Section B - Insurance Company Valuation Flashcards
Goldfarb: Dividend Discount Model Formulas
V0 = PV(Div) + PV(TV)
TV = Terminal Value = Divfinal(1+g) / (k-g)
PV(TV) = TV / (1+k)n
PV(Div) = ∑E[Divt] / (1+k)t
Divt = NIt • (1-Dividend Ratio)
Goldfarb: What are the disadvantages of the Dividend Discount Rate Model (DDM)?
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
Goldfarb: Dividend Growth Rates beyond Forecast Horizon
g = ?
g = plowback • ROE
- plowback refers to the portion of earnings retained and reinvested
- ROE is the income generated on reinvestment
Goldfarb: Dividend Discount Rate Model
Key Assumptions
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
Goldfarb: Rate of Return CAPM Formula
k = r<em>f</em> +β•E[Rm]
Goldfarb: Briefly describe how high growth rates affect dividends.
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)
Goldfarb: Briefly explain how high growth rates affect the risk-adjusted rate of return.
Firms with high growth rates tend to be riskier which drives the risk-adjusted rate up.
Goldfarb: Briefly describe two ways of determining beta used in CAPM.
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
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.
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
Goldfarb: Risk-free Rate Options for CAPM
Should be based on current yields on risk-free securities:
- 90 Day T-Bill - free of both credit and reinvestment rate risk
- Maturity Matched T-Notes - maturity matches the average maturity of cashflows
- 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
Goldfarb: When determining the risk-free rate based on T-Bonds, what do you need to do before you can use the rate?
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.
Goldfarb: Considerations in Selecting an Appropriate Equity Risk Premium
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
Goldfarb: Briefly describe sensitivity analysis.
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
Goldfarb: Table to set up for the DDM.
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.
Goldfarb: What is Free Cash Flow?
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.
Goldfarb: Free Cash Flow to Equity Formula

Goldfarb: FCFE Method Formulas
PV(FCFE) = ∑FCFEt / (1+k)t
TV = FCFEfinal(1+g) / (k-g)
PV(TV) = TV / (1+k)n
V0 = PV(FCFE) + PV(TV)
Goldfarb: FCFE Growth Formulas
Reinvested Capital = ?
Reinvestment Rate = ?
Horizon Growth Rate = ?
Forecast Horizon Growth Rate = ?
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 Rateselected • ROEselected
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 = FCFEt / FCFEt-1 - 1
Goldfarb: What are the issues with the FCFF method for insurance companies?
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
Goldfarb: How are Loss & LAE reserves treated in the FCFE method?
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.
Goldfarb: What are the advantages and disadvantages of the FCFE method?
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
Goldfarb: What are the assumptions underlying the FCFE method?
- 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.
Goldfarb: In theory, the dividend discount model and the discounted cash flow model should use different discount rates. Why?
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.
Goldfarb: Set up the table used to solve for FCFE.
Year as column headers
- Net Income after tax
- Beginning Equity
- Required Capital
- Increase in Required Capital
- FCFE
- ROE
- Reinvestment Rate


