked-in or tied capital)

Question 2

Formulas for market value of equity - Profits to Shareholder Method

Answer 2

EV = Free capital + PV (profits to shareholder)

Profits to shareholder = after tax profits + after tax inv income on capital - increase in locked in capital

After tax profit = premiums + Inv income - ben - exp - increase in stat rsv - tax on income

Tax on income = tax rate x (prem + inv inv - ben - exp - increase in tax reserve)

Discount using hurdle rate.

Question 3

Formulas for market value of equity - Cost of Capital Method

Answer 3

EV = free capital + locked in capital + PV(after-tax profits) + PV(cost of capital)

cost of capital = h x locked in capital - after tax inv income on capital

h = hurdle rate
Discount using hurdle rate

Question 4

Formulas illustrating the change in embedded value over time (130,135)

Answer 4

From first study note:
1. Group block EV(t+1) = EV(t) * (1+d) + (d-I) * tied capital - after-tax profits(t) + VNB(t)

2. Company EV(t+1) = EV(t) * (1+d) + d * tied capital + VNB(t)
   d=discount rate, I=after tax interest rate, VNB=value new business

From second study note (for company):

1. EV(t+1) = EV(t) + normal increase in EV + value added by new sales - dividends paid + unexpected change in EV
2. Normal increase in EV = (EV(t) - free capital) * h + free capital * i, where i is the after-tax investment income rate
3. Value added by new sales = PV(future after-tax profits on new sales) - PV(future cost of capital to support those sales)
4. An unexpected change in EV could occur for various reasons, such as actual experience being different than expected, a change in an EV assumption, or a capital injection