Cost of Capital & Leverage - Lecture Notes

Final Exam Hints

• The final exam will cover approximately 80% of the hinted topics.

• Good grades on assignments/quizzes can only get you so far; the final exam is crucial for distinction or high distinction.

• Employers look for differentiators; GPA is key.

• The last quiz is open; don't forget to complete it.

Cost of Capital

• This is the last topic, closely linked with leverage.

• It's the final piece of capital budgeting.

• Capital budgeting involves NPV, IRR, and PI.

• Two key inputs for capital budgeting:

  • Future cash flows (estimated in the previous lecture).

  • Discount rate (cost of capital or WACC, the topic of this lecture).

• A proper discount rate is needed to discount future cash flows to their present value.

• The appropriate discount rate reflects the cost of using capital.

• If a project earns less than the cost of capital, it results in a loss.

Sources of Capital

• Companies raise capital through:

  • Issuing shares (equity).

  • Borrowing money (debt).

• The cost of capital stems from debt and equity.

Risk Adjustment

• Different projects have different risks.

  • Riskier projects should have higher discount rates to compensate for the increased risk.

  • Failing to adjust for risk would lead to only selecting low-risk projects.

Focus

• The focus is on determining the cost of using different capital sources.

Cost of Capital - Debt vs Equity

• Debt:

  • Predetermined and fixed costs (face value, coupon rate).

• Equity:

  • Ordinary shares: Dividend payments are not guaranteed, depending on the directors.

  • Preference shares: Dividend yield is predetermined, similar to bonds.

Cost of Ordinary Shares

• Investors require a return on their investment in ordinary shares (either through dividends or capital gains).

• If a company cannot provide a return, investors will not buy its shares.

• Dividend Discount Model and Capital Asset Pricing Model (CAPM) can find the returns.

  • Capital Asset Pricing Model (CAPM): This model will be tested in the final exam.

Weighted Average Cost of Capital (WACC)

• Similar to a weighted average method.

• For example, if a company's capital is 50% debt and 50% equity, WACC is calculated as:

  • WACC = (0.5 \times \text{Cost of Debt}) + (0.5 \times \text{Cost of Equity})

WACC Formula

• WACC = (E/V \times RE) + (P/V \times RP) + (D/V \times RD \times (1 - Tc))

  • Where:

    • R_E = Cost of equity (ordinary share).

    • R_P = Cost of preference share.

    • R_D = Cost of debt.

    • E = Market value of equity.

    • P = Market value of preference shares.

    • D = Market value of debt.

    • V = Total value of capital (E + P + D).

    • T_c = Corporate tax rate.

Corporate Tax Rate and Imact

• In Australia, the corporate tax rate is generally 30% for large companies and 25% for small companies.

• Interest payments on debt are tax-deductible, which reduces taxable income.

• The tax savings from interest expense effectively lower the cost of debt.

• 
  \text{After-tax cost of debt}= \text {Interest Rate} \times (1 - \text{Tax Rate})

• Dividends on ordinary and preference shares are not tax-deductible.

WACC - Values

• It is important to use market values rather than book values when calculating WACC.

• Market values reflect the current cost of raising capital.

• Book values are based on historical data and may not be relevant.

• WACC is used to evaluate future cash flows of potential projects.

Cost of Equity

• Calculated using:

  • Capital Asset Pricing Model (CAPM).

  • Dividend Growth Model.

Capital Asset Pricing Model (CAPM)

• RE = Rf + \beta \times (Rm - Rf)

  • Where:

    • R_E = Required rate of return for equity.

    • R_f = Risk-free rate (typically the rate on government bonds).

    • \beta = Beta (measure of systematic risk).

    • R_m = Market return.

    • (Rm - Rf) = Market risk premium.

• Beta: Measures systematic or market risk.

• Market risk premium: Compensation for bearing systematic risk.

Dividend Discount Model

• Constant dividend growth model.

• P0 = \frac{D1}{r - g}

  • Where:

    • P_0 = Current share price.

    • D_1 = Expected dividend next year.

    • r = Required rate of return (cost of equity).

    • g = Constant growth rate of dividends.

• Rearranging the above formula:

  • r = \frac{D1}{P0} + g

Model Selection

• Choose the model based on data availability.

• CAPM is used if beta, risk-free rate, and market risk premium are available.

• Dividend Discount Model is used if the next period's dividend, current share price, and growth rate are available.

• Be flexible and ready to use either model as questions are made to trick you in using the model that has all the available information.

CAPM vs. Dividend Growth Model

• CAPM incorporates risk (beta).

  • Relies on historical data (stock prices) to predict the future.

• Dividend Growth Model implies that current share price is the present value of all future potential cash flows

  • More sensitive to input values like growth rate.

Cost of Debt

• It is the YTM, yield to maturity and not coupon rate of its existing debt.

• Yield to maturity (market yield) is the discount rate used to calculate the fair value of a bond.

Cost of Preference Shares

• Preference share dividends are fixed and can last forever, thus the model sees it as a perpetuity.

• P_0 = \frac{D}{r}

  • Where:

    • D = Fixed dividend payment.

    • r = Required rate of return.

• Rearranged Formula:

  • r = \frac{D}{P_0}

Tax Shield

• Apply tax rate only to debt because interest payments are tax deductible.

Comprehensive Example

• Equity: 50,000,000 shares outstanding, market price $80 per share, beta 1.15, market premium 9%, risk-free rate 5%.

• Debt: $100,000,000 in outstanding debt, market value 110,000,000, yield to maturity 8.1%.

• Tax rate: 40%.

Steps

1. Calculate the total market value of equity 50,000,000 \times 80 = 4,000,000,000.

2. Determine the capital structure weights.

3. Cost of Equity (CAPM): R_E = 5 + 1.15 \times 9 = 15.35 \%

4. Cost of Debt (After-tax): 8.1 \times (1 - 0.4) = 4.86 \% .

5. Calculating WACC with CAPM and After-Tax Cost of Debt:

   • Total Value: 4,000,000,000 + 110,000,000 = 4,110,000,000

   • WACC: (\frac{4,000,000,000}{4,110,000,000} \times 15.35) + (\frac{110,000,000}{4,110,000,000} \times 4.86) =13.09\% .

Impacts on WACC

• Different companies can have different WACCs, but why?

  • This is mostly determined by the risk level of the company.

• The relationship between risk, cost of capital, and WACC: Higher risk leads to a higher required return and a higher WACC.

When to Use WACC

• WACC represents average risk, and can only be use if:

  1. The project has an average risk to the company.

  2. The project will not change the company's capital structure.

Impact of Leverage

• Will different ways of capital raising affect your firm value?

Unleveraged vs. Leveraged Firms

• Firm U: Unleveraged (financed entirely by equity).

• Firm L: Leveraged (financed by a combination of equity and debt).

• Assume both firms have the same assets, earning power, and risk profile.

Example - Firm U and Firm L

• Both firms have $10,000 invested in assets and EBIT = 1500.

• Firm U: entirely financed by $10,000 equity.

• Firm L: $4000 equity and $6000 debt, with 10\% interest rate.

• Interest Expense = 6000 \times 0.1 = 600.

Income Statement Comparison

• Initial Observation: It seems that by generating debt you earned more than the equity.

• By using dept, the shareholder ends up being pay more, so where does the other 5\% come from?

Combining D/E Returns

• Tax savings, using less tax = paying debts.

Real World Scenario

1. Example with 50% chance firm will make money, firm will lose money, and another % chance it goes even better.

2. Now apply to the firm U and firm L.

3. If go good, U will earn 3.5 \%, but if goes bad it loses 3.5 \%, and both around the gap is 3.5 \%.

4. For firm L, it can earn more near 9\% ish, and lose similar amount.