Market and Embedded Value

Question 1

Formulas for market value of equity (126)

Answer 1

1. Market value of equity = market value of assets - market value of liabilities
   MV(E) = MV(A) - MV(L)
2. Market value of equity = franchise value + market value of tangible assets - present value of liabilities + put option value
   MV(E) = FV + MV(TA) - PV(L) + PO
3. Relationship between market value and firm risk exposure:
   a. MV increases as insolvency risk increases (put option value increases)
   b. MV increases as firm decreases in insolvency risk (franchise value increases)

Question 2

Formulas for calculating embedded value (127)

Answer 2

For a block of business:
1. Embedded value = PV(after-tax profits) + cost of capital
2. Cost of capital = PV(future tied capital releases minus increases) + PV(after-tax income earned on tied capital) - tied capital
For the company as a whole:
1. Embedded value = PV(after-tax profits) + cost of capital + tied capital + free capital = PV(after-tax profits) - PV(increase in locked-in capital) + PV(after-tax investment income on capital) + free capital

Question 3

Uses of embedded value for a block of business (128)

Answer 3

1. To set a value on a block of business for sale or purchase
2. As a part of the calculation of the value of a company. The company’s value would also include the value of future new business.
3. To ensure that new business sold is generating an increase in value
4. To determine compensation for sales staff
5. To measure the impact of specific management actions on the long-term value of the company

Question 4

Definition of embedded value (133)

Answer 4

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 5

Formulas for calculating embedded value for a company (134)

Answer 5

These two methods are equivalent. Present values are discounted using the hurdle rate (h).

1. Profits to shareholders method
   a. Embedded value = free capital + PV(profits to shareholders)
   b. Profits to shareholders = after-tax profits + after-tax investment income on capital - increase in locked-in capital
   c. After-tax profit = premiums + investment income - benefits - expenses - increase in statutory reserve - tax on income
   d. Tax on income = tax rate * (premiums + investment income - benefits - expenses - increase in tax reserve)
2. Cost of capital method
   a. Embedded value = free capital + locked-in capital + PV(after-tax profits) - PV(cost of capital)
   b. Cost of capital = h * locked-in capital - after-tax investment income on capital

Question 6

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

Answer 6

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