Corporate Finance: Essay Quiz WACC, IRR and Trade - Off Model

E&C Corporation has RM150 million worth of common stock on which investors require a 15% rate of return. It has RM30 million in bonds that offer a 7% return.

• Calculate the WACC for E&C Corporation if they are subject to a 35% tax rate.
• Recompute E&Cs' WACC assuming the firm has RM80 million in debt and RM120 million in stock.
• After reviewing part (i) and (ii) above, explain why the WACC calculated in part (ii) may not be the correct answer if the capital structure changes.

Answer:

Calculate the WACC for E&C Corporation if they are subject to a 35% tax rate.

To calculate the Weighted Average Cost of Capital (WACC) for E&C Corporation, we will use the following formula:

$$\text{<span style="font-family: verdana;"><span style="font-size: small;">WACC</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">E</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">V</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">e</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">D</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">V</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">d</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">T</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">)</span></span>$$

Where:

• $E$ = Market value of equity (common stock)
• $D$ = Market value of debt (bonds)
• $V$ = Total market value of the firm (equity + debt)
• $r_e$ = Cost of equity
• $r_d$ = Cost of debt
• $T$ = Corporate tax rate

Given Data

• Common Stock (Equity): RM150 million
• Bonds (Debt): RM30 million
• Cost of Equity ($r_e$): 15% or 0.15
• Cost of Debt ($r_d$): 7% or 0.07
• Tax Rate ($T$): 35% or 0.35

Step-by-Step Calculation

1. Calculate Total Value (V):
   $$V=E+D=RM150\text{million}+RM30\text{million}=RM180\text{million}$$
2. Calculate Proportions:
   • Proportion of equity:
   $$\frac{E}{V}=\frac{RM150\text{million}}{RM180\text{million}}=0.8333$$
   • Proportion of debt:
   $$\frac{D}{V}=\frac{RM30\text{million}}{RM180\text{million}}=0.1667$$
3. Calculate After-Tax Cost of Debt:
   • After-tax cost of debt:
   $$r_d(1-T)=0.07(1-0.35)=0.07\times 0.65=0.0455$$
4. Calculate WACC:
   Now substituting all values into the WACC formula:
   $$\text{WACC}=(0.8333\cdot 0.15)+(0.1667\cdot 0.0455)$$
   Calculating each part:
   • Equity component:
   $$0.8333\cdot 0.15=0.125$$
   • Debt component:
   $$0.1667\cdot 0.0455=0.0076$$
5. Final WACC Calculation:
   Adding both components together:
   $$WACC=0.125+0.0076=0.1326$$

Thus, the WACC for E&C Corporation is approximately 13.26%.

Recompute E&Cs' WACC assuming the firm has RM80 million in debt and RM120 million in stock.

Answer:

To recompute the WACC for E&C Corporation with the new values of RM80 million in debt and RM120 million in equity, we will follow the same formula as before:

$$\text{WACC}=(\frac{E}{V}\cdot r_e)+(\frac{D}{V}\cdot r_d\cdot (1-T))$$

Given Data

• Equity (E): RM120 million
• Debt (D): RM80 million
• Cost of Equity ($r_e$): 15% or 0.15
• Cost of Debt ($r_d$): 7% or 0.07
• Tax Rate (T): 35% or 0.35

Step-by-Step Calculation

1. Calculate Total Value (V):
   $$V=E+D=RM120\text{million}+RM80\text{million}=RM200\text{million}$$
2. Calculate Proportions:
   • Proportion of equity:
   $$\frac{E}{V}=\frac{RM120\text{million}}{RM200\text{million}}=0.6$$
   • Proportion of debt:
   $$\frac{D}{V}=\frac{RM80\text{million}}{RM200\text{million}}=0.4$$
3. Calculate After-Tax Cost of Debt:
   • After-tax cost of debt:
   $$r_d(1-T)=0.07(1-0.35)=0.07\times 0.65=0.0455$$
4. Calculate WACC:
   Now substituting all values into the WACC formula:
   $$\text{WACC}=(0.6\cdot 0.15)+(0.4\cdot 0.0455)$$
   Calculating each part:
   • Equity component:
   $$0.6\cdot 0.15=0.09$$
   • Debt component:
   $$0.4\cdot 0.0455=0.0182$$
5. Final WACC Calculation:
   Adding both components together:
   $$WACC=0.09+0.0182=0.1082$$

Thus, the recomputed WACC for E&C Corporation is approximately 10.82%.

Comment on the following statement: The internal rate of return method is superior to the NPV method because we do not need to know the required rate of return in order to calculate it. Do you agree, discuss.

Answer:

The statement that "the internal rate of return (IRR) method is superior to the net present value (NPV) method because we do not need to know the required rate of return in order to calculate it" raises important points for discussion. Here’s a comprehensive analysis of both methods and the implications of this statement.

Understanding IRR and NPV

Internal Rate of Return (IRR)

• Definition: IRR is the discount rate at which the net present value of an investment is zero. It represents the expected annualized return on an investment.
• Advantage: One of the key advantages of IRR is that it does not require a predetermined required rate of return to calculate. This can make it appealing in situations where investors are uncertain about what rate to use.
• Limitations: However, IRR can be misleading, especially in cases where cash flows are non-conventional (i.e., alternating between positive and negative). In such cases, multiple IRRs can exist, complicating decision-making.

Net Present Value (NPV)

• Definition: NPV calculates the present value of cash inflows and outflows using a specified discount rate (the required rate of return). It provides a dollar amount that represents the value added by an investment.
• Advantage: NPV is generally considered more reliable because it takes into account the time value of money and provides a clear indication of how much value an investment will add to the firm. It requires knowledge of the required rate of return, which aligns with the opportunity cost of capital.
• Limitations: The need to specify a required rate of return can be seen as a disadvantage, particularly if there is uncertainty about what that rate should be.

Discussion

Agreement with the Statement

While it is true that IRR does not require a predetermined required rate of return for its calculation, I would argue that this does not inherently make it superior to NPV for several reasons:

1. Decision-Making Clarity:
   • NPV provides a straightforward financial metric (in monetary terms) that indicates whether an investment will create or destroy value. A positive NPV means the project is expected to generate more cash than what is needed to cover its costs, making it easier for decision-makers to assess profitability.
2. Risk Assessment:
   • The required rate of return reflects the risk associated with an investment. By using NPV, investors can adjust this rate based on their risk tolerance and market conditions. This flexibility allows for better alignment with strategic goals.
3. Handling Non-Conventional Cash Flows:
   • As mentioned earlier, IRR can produce multiple values or fail to provide a clear decision criterion when cash flows are irregular. NPV consistently provides one clear answer regardless of cash flow patterns.
4. Reinvestment Rate Assumption:
   • IRR assumes that intermediate cash flows are reinvested at the same rate as the IRR itself, which may not be realistic. In contrast, NPV assumes reinvestment at the firm's required rate of return, which is often more conservative and practical.

While the ability to calculate IRR without knowing the required rate of return may seem advantageous, it does not make it superior to NPV. Each method has its strengths and weaknesses; however, NPV's clarity in financial decision-making and its alignment with risk considerations generally make it a more robust tool for evaluating investments. Therefore, I would argue that both methods should be used complementarily rather than one being deemed superior to the other.

What do you need to know to determine the optimal capital structure for a firm in the trade - off model?

Answer:

To determine the optimal capital structure for a firm using the trade-off model, several key factors must be considered. The trade-off theory posits that firms balance the benefits and costs of debt and equity financing to maximize their overall value. Here are the main elements to evaluate:

Key Factors in Determining Optimal Capital Structure

1. Interest Tax Shield:
   • Debt financing provides tax advantages because interest payments are tax-deductible. This creates an "interest tax shield," which can significantly enhance a firm's value by reducing its taxable income.
2. Cost of Financial Distress:
   • As a firm increases its leverage (debt), the risk of financial distress rises. This includes potential bankruptcy costs and other non-bankruptcy costs such as loss of customers or suppliers' confidence. Understanding these costs is crucial for determining how much debt is optimal.
3. Bankruptcy Costs:
   • Direct bankruptcy costs (legal and administrative expenses) and indirect costs (lost sales, impaired relationships with stakeholders) must be assessed. These costs increase with higher levels of debt, which can offset the benefits of tax shields.
4. Operating Leverage:
   • Firms with high operating leverage (fixed costs relative to variable costs) may face greater risks when adding debt, as they have less flexibility to adjust their cost structure in response to downturns in revenue.
5. Firm-Specific Factors:
   • Characteristics such as industry norms, business risk, growth opportunities, and asset structure influence the optimal capital structure. For instance, firms in stable industries may afford higher debt levels compared to firms in volatile sectors.
6. Market Conditions:
   • Economic conditions, interest rates, and market perceptions can affect a firm's ability to raise debt or equity. Favorable market conditions may allow firms to take on more debt at lower costs.
7. Target Debt Ratio:
   • Firms often establish a target debt-to-equity ratio based on the trade-off between tax benefits and bankruptcy risks. The optimal capital structure is achieved when this target ratio maximizes firm value while minimizing the weighted average cost of capital (WACC).
8. Agency Costs:
   • The potential conflicts between shareholders and debt holders (agency problems) can influence capital structure decisions. High levels of debt may lead to riskier behavior from management, impacting overall firm value.
9. Incremental Analysis:
   • Firms should evaluate the marginal benefits of additional debt against the marginal costs associated with increased financial risk. This analysis helps in identifying the point where adding more debt no longer enhances value.

Determining the optimal capital structure in the trade-off model requires a comprehensive understanding of both the benefits and risks associated with different financing options. By carefully analyzing these factors, firms can find a balance that maximizes their value while managing financial risk effectively

source: Corporate Finance First Semester Examination Academic Session 2011/2012, Master of Business Administration, Universiti Sains malaysia