Week Seven - Flashcards - Cost of Capital

Cost of capital (hurdle rate)

The minimum risk-adjusted rate of return an investment project must earn to satisfy providers of finance and create firm value.

Ex-dividend share price calculation ($S_{0,\text{XD}}$) from cum-dividend price

$S_{0,\text{XD}} = S_{0,\text{cum-div}} - D_0$, calculated by deducting the imminent dividend from the cum-dividend price.

Dividend Valuation Model (DVM) for zero dividend growth

$k_e = \frac{D_1}{S_{0,\text{XD}}}$, where $D_1$ is the constant annual dividend and $S_{0,\text{XD}}$ is the current ex-dividend share price.

Gordon Growth Model formula for cost of equity ($k_e$)

$k_e = \frac{D_0(1+g)}{S_{0,\text{XD}}} + g$, where $D_0$ is the dividend just paid, $g$ is the constant dividend growth rate, and $S_{0,\text{XD}}$ is the ex-dividend share price.

Historical compound growth rate formula ($g$)

$g = \left(\frac{D_n}{D_0}\right)^{\frac{1}{n}} - 1$, where $n$ represents the number of elapsed growth periods between the first and last dividends.

Earnings retention model formula for dividend growth ($g$)

$g = r \times b$, where $r = \frac{\text{profit after tax}}{\text{opening net assets}}$ and $b = \frac{\text{retained profit}}{\text{profit after tax}}$.

Capital Asset Pricing Model (CAPM) cost of equity formula

$k_e = r_f + \beta(r_m - r_f)$, where $r_f$ is the risk-free rate, $\beta$ is systematic risk, and $(r_m - r_f)$ is the equity market risk premium.

Cost of irredeemable preference shares ($k_p$)

$k_p = \frac{D_1}{S_{0,\text{XD}}}$, where dividend $D_1$ is calculated on the nominal value and provides no tax relief.

After-tax cost of irredeemable debt ($k_d(1-t_c)$)

$k_d(1-t_c) = \frac{I_1(1-t_c)}{B_{0,\text{XI}}}$, where $I_1$ is annual interest, $t_c$ is the corporate tax rate, and $B_{0,\text{XI}}$ is the ex-interest debt market price.

Linear interpolation formula for bond Internal Rate of Return (IRR)

$\text{IRR} \approx L + \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \times (H - L)$, where $L$ is the lower discount rate and $H$ is the higher discount rate.

Decision rule for convertible bond terminal cash flow

Investors are assumed to choose the higher payoff between the cash redemption value and the conversion value ($\text{conversion ratio} \times \text{future share price}$).

Cost and weighting of bank loans in WACC

Cost is given by $\text{interest rate} \times (1 - t_c)$ and is weighted using book value because no traded market price exists.

Weighted Average Cost of Capital (WACC) formula

$\text{WACC} = \frac{k_e S + k_d(1-t_c)B}{S + B}$, where $S$ and $B$ are the market values of equity and debt, with tax relief applied solely to debt.

Three core assumptions for applying current WACC as an appraisal discount rate

1. Capital structure (gearing) remains unchanged. 2. Business (operating) risk of the project matches the firm. 3. Financing is sourced from general corporate funds rather than project-specific facilities.