15.1 Assumptions

Key assumptions are cost of captial \(k\) and growth rate \(g\)

It is good to sensitivity test these assumptions on the model output

15.1.1 Risk Adjusted Discount Rate

Recognize the risky cashflow by discounting them at a rate higher than the risk-free rate based on CAPM

\[\begin{equation} k = r_f + \beta \left [ \mathrm{E}(r_m) - r_f \right ] \tag{15.1} \end{equation}\]

  • Risk of an investment depends on the rest of an investor’s portfolio. We focus instead on equilibrium rates of return

  • Different BU has different risk profile \(\Rightarrow\) Different discount rates

  • Discount rates can vary by period if business mix change

  • Cash flow can have the different risk profile (premium, investment income, paid losses)

  • Simplification is to use average discount rate for the portfolio

Alternative way to account for the risky cash flow is to convert the cash flow to certainty equivalent cash flows and discount with risk free instead of the cost of capital

  • Reflect the risk in the cashflow directly

Risk free Rate: \(r_f\)

  • 90 days t-bill

  • Maturity matched t-notes

  • 20 years T-bonds less liquidity & term premium (~1.2%)

Market Risk Premium: \(\mathrm{E}(r_m) - r_f\)

  • 6-8% historically

  • \(r_f\) here should be consistent with the one use for CAPM

  • Arithmetic average should be used when forecasting over 1 year (geometric average when forecasting over multiple years)

  • Need to sensitivity test

Systematic Market Risk: \(\beta\)

  • Based on regression on stock return vs market return

  • Using industry \(\beta\)

    • Mix of business needs to be similar to industry

    • Industry \(\beta\) should be adjusted for differences in the industry leverage and company leverage

  • \(\beta\) will be higher for firms with more leverage, riskier business units

    • Alternative is to use all equity \(\beta\) to remove bias from leverage

    • Higher growth should have higher \(\beta\)

  • Insurance company has additional leverage from policyholder liabilities

  • Can assume total leverage of insurance companies is similar

15.1.2 Growth Rate

Used for the period after the forecast horizon

Table 15.1: Growth rate for each method
Method Growth Rate: \(g\)
DDM \(ROE \times \rho\)
FCFE \(ROE \:\: \times\) [Reinvestment Rate]
AE At most the growth in book value

Return on Equity: \(ROE\)

\(\dfrac{NI}{BE} = \dfrac{\text{Net Income after Tax}}{\text{Beginning Equity}}\)

Plowback Ratio: \(\rho\)

% of \(NI\) that is reinvested in the firm (e.g. dividend payout ratio)

  • Company that have high growth should retain more earnings

Reinvestment Rate:

\(\dfrac{\Delta Capital}{NI}\)