Section B - Insurance Company Valuation

Question 1

Goldfarb: Dividend Discount Model Formulas

Answer 1

V₀ = PV(Div) + PV(TV)

TV = Terminal Value = Div_final(1+g) / (k-g)

PV(TV) = TV / (1+k)ⁿ

PV(Div) = ∑E[Div_t] / (1+k)^t

Div_t = NI_t • (1-Dividend Ratio)

Question 2

Goldfarb: What are the disadvantages of the Dividend Discount Rate Model (DDM)?

Answer 2

Disadvantages

• Actual dividend payments are discretionary and difficult to forecast
• Terminal value is sensitive to assumptions and can represent the majority of the valuation
• Stock buybacks mean a more liberal definition of “dividend” is needed for the DDM

Question 3

Goldfarb: Dividend Growth Rates beyond Forecast Horizon

g = ?

Answer 3

g = plowback • ROE

• plowback refers to the portion of earnings retained and reinvested
• ROE is the income generated on reinvestment

Question 4

Goldfarb: Dividend Discount Rate Model

Key Assumptions

Answer 4

DDM valuation is driven by the following assumptions:

• Expected dividends during the forecast horizon
• Dividend growth rates beyond the forecast horizon
• Appropriate risk-adjusted discount rate

Question 5

Goldfarb: Rate of Return CAPM Formula

Answer 5

k = r_<em>f</em> +β•E[R_m]

Question 6

Goldfarb: Briefly describe how high growth rates affect dividends.

Answer 6

High growth rates and high dividends are not sustainable at the same time.

This means that high growth rates will be offset by lower dividend amounts.

(Q EP 1a)

Question 7

Goldfarb: Briefly explain how high growth rates affect the risk-adjusted rate of return.

Answer 7

Firms with high growth rates tend to be riskier which drives the risk-adjusted rate up.

Question 8

Goldfarb: Briefly describe two ways of determining beta used in CAPM.

Answer 8

Firm Beta

• Calculated with linear regression of the firm’s historical stock returns vs. market returns
• Disadvantage - often unreliable for individual firms due to statistical issues and changes in the firm’s risk over time

Industry Beta

• Mean or median beta for industry
• Disadvantage - doesn’t always reflect the firm to the extent the firm’s risk differs from industry
• Advantage - more stable and reliable than the historical firm beta

Question 9

Goldfarb: If an industry beta is used to determine the risk-adjusted discount rates, briefly describe two adjustments that may need to be made to beta.

Answer 9

Industry-average Beta is more stable, but should be reviewed and possibly adjusted to reflect:

Mix of Business

• Only use firms with comparable mixes of business
• May drop number of firms significantly which can reduce the reliability of the result

Financial Leverage

• Higher leverage (debt) makes the cash flows to equity riskier and should be reflected with a higher Beta
• To make Betas more comparable, we could “de-lever” the equity Beta to compare to “all-equity Beta” to the industry

Question 10

Goldfarb: Risk-free Rate Options for CAPM

Answer 10

Should be based on current yields on risk-free securities:

1. 90 Day T-Bill - free of both credit and reinvestment rate risk
2. Maturity Matched T-Notes - maturity matches the average maturity of cashflows
3. T-Bonds - most stable option, makes the most sense for corporate decision-making and can better match the duration of the market portfolio and cashflows

Question 11

Goldfarb: When determining the risk-free rate based on T-Bonds, what do you need to do before you can use the rate?

Answer 11

When estimating the risk-free rate, we should subtract the liquidity premium from the T-Bond yield to put it on par with other risk-free investments.

• T-Bonds tend to be long term and therefore include a liquidity risk premium.

Question 12

Goldfarb: Considerations in Selecting an Appropriate Equity Risk Premium

Answer 12

Short-Term vs. Long-Term Risk Free Rate as a Benchmark

• Market risk premium
• Important to use the same risk-free rate in the CAPM formula

Arithmetic vs. Geometric Averages

• Arithmetic Average - best for single period forecasts
• Geometric Average - best for multi-period forecasts/long-term averages

Historical vs. Implied Risk Premiums

• Historical Average - need to select an appropriate time period
• Implied - the risk premium is implied by the current market prices

Question 13

Goldfarb: Briefly describe sensitivity analysis.

Answer 13

Sensitivity Analysis

DDM and FCFE models are sensitive to growth and discount rate assumptions.

Sensitivity analysis shows the valuations using a range of discount rate and growth rate beyond the forecast horizon assumptions.

High-growth/low-discount rate and low-growth/high-discount rate combinations are unlikely because these assumptions are not independent.

• Rapid growth is unlikely without increased risk

Question 14

Goldfarb: Table to set up for the DDM.

Answer 14

Time/Years across the top

• Income after Tax
• Dividends Paid
• Beginning Equity
• Ending Equity
• ROE
• Growth Rate

Look at growth and ROE over time and select a growth rate to calculate the terminal value.

Question 15

Goldfarb: What is Free Cash Flow?

Answer 15

Free Cash Flow

All the cash that could be paid as dividends or other payments to capital providers (adjusted for investments) to support current operation and expected growth.

Question 16

Goldfarb: Free Cash Flow to Equity Formula

Answer 16

Question 17

Goldfarb: FCFE Method Formulas

Answer 17

PV(FCFE) = ∑FCFE_t / (1+k)^t

TV = FCFE_final(1+g) / (k-g)

PV(TV) = TV / (1+k)ⁿ

V₀ = PV(FCFE) + PV(TV)

Question 18

Goldfarb: FCFE Growth Formulas

Reinvested Capital = ?

Reinvestment Rate = ?

Horizon Growth Rate = ?

Forecast Horizon Growth Rate = ?

Answer 18

Reinvested Capital = Change in Capital

• this is also known as the increase in required capital

Reinvestment Rate = Reinvested Capital / Net Income

• similar to plowback (what we are keeping to reinvest)

Horizon Growth Rate (HGR) = Reinvestment Rate_selected • ROE_selected

HGR = Reinvested Capital / Beginning Capital = (NI - FCFE) / Beg Capital

• just another version of the same formula
• if there is No net borrowing or other impacts, then we can use NI - FCFE

Forecast Horizon Growth Rate = g = FCFE_t / FCFE_t-1 - 1

Question 19

Goldfarb: What are the issues with the FCFF method for insurance companies?

Answer 19

Goldfarb prefers the FCFE method over the FCFF due to several reasons:

→FCFF values equity indirectly as the value of the firm net the market value of debt.

• Policyholder Liabilities vs. Debt - FCFF treats debt similarly to equity as a source of capital. The distinction between PH liabilities and debt is arbitrary and there’s no good reason to treat them differently. (as per Goldfarb)
• WACC - FCFF uses the weighted average cost of capital (WACC) to discount free cash flows. This reflects risk to both debt and equity holders, but it’s difficult to define WACC because of PH liabilities.
• APV - Adjusted present value method uses the all-equity discount rate to derive the value of the firm without considering debt-holders’ claims, tax consequences of debt or the impact of debt on the riskiness of the EQH’s claims

Question 20

Goldfarb: How are Loss & LAE reserves treated in the FCFE method?

Answer 20

Increase in Loss & LAE reserves show up in both Non-Cash Charges and Capital Expenditures so they cancel out in the rest of the FCFE formula and are reflected in Net Income.

Question 21

Goldfarb: What are the advantages and disadvantages of the FCFE method?

Answer 21

Disadvantages

• Adjusting projected Net Income to calculate forecasted free cash flows makes the interpretation of FCFE difficult.
  
  • FCFE may bear little resemblance to internal forecasts
• May be difficult to assess reasonableness of cash flow/growth rates

Advantages

• Relatively simple to understand
• Focused on the firm’s net cash flow generating capacity

Question 22

Goldfarb: What are the assumptions underlying the FCFE method?

Answer 22

• FCFE method assumes that free cash flow not paid immediately as dividends can be invested to earn an appropriate risk-adjusted return
• Assume an average discount rate for the entire FCFE cash flows
  
  • P&C insurers will have cash flows from different investible assets (stocks, bonds, etc.) as well as liability cash flows in theory
  • These assets have different discount rates, but for practicality, we use a single discount rate.

Question 23

Goldfarb: In theory, the dividend discount model and the discounted cash flow model should use different discount rates. Why?

Answer 23

The DDM and the FCFE models should use different discount rates due to the riskiness of the cashflows paid to the shareholders.

• DDM assumes that dividends are paid to shareholders and the rest is invested in marketable securities. This is more risky as a larger portion of risk is coming from marketable securities than from underwriting risk.
• FCFE pays out all cashflows to shareholders and therefore is less risky.

Question 24

Goldfarb: Set up the table used to solve for FCFE.

Answer 24

Year as column headers

• Net Income after tax
• Beginning Equity
• Required Capital
• Increase in Required Capital
• FCFE
• ROE
• Reinvestment Rate

Question 25

Goldfarb: Abnormal Earning Method Formulas

Answer 25

AE_t = NI_t - k•BV_t-1 = (ROE_t - k)•BV_t-1

V₀ = BV₀ + ∑PV(AE)

• Note that we use k, which is the discount rate, to derive the normal earnings not ROE
  
  • the difference between ROE and required ROR falls to zero in a finite period due to competition for abnormal earnings
• There is no growth assumed for the terminal value - just decline over certain number of periods
  
  • sometimes the question gives you growth to trick you

Question 26

Goldfarb: Advantages of the Abnormal Earnings Method

Answer 26

Advantages

• Net Income doesn’t need to be adjusted to calculate cash flows
• Emphasizes the ability of the firm to generate abnormal earnings, the real source of value creation
• Less importance is placed on the terminal value which can be highly sensitive to assumptions

Note: Accounting rules that distort earnings also distort book value and will “self correct” over time so we can use accounting values.

Question 27

Goldfarb: What adjustments need to be made to the beginning book value for the abnormal earnings method?

Answer 27

• Remove any systematic bias in reported assets and liabilities (e.g. restating reported loss reserves)
• Remove intangible assets (e.g. goodwill, reputation, etc.) to isolate tangible book value

Question 28

Goldfarb: What do you need to keep in mind regarding Abnormal Earning Horizon?

Answer 28

• Unreasonable to assume that AE will continue in perpetuity
• Each year, decrease AE by 1/(n+1) times latest year

Question 29

Goldfarb: Set up the table for AE method.

Answer 29

Columns are years

• Net Income after Tax
• Regulatory Capital
• Normal Earnings (Regulatory Capital x k)
• Abonormal Earnings

Question 30

Goldfarb: Why is it difficult for investors outside the company to create reliable forecasts?

Answer 30

• Outsiders might not have sufficiently detailed data to create projections
• May be difficult to estimate growth and rate adequacy
• May be difficult to forecast financials for even short forecast horizons

Question 31

Goldfarb: P-E Ratio Formulas

Answer 31

Question 32

Goldfarb: P-BV Ratio Formulas

Answer 32

Question 33

Goldfarb: What are alternative uses for P-E and P-BV Ratios?

Answer 33

Validation of Assumptions

Calculate the P-E or P-BV ratio using the firm valuation and compare it to the ratio implied by the market value of peer companies.

Shortcut to Valuation

Use the average multiple from peer companies to value the firm.
Terminal Value

Multiples can help with estimating the terminal value for one of the other methods.

Question 34

Goldfarb: If we assume that ROE will decline to the cost of capital after n years as competitors enter the market, we can obtain the following P-BV ratio:

P₀ / BV₀ = ?

Answer 34

P₀/BV₀ = 1 + {(ROE-k) / (k-g) • [1 - ((1+g) / (1+k))ⁿ]}

• this formula assumes constant ROE for n years, followed by a drop in the ROE to the same level as the cost of capital
  
  • watch for this in questions!

Question 35

Goldfarb: Market vs. Transaction Multiples

Answer 35

Market Multiples - P-E and P-BV ratios based on market prices

Transaction Multiples - Multiples based on transaction prices

• e.g. IPO or M&A prices

Question 36

Goldfarb: Transaction Multiples

Advantages & Disadvantages

Answer 36

Advantages

• Price is based on the negotiation between sophisticated parties (more meaningful than multiples based on current market prices)

Disadvantages

• Control Premiums - M&A pricing may be misleading because buyer pays a premium to make different strategic decisions
• Overpricing in M&A Transactions - based on history, acquiring firms tend to overpay to over take a company
• Underpricing in IPO Transactions
• Reported Financial Variables - transaction price may be reliable but the reported multiple may be based on other financial forecasts
• Underlying Economic Assumptions - transaction multiples use past periods so they may not be appropriate any longer (changes to inflation, interest rates, growth rates, etc.)

Question 37

Goldfarb: Considerations when Selecting “Pure Play” Peer Companies for Multiples Valuation

Answer 37

Peers should be comparable:

• Business (products, markets, etc.)
• ROE
• Financial Leverage
• Growth Rates

Question 38

Goldfarb: Why is valuing equity as a call option impracticable for an insurance company?

(Limitations of Option Pricing Methods)

Answer 38

The value would be a call option on the company’s assets with a strike price equal to the face value of debt.

Problems:

• Debt isn’t well defined for an insurance company
  
  • PH liabilities are indistinguishable from other forms of debt for the equity holders
• There is no clear single expiration date for an insurer’s debt, considering policyholder liabilities

Question 39

Goldfarb: List the types of Real Options

Answer 39

Abandonment Option - option to end a project early and recover the net liquidation proceeds

• American Put Option on value of project with strike = net liquidation proceeds

Expansion Option - option to expand the scope of a successful project to capture more profits

• American Call Option on gross value additional capacity with strike = cost of creating capacity

Contraction Option - Option to scale back the scope of a project

• American Put Option on gross value lost capacity with strike = cost savings

Option to Deter - Option to hold off on project until there is more information

• American Call Option on value of project

Option to Extend - Option to extend the life of a project by paying a fixed price

• European Call Option on asset’s future value

Question 40

Goldfarb: What are the practical difficulties with real option valuation?

Answer 40

• Difficult to identify new businesses where real option value exists
• Difficult to assess the current value of these new businesses
• Difficult to determine whether the firm has the ability to enter the business at a fixed price or at a price that differs from the market value

Note: The value of the real option would be added to the firm valuation.

Question 41

Goldfarb: Real Option Valuation Formulas

Answer 41