Bài 1:
Domestic CAPM:
a) Cost of equity (Re) using CAPM:
Re = krf + β * (km - krf) = 3.60% + 1.05 * (9.00% - 3.60%) = 9.00%
b) Cost of debt (Rd):
Given the company credit risk premium is 4.40%, the cost of debt is:
Rd = krf + Company credit risk premium = 3.60% + 4.40% = 8.00%
c) Weighted average cost of capital (WACC):
Using the formula WACC = (E/V) * Re + (D/V) * Rd * (1 - t), where E/V is 70% and D/V is
30%:
WACC = (0.70 * 0.09) + (0.30 * 0.08 * (1 - 0.35)) = 0.063 + 0.052 = 0.115 = 11.50%
International ICAPM:
a) Cost of equity (Re) using ICAPM:
Re = krf + β_international * (km - krf) = 3.60% + 0.85 * (8.00% - 3.60%) = 7.10%
b) Cost of debt (Rd):
Same as before, the cost of debt is 8.00%.
c) Weighted average cost of capital (WACC):
Using the same formula with E/V as 70% and D/V as 30%:
WACC = (0.70 * 0.071) + (0.30 * 0.08 * (1 - 0.35)) = 0.0497 + 0.052 = 0.1017 = 10.17%
To summarize:
Domestic CAPM: International ICAPM:
Cost of equity (Re): 7.10% Cost of equity (Re): 9.00%
Cost of debt (Rd): 8.00% Cost of debt (Rd): 8.00%
WACC: 10.17% WACC: 11.50%
Bài 2:
a) Cost of debt, after-tax in pounds (£):
Given the corporate income tax rate (Tc) is 19% and McLaren's cost of debt is 4.00%:
Cost of debt, after-tax = Cost of debt * (1 - Tax rate) = 4.00% * (1 - 0.19) = 3.24%
b) Cost of equity in pounds (£):
McLaren's cost of equity can be calculated using the Capital Asset Pricing Model (CAPM):
Re = Risk-free rate + Beta * Equity market risk premium = 4.20% + 0.85 * 4.50% = 7.72%
c) Market capitalization in pounds (£):
Market capitalization = Number of shares outstanding * Share price = 210,000,000 * £50.00
= £10,500,000,000.00
d) Total value of equity outstanding in pounds (£):
Total value of equity outstanding = Market capitalization = £10,500,000,000.00
e) Proportion of capital structure that is debt:
Debt proportion = Debt outstanding / Total value of capital structure
= £550,000,000.00 / (£550,000,000.00 + £10,500,000,000.00)
= 0.0491 or 4.91%
f) Proportion of capital structure that is equity:
Equity proportion = Equity value / Total value of capital structure
= £10,500,000,000.00 / (£550,000,000.00 + £10,500,000,000.00) = 95.09%
g) Weighted Average Cost of Capital (WACC):
WACC = (Equity proportion) * Cost of equity + (Debt proportion) * (Cost of debt * (1 - Tax
rate)) = 0.9509 * 7.72% + 0.0491 * (3.24%) = 7.34%
h) WACC with a higher beta (1.30):
Recalculate the cost of equity using the higher beta of 1.30:
Re_new = 4.20% + 1.30 * 4.50% = 10.95%
Recalculate WACC using the new cost of equity:
WACC_new = (Equity proportion) * Cost of equity_new + (Debt proportion) * (Cost of debt * (1
- Tax rate)) = 0.9509 * 10.95% + 0.0491 * (3.24%) = 10.40%
To summarize:
a) Cost of debt, after-tax: 3.24%
b) Cost of equity: 7.72%
c) Market capitalization: £10,500,000,000.00
d) Total value of equity outstanding: £10,500,000,000.00
e) Proportion of debt in capital structure: 4.91%
f) Proportion of equity in capital structure: 95.09%
g) WACC with β = 0.85: 7.34%
h) WACC with β = 1.30: 10.40%
Bài 3:
1. Cost of Debt (Kd):
Kd = ka * (1 - t)
Where ka is the estimate of Dhaka's cost of debt in the U.S. market and t is the corporate tax rate.
2. Cost of Equity (Ke):
Ke = Risk-free rate + β * (Market return - Risk-free rate)
Where β is the beta of Dhaka, and the market return is the estimate of market return.
3. Weighted Average Cost of Capital (WACC):
WACC = (E/V) * Ke + (D/V) * Kd
Given the provided information and assumptions, let's calculate the prospective costs of debt and
the WACC for Dhaka using both Barclays and NatWest's estimates.
Using Barclays' Estimates:
a) Cost of Debt (Kd):
For Barclays, ka = 8.5% and t = 35%
Kd = 8.5% * (1 - 0.35) = 5.525%
b) Cost of Equity (Ke):
For Barclays, β = 0.93 and Market return = 9.0%
Ke = 4.0% + 0.93 * (9.0% - 4.0%) = 8.65%
c) Weighted Average Cost of Capital (WACC):
For Barclays, D/V = 19.0% and E/V = 65%
WACC = (0.65 * 8.65%) + (0.19 * 5.525%) = 5.61725% + 1.04975% = 6.667%
Using NatWest's Estimates:
a) Cost of Debt (Kd):
For NatWest, ka = 8.8% and t = 40%
Kd = 8.8% * (1 - 0.40) = 5.28%
b) Cost of Equity (Ke):
For NatWest, β = 0.88 and Market return = 12.0%
Ke = 4.0% + 0.88 * (12.0% - 4.0%) = 11.04%
c) Weighted Average Cost of Capital (WACC):
For NatWest, D/V = 19.0% and E/V = 60%
WACC = (0.60 * 11.04%) + (0.19 * 5.28%) = 6.624% + 1.0032% = 7.6272%
To summarize:
Using Barclays' Estimates: Using NatWest's Estimates:
Prospective Cost of Debt (Kd): 5.525% Prospective Cost of Debt (Kd): 5.28%
Prospective WACC: 6.667% Prospective WACC: 7.6272%
Bài 4: To calculate Genedak-Hogan's cost of equity before and after international diversification
of its operations, with and without the hypothetical additional risk premium, we'll use the Capital
Asset Pricing Model (CAPM) formula:
Cost of Equity (Ke) = Risk-free rate + Beta * (Market risk premium + Additional equity risk
premium)
Where:
- Risk-free rate (krf)
- Beta (β)
- Market risk premium (km - krf)
- Additional equity risk premium for internationalization (RPM)
Calculate the costs of equity for the different scenarios:
Before Diversification, Without Additional Risk Premium:
- β: 0.88
- RPM: 0.0%
- Market risk premium: 28.0% - 7.2% = 20.8%
Ke = 4.0% + 0.88 * (20.8%) = 4.0% + 18.304% = 22.304%
Before Diversification, With Additional Risk Premium:
- β: 0.88
- RPM: 3.0%
- Market risk premium: 28.0% - 7.2% = 20.8%
Ke = 4.0% + 0.88 * (20.8% + 3.0%) = 4.0% + 20.184% = 24.184%
After Diversification, Without Additional Risk Premium:
- β: 0.76
- RPM: 0.0%
- Market risk premium: 26.0% - 7.0% = 19.0%
Ke = 4.0% + 0.76 * (19.0%) = 4.0% + 14.44% = 18.44%
After Diversification, With Additional Risk Premium:
- β: 0.76
- RPM: 3.0%
- Market risk premium: 26.0% - 7.0% = 19.0%
Ke = 4.0% + 0.76 * (19.0% + 3.0%) = 4.0% + 17.24% = 21.24%
Summary:
Before Diversification:
- Without Additional Risk Premium: Ke = 22.304%
- With Additional Risk Premium: Ke = 24.184%
After Diversification:
- Without Additional Risk Premium: Ke = 18.44%
- With Additional Risk Premium: Ke = 21.24%
Comments on the Discussion:
The cost of equity is a critical factor in determining a company's overall cost of capital. In this
case, the debate seems to revolve around the impact of international diversification on the
company's risk profile and thus its cost of equity.
Before diversification, the cost of equity is higher, both with and without the additional risk
premium. This suggests that the company's operations are perceived as riskier when it is not
diversified internationally.
After diversification, the cost of equity decreases, indicating that international diversification has
led to a reduction in the company's perceived riskiness. This aligns with the common
understanding that diversification across different markets and geographies can reduce the
overall risk of a company.
Furthermore, the additional risk premium for internationalization adds an extra layer of
perceived risk due to operating in foreign markets. This premium is added to the basic CAPM
cost of equity to account for the potential challenges and uncertainties associated with
international operations.
In conclusion, the discussion highlights that international diversification can lead to a decrease in
the cost of equity, as the company's risk profile becomes more diversified. However, the added
risk premium for internationalization reflects the uncertainties that can arise from operating in
new markets. The final decision on which scenario to adopt would depend on the company's
strategic goals, risk tolerance, and evaluation of potential benefits and challenges associated with
international expansion.
Bài 5: Calculate the weighted average cost of capital (WACC) for Genedak-Hogan before and
after international diversification under the given assumptions and scenarios.
Before Diversification:
a) Calculate WACC before international diversification:
First, calculate the cost of equity (Ke) using the CAPM formula with the given parameters:
Ke = krf + β * (km - krf + RPM) = 5.5% + 0.76 * (7.2%) = 11.212%
Then, calculate the cost of debt (Kd) using the given value:
Kd = 7.2%
Now, calculate WACC using the formula:
WACC = (D/V) * Kd * (1 - t) + (E/V) * Ke = (0.38 * 7.2% * (1 - 0.35)) + (0.62 * 11.212%)
= 4.68% + 6.94844% = 11.62844%
After Diversification:
b) Calculate WACC after international diversification:
Repeat the same process as above with the given parameters for the "After Diversification"
scenario:
Ke = krf + β * (km - krf + RPM) = 5.5% + 0.88 * (7.0%) = 11.46%
Kd = 7.0%
WACC = (D/V) * Kd * (1 - t) + (E/V) * Ke = (0.32 * 7.0% * (1 - 0.35)) + (0.68 * 11.46%)
= 4.55% + 7.80368% = 12.35368%
Adding Hypothetical Risk Premium:
c) Calculate WACC after adding a hypothetical risk premium to the cost of equity:
Using the same parameters for the "After Diversification" scenario but adding a 3.0% risk
premium to the cost of equity:
Ke = krf + β * (km - krf + RPM) = 5.5% + 0.88 * (7.0% + 3.0%) = 16.94%
Kd = 7.0%
WACC = (D/V) * Kd * (1 - t) + (E/V) * Ke = (0.32 * 7.0% * (1 - 0.35)) + (0.68 * 16.94%)
= 4.55% + 11.5252% = 16.0752%
Discussion of Results:
a) Yes, the reduction in debt costs has reduced the firm's weighted average cost of capital. The
WACC before diversification was 11.62844%, while after diversification, it dropped to
12.35368%, indicating that diversification reduced the cost of capital.
b) However, if the market adds a 3.0% risk premium due to international diversification, the
benefits of lower debt costs are overshadowed by the higher required return on equity. The
WACC with the added risk premium is 16.0752%, which is higher than both the scenarios
without the risk premium. This suggests that the perceived increased risk associated with
international operations can counteract the reduction in the cost of capital resulting from lower
debt costs.
In summary, the impact of international diversification on costs of capital is complex. While it
can lead to reduced debt costs and initially lower WACC, the market's perception of increased
risk due to international operations can offset these benefits, resulting in a higher overall cost of
capital.
Bài 13.5:
WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)
Where:
- E/V: Proportion of equity in the capital structure (equity value / total value)
- Re: Cost of equity
- D/V: Proportion of debt in the capital structure (debt value / total value)
- Rd: Cost of debt
- Tc: Corporate tax rate
Given information:
- Cost of debt (Rd): 7%
- Risk-free rate (Rf): 3% (10-year U.S. Treasury yield)
- Market risk premium (Rm - Rf): 8% - 3% = 5%
- Expected return on the market portfolio (Rm): 8%
- Corporate tax rate (Tc): 39%
- Optimal capital structure: 60% debt and 40% equity
Let's calculate the WACC for both scenarios:
a. When Houston's beta is estimated at 1.1:
First, calculate the cost of equity (Re) using the Capital Asset Pricing Model (CAPM):
Re = Rf + Beta * (Rm – Rf) = 3% + 1.1 * 5% = 8.5%
Plug in the values into the WACC formula:
E/V = 40% = 0.40
D/V = 60% = 0.60
Tc = 39% = 0.39
Rd = 7% = 0.07
WACC = (0.40 * 0.085) + (0.60 * 0.07 * (1 - 0.39)) = 0.034 + 0.0252 = 0.0592 = 5.92%
b. When Houston's beta is estimated at 0.8:
Using the same steps, first calculate the cost of equity (Re):
Re = Rf + Beta * (Rm – Rf) = 3% + 0.8 * 5% = 7%
Plug in the values into the WACC formula again:
E/V = 40% = 0.40
D/V = 60% = 0.60
Tc = 39% = 0.39
Rd = 7% = 0.07
WACC = (0.40 * 0.07) + (0.60 * 0.07 * (1 - 0.39)) = 0.028 + 0.0252 = 0.0532 = 5.32%
The answers are:
a. When Houston's beta is 1.1, the weighted average cost of capital is 5.92%.
b. When Houston's beta is 0.8, the weighted average cost of capital is 5.32%.
