FNCE30011 · Essentials Of Corporate Valuation
Estimating Discount Rates
A DCF is only as good as the rate you discount at, so this chapter builds the cost-of-capital inputs from the ground up. The cost of equity comes from the CAPM and the security market line, ke = rf + β(rM − rf): only systematic risk is priced, and beta is the one company-specific input. The Fama–French three-factor model is the alternative, adding size (SMB) and value (HML) premia to the market factor. The centrepiece is the beta workhorse: a listed comparator's equity beta carries its leverage, so you de-lever it to an asset beta — βu = (1−L)βe + Lβd — average across comparators, then re-lever to your firm's target L (with investment-grade debt, βd ≈ 0, so βe = βu/(1−L)). The course convention is L = D/V, deliberately matching the form on the provided formula sheet, so the (1−L) levering formula is used rather than the Hamada D/E version. The cost of debt follows from the credit spread, y = rf + CS = rf + RP + DP, with investment-grade y ≈ kd.
What this chapter covers
- 015.1 CAPM and the security market line — only systematic risk is priced
- 025.2 Beta as the one company-specific input; the market and risk-free anchors
- 035.3 The Fama-French three-factor alternative (market + size SMB + value HML)
- 045.4 De-levering a comparator's equity beta to an asset beta
- 055.5 Re-levering the asset beta to your firm's target leverage (L = D/V)
- 065.6 Cost of debt from the credit spread: y = rf + CS, investment-grade y ≈ kd
Worked example: de-lever, re-lever, then CAPM
- +1Identify. The comparator's beta carries its leverage — de-lever to an asset beta, then re-lever to the target's L, then apply CAPM.
- +1De-lever. With βd = 0, βu = (1−L)βe = (1−0.45)(1.20) = 0.66.
- +1Re-lever to L = 0.25: βe = βu/(1−L) = 0.66/0.75 = 0.88.
- +1CAPM. ke = rf + β(MRP) = 3.5% + 0.88(6.0%) = 3.5% + 5.28% = 8.78%.
- +1Sanity-check. The target is less levered than the comparator, so its equity beta and ke should be lower — and they are (0.88 < 1.20). Average across several comparators in practice.
Key terms
- CAPM / security market line
- ke = rf + β(rM − rf): expected return rises linearly with beta. Only systematic (non-diversifiable) risk earns a premium; firm-specific risk is not priced.
- Beta (β)
- The sensitivity of a stock's return to the market — the one company-specific CAPM input. Equity beta reflects both business risk and leverage; asset (unlevered) beta strips the leverage out.
- De-lever / re-lever
- βu = (1−L)βe + Lβd removes a comparator's leverage to an asset beta; re-levering to your firm's L reverses it. With βd ≈ 0 (investment grade), βe = βu/(1−L). Convention: L = D/V.
- Fama-French three-factor model
- ke = rf + βM(MRP) + βSMB(SMB) + βHML(HML): augments the market factor with a size premium (SMB) and a value premium (HML). The alternative to CAPM for the cost of equity.
- Credit spread / cost of debt
- y = rf + CS = rf + risk premium + default premium. The promised yield on the firm's debt; for investment-grade names the yield y is a good proxy for the expected cost of debt kd.
Estimating Discount Rates FAQ
Why de-lever a comparator's beta before using it?
A listed comparator's equity beta reflects both its business risk and its own leverage. If your firm carries a different debt level, applying that raw equity beta imports the wrong financial risk. So you strip the comparator's leverage to an asset beta (βu), which reflects business risk alone, then re-lever to your firm's target L. Skipping the two-step is the classic discount-rate error in this chapter.
Why does the course use L = D/V rather than the Hamada D/E form?
Because the provided exam formula sheet expresses leverage as L = D/V, so the levering formula is βu = (1−L)βe + Lβd, not the textbook Hamada βe = βu[1 + (1−T)D/E]. Match the sheet: use (1−L) and D/V throughout so your beta levering is consistent with the rest of the WACC machinery in the subject.
What does CAPM mean by 'only systematic risk is priced'?
Diversifiable (firm-specific) risk can be eliminated by holding a diversified portfolio, so the market pays no premium for bearing it. Only systematic risk — the part that moves with the market, measured by beta — cannot be diversified away and therefore earns the risk premium β(rM − rf). That is why beta, not total volatility, is the CAPM's measure of risk.
When is the bond yield a good proxy for the cost of debt?
For investment-grade firms, the promised yield y = rf + credit spread is close to the expected return on the debt kd, because default risk is low and the gap between promised and expected yield is small. For sub-investment-grade or distressed debt the yield overstates kd (it bakes in a large default premium that is not all expected return), so the proxy weakens.
Exam move
The beta two-step is the highest-value drill: de-lever every comparator with βu = (1−L)βe + Lβd, average the asset betas, then re-lever to your firm's L — and always use the course's L = D/V convention to match the formula sheet. Keep CAPM and the credit-spread cost of debt beside it (ke = rf + β·MRP; y = rf + CS ≈ kd). Sanity-check direction every time: a less-levered firm should have a lower equity beta and a lower ke. Knowing when to de-lever versus re-lever, not the algebra, is what the marks reward.
