Question 1

A firm has a market value of assets of $50,000.It borrows $10,000 at 7%.If the unlevered cost of equity is 15%,what is the firm's cost of equity capital?

Accepted Answer

The formula to calculate the cost of equity capital of a levered firm is as follows:

Cost of Equity = Unlevered Cost of Equity + (Debt to Equity Ratio * (Unlevered Cost of Equity - After Tax Cost of Debt))

Here, 
Unlevered Cost of Equity = 15%
Debt to Equity Ratio = 10,000 / 50,000 = 0.2
After Tax Cost of Debt = (1- Tax Rate) * Interest Rate = (1- 0.21) * 7% = 5.53%

Substituting the values, we get:

Cost of Equity = 15% + (0.2 * (15% - 5.53%)) = 16.94% ≈ 17%

Therefore, the best choice is C, 17%.

Question 2

A new business requires a $20,000 investment today,and will generate a one-time cash flow of $25,000 after one year.The business will be financed with 50% equity and 50% debt.If the firm can borrow at 7%,what is the return on levered equity?

Accepted Answer

The return on levered equity can be calculated using the formula: Return on Equity = [(Cash Flow - Investment - Interest) / Equity]. Here, the cash flow is $25,000, the investment is $20,000, and the debt portion is 50% of $20,000, which is $10,000. The interest on the debt at 7% is $700 ($10,000 * 7%). The equity portion is also $10,000 (50% of $20,000). Plugging these numbers into the formula gives: [(25,000 - 20,000 - 700) / 10,000] = 4,300 / 10,000 = 43%.

Question 3

A firm has a market value of assets of $50,000.It borrows $10,000 at 5%.If the unlevered cost of equity is 15%,what is the firm's cost of equity capital?

Accepted Answer

The firm's cost of equity capital can be calculated using the Modigliani-Miller Proposition II with taxes. The formula is: $r_E = r_0 + (r_0 - r_D) \times (D/E)$, where $r_E$ is the cost of equity, $r_0$ is the unlevered cost of equity, $r_D$ is the cost of debt, $D$ is the value of debt, and $E$ is the value of equity. Here, $r_0 = 15\%$, $r_D = 5\%$, $D = \$10,000$, and $E = \$50,000 - \$10,000 = \$40,000$. Plugging these values into the formula gives: $r_E = 15\% + (15\% - 5\%) \times (\$10,000/\$40,000) = 15\% + 10\% \times 0.25 = 15\% + 2.5\% = 17.5\%$.

Question 4

In general,issuing equity may not dilute the ownership of existing shareholders if:

Accepted Answer

Issuing equity will not dilute the ownership of existing shareholders if the new shares are sold at a fair price. This means that the price of the new shares reflects the true value and potential of the company, and existing shareholders are not losing any value by the issuance of new shares. The other options (A, C, D, and E) do not necessarily guarantee that the ownership of existing shareholders will not be diluted.

Question 5

A new business requires a $20,000 investment today,and will generate a one-time cash flow of $25,000 after one year.The business will be financed with 60% equity and 40% debt.If the firm can borrow at 10%,what is the return on levered equity?

Accepted Answer

The return on levered equity can be calculated using the formula: Return on Equity = [(Cash Flow - Debt Payment - Initial Equity Investment) / Initial Equity Investment] * 100%. Here, the debt portion is 40% of $20,000, which is $8,000, and the equity portion is 60% of $20,000, which is $12,000. The debt payment after one year, considering a 10% interest rate, is $8,000 * 10% = $800, making the total debt payment $8,800. The cash flow after one year is $25,000. Therefore, the return on equity is [(25,000 - 8,800 - 12,000) / 12,000] * 100% = 35%.

Question 6

According to MM Proposition I,the stock price for With is closest to:

Accepted Answer

According to MM Proposition I, the value of a firm is not affected by its capital structure. Since With and Without have the same earnings before interest and taxes (EBIT) of $300,000 and the same tax rate of 40%, their values and stock prices should be the same.
Thus, the stock price for With should be:

Stock price = Value of With / Number of shares
Stock price = ($300,000 × (1 - 0.40)) / 50,000 shares
Stock price = $180,000 / 50,000 shares
Stock price = $3.60

However, the question asks for the closest stock price, and C) $6.00 is the closest to $3.60. Therefore, the best choice is C) $6.00.

Question 7

Under perfect capital markets,which of the following statements is regarding capital structure is most accurate?

Accepted Answer

Under perfect capital markets, the capital structure decision does not affect the total value of the firm or the amount of capital it can raise as long as the firm's choice of securities does not change the cash flows generated by its assets. This is because investors can replicate the firm's financing choices on their own if the market is perfect. Therefore, the value of the firm is determined by its cash flows, and not by its choice of capital structure.

Question 8

A firm requires an investment of $20,000.The firm's debt cost of capital is 6%,and its return on equity is 15%.If the firm's pre-tax WACC is 10.5%,how much did the firm borrow?

Accepted Answer

The firm's pre-tax WACC (Weighted Average Cost of Capital) is given as 10.5%, which is a weighted average of the cost of debt and the cost of equity. The formula for WACC is:$$WACC = \frac{D}{V} \times Rd + \frac{E}{V} \times Re$$where $D$ is the amount of debt, $E$ is the equity, $V = D + E$ is the total financing (which is $20,000 in this case), $Rd$ is the cost of debt (6%), and $Re$ is the cost of equity (15%).Given that the WACC is 10.5%, we can set up the equation:$$10.5\% = \frac{D}{20,000} \times 6\% + \frac{20,000 - D}{20,000} \times 15\%$$Solving for $D$, we find that $D = $10,000$. This means the firm borrowed $10,000.

Question 9

A firm requires an investment of $40,000 and borrows $10,000 at 8%.If the return on equity is 20%,what is the firm's pre tax WACC?

Accepted Answer

The answer of A firm requires an investment of $40,000...

Question 10

A firm requires an investment of $20,000.The firm's debt cost of capital is 5%,and its return on equity is 12%.If the firm's pre-tax WACC is 7.8%,how much equity did the firm use for its investment?

Accepted Answer

The correct answer is A.The WACC formula is:WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)where:E = market value of equityV = total value of the firmRe = cost of equityD = market value of debtRd = cost of debtTc = corporate tax rateWe are given that:WACC = 7.8%Rd = 5%Re = 12%We can solve for E/V:E/V = WACC / (Re - Rd * (1 - Tc))E/V = 7.8% / (12% - 5% * (1 - 0))E/V = 0.4Therefore, the firm used 40% equity for its investment.E = 0.4 * $20,000 = $8,000

Question 11

A new business requires a $20,000 investment today,and will generate a one-time cash flow of $25,000 after one year.The business will be financed with 20% equity and 80% debt.If the firm can borrow at 4%,what is the return on levered equity?

Accepted Answer

The cost of debt is 80% x 4% = 3.2%. 
The cost of equity can be solved using the formula: 
return on levered equity = return on unlevered equity + (return on unlevered equity - cost of debt) x (debt/equity) 
Assuming the unlevered cost of equity is 20% (1/5), 
return on levered equity = 20% + (20% - 3.2%) x (4/1) = 108.8% 
Rounding to the nearest whole percent gives us the answer of 109%.

Question 12

A firm requires an investment of $30,000 and borrows $10,000 at 6%.If the return on equity is 15%,what is the firm's pre tax WACC?

Accepted Answer

Weighted Average Cost of Capital (WACC) = (Cost of Equity x % Equity) + (Cost of Debt x %Debt)

Given:

Investment = $30,000
Borrowed amount = $10,000
Cost of debt (interest rate) = 6%
Cost of equity = 15%

Total financing = $30,000 + $10,000 = $40,000

% Equity = $30,000/$40,000 = 0.75 or 75%
% Debt = $10,000/$40,000 = 0.25 or 25%

WACC = (0.15 x 0.75) + (0.06 x 0.25) = 0.1125 or 11.25%

Therefore, the closest answer is C) 12%.

Question 13

Assume that MM's perfect capital markets conditions are met and that you can borrow and lend at the same 5% rate as With.You have $5000 of your own money to invest and you plan on buying Without stock.Using homemade leverage,how much do you need to borrow in your margin account so that the payoff of your margined purchase of Without stock will be the same as a $5000 investment in With stock?

Accepted Answer

To replicate the payoff of a $5000 investment in With stock using homemade leverage, you need to borrow an amount equal to your own investment, which is $5000. This allows you to double your investment in Without stock, mimicking the leverage effect of investing in With stock.

Question 14

Leverage can ________ a firm's expected earnings per share,but does not necessarily increase the share price.

Accepted Answer

Leverage can increase a firm's expected earnings per share because it allows the firm to use debt to finance its operations and investments, which can result in higher profits. However, this doesn't necessarily translate to an increase in the share price as other factors such as market conditions and investor sentiment also play a role in determining stock prices.

Question 15

A firm has a market value of assets of $50,000.It borrows $10,000 at 3%.If the unlevered cost of equity is 15%,what is the firm's cost of equity capital?

Accepted Answer

The formula to calculate the cost of equity with leverage is:
Cost of Equity = Unlevered Cost of Equity + (Debt/Equity) * (Unlevered cost of Equity - Interest Rate on Debt)

Here, Debt = $10,000 and Interest Rate on Debt = 3%, and Equity = $50,000 - $10,000 = $40,000

Using the formula: 
Cost of Equity = 15% + (10,000 / 40,000) * (15% - 3%) 
Cost of Equity = 18%

Therefore, the firm's cost of equity capital is 18%. Answer choice D is correct.

Question 16

When investors use leverage in their own portfolios to adjust the leverage choice made by the firm,it is referred to as:

Accepted Answer

When investors use their own leverage to adjust the firm's leverage, it is referred to as homemade leverage. This is because investors are essentially "making their own" leverage choices instead of relying solely on the firm's decisions. Options A, B, D, and E are not relevant to this concept.

Question 17

A firm requires an investment of $20,000,and will be financed with 50% equity and 50% debt.If the firm's debt cost of capital is 6%,and its return on equity is 15%,what is the firm's pre-tax WACC?

Accepted Answer

The correct answer is A.The WACC is calculated as follows:WACC = (E/V) * Re + (D/V) * Rd * (1 - T)where:E = market value of equityV = total value of the firmRe = cost of equityD = market value of debtRd = cost of debtT = corporate tax rateIn this case, we have:E = $10,000V = $20,000Re = 15%D = $10,000Rd = 6%T = 0Therefore, the WACC is:WACC = (10,000/20,000) * 15% + (10,000/20,000) * 6% * (1 - 0)= 10.5%

Question 18

A new business requires a $20,000 investment today,and will generate a one-time cash flow of $25,000 after one year.The business will be financed with 50% equity and 50% debt.If the firm can borrow at 7%,what is the pre-tax WACC?

Accepted Answer

The pre-tax Weighted Average Cost of Capital (WACC) is calculated by taking the weighted average of the cost of equity and the cost of debt. Since there is no specific cost of equity given, we can calculate the overall return required from the investment, which is ($25,000 - $20,000) / $20,000 = 25%. Given that the debt portion is financed at 7%, and assuming the cost of equity equals the overall return required (since it's not specified), the WACC is the average of these two, weighted by their respective proportions in the financing mix (50% equity at 25% and 50% debt at 7%). Thus, WACC = (0.5 * 25%) + (0.5 * 7%) = 12.5% + 3.5% = 16%. However, none of the provided options match this calculation directly, suggesting a misunderstanding in the calculation process or a misinterpretation of the question's requirements. Given the options, the closest to a logical answer based on the information provided would be to consider the overall return of 25% as the answer, assuming the question intended to ask for the return on the investment rather than the traditional calculation of WACC.

Question 19

Assume that MM's perfect capital markets conditions are met and that you can borrow and lend at the same 5% rate as With.You have $5000 of your own money to invest and you plan on buying Without stock.Using homemade leverage you borrow enough in your margin account so that the payoff of your margined purchase of Without stock will be the same as a $5000 investment in With stock.The number of shares of Without stock you purchased is closest to:

Accepted Answer

The answer of Assume that MM's perfect capital markets conditions...

Question 20

Which of the following is one of the characteristics of perfect capital markets?

Accepted Answer

Perfect capital markets have the feature of investors and firms trading the same set of securities at competitive market prices equal to the present value (PV) of their future cash flows. The other options are not characteristics of perfect capital markets. Option A describes the efficient market hypothesis, Option B describes a tax-efficient market, Option C concerns financing decisions impact on cash flows, and Option E describes an idealized market environment.

Quiz 16: Capital Structure