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Online Test: Corporate Finance

This note contains the questions, options, correct answers, and detailed step-by-step solutions for the Corporate Finance Online Test.

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Question 1: Building Loan Annuity

For a building loan contract, a student’s grandmother has paid 2,500 EUR at the end of each year on an account for her grandson. Interest is paid at the end of each year, the rate equals 3% with compounding interest. To what value is the account balance after 30 years closest to?

• A. 95,000 EUR
• B. 120,000 EUR
• C. 75,000 EUR
• D. 82,500 EUR

Solution & Explanation

This is an ordinary annuity (payments at the end of each year).

Given parameters:

• $\text{PMT}=2,500\text{ EUR}$
• $r=3\%=0.03$
• $n=30\text{ years}$

Formula for Future Value of an Ordinary Annuity (FV):
$FV=\text{PMT}\times \frac{(1+r{)}^n-1}{r}$

Calculation:
$FV=2,500\times \frac{(1.03{)}^{30}-1}{0.03}$
$FV=2,500\times \frac{2.42726-1}{0.03}$
$FV=2,500\times 47.5754=118,938.50\text{ EUR}$

The calculated value of $118,938.50\text{ EUR}$ is closest to 120,000 EUR (Option B).

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Question 2: Effective Annual Rate (EAR)

A bank quotes a nominal annual interest rate of 12%, compounded monthly. What is the effective annual rate (EAR), closest value?

• A. 12.00%
• B. 12.55%
• C. 12.36%
• D. 12.68%

Solution & Explanation

Given parameters:

• Nominal annual interest rate ($r_{\text{nom}}$) = $12\%=0.12$
• Compounding periods per year ($m$) = $12$ (monthly)

Formula for Effective Annual Rate (EAR):
$EAR={\left(1+\frac{r_{\text{nom}}}{m}\right)}^m-1$

Calculation:
$EAR={\left(1+\frac{0.12}{12}\right)}^{12}-1$
$EAR=(1.01{)}^{12}-1$
$EAR\approx 1.126825-1=12.6825\%$

The closest value is 12.68% (Option D).

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Question 3: Stock Valuation (Gordon Growth Model)

A stock just paid an annual dividend of 2.00 EUR. Dividends are expected to grow at a constant rate of 4% per year forever, and the required rate of return is 9%. What is the intrinsic value of the stock today?

• A. 40.00 EUR
• B. 41.60 EUR
• C. 23.11 EUR
• D. 16.00 EUR

Solution & Explanation

We use the Gordon Growth Model to value the stock.

Given parameters:

• Dividend just paid ($D_0$) = $2.00\text{ EUR}$
• Growth rate ($g$) = $4\%=0.04$
• Required rate of return ($r$) = $9\%=0.09$

Step 1: Calculate the expected dividend next year ($D_1$):
$D_1=D_0\times (1+g)=2.00\times (1+0.04)=2.08\text{ EUR}$

Step 2: Calculate the intrinsic value ($P_0$):
$P_0=\frac{D_1}{r-g}=\frac{2.08}{0.09-0.04}=\frac{2.08}{0.05}=41.60\text{ EUR}$

The correct answer is 41.60 EUR (Option B).

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Question 4: Diversification Theory

Which of the following statements about diversification is correct?

• A. The expected return of a portfolio decreases as more securities are added, regardless of their risk.
• B. Diversification can substantially reduce unsystematic (firm-specific) risk, but systematic (market) risk remains.
• C. Holding a large number of different stocks eliminates both systematic and unsystematic risk.
• D. Systematic risk can be diversified away, whereas unsystematic risk is rewarded with a risk premium.

Solution & Explanation

• Unsystematic (firm-specific) risk can be reduced through diversification because the specific events affecting individual companies tend to cancel each other out in a large portfolio.
• Systematic (market) risk (e.g., interest rate changes, recessions) affects the entire market and cannot be diversified away. Only systematic risk is rewarded with a risk premium in equilibrium (according to the CAPM).

Therefore, Option B is correct.

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Question 5: Stock Dividends

Which of the following is a characteristic of “stock dividends”?

• A. They increase the company’s cash reserves.
• B. They are mandatory payments that companies must make annually.
• C. They involve a cash payment to shareholders from the company’s earnings.
• D. They result in the distribution of additional shares of the company’s stock to existing shareholders.

Solution & Explanation

• A stock dividend is a payout of additional shares of stock rather than cash.
• It does not change the company’s assets/cash reserves (so A and C are incorrect).
• It is not mandatory (so B is incorrect).
• The main effect is an increase in the number of outstanding shares and a proportional decrease in the stock price per share, leaving the total value of ownership unchanged.

Therefore, Option D is correct.

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Question 6: Bond Types

Which of the following statements about different types of bonds is most likely correct?

• A. A perpetual bond has a fixed maturity date after which the principal amount is repaid.
• B. In a reverse convertible bond, the issuer can choose to repay with shares instead of cash.
• C. A zero-coupon bond pays fixed interest payments over its lifetime.
• D. An option bond allows the bond to be exchanged against stocks at a predetermined date.

Solution & Explanation

• Reverse convertible bonds are structured products where the issuer has the option to deliver a predetermined number of shares of stock instead of par value in cash at maturity (usually if the share price drops below a certain threshold).
• Let’s look at the others:
  • Perpetual bonds have no maturity date and pay interest forever.
  • Zero-coupon bonds do not make periodic interest payments; they are issued at a discount and redeemed at face value.
  • An option bond (or bond with warrants) grants option rights, but the option to convert/exchange is held by the investor, not the bond automatically.

Therefore, Option B is correct.

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Question 7: Time Value of Money

The “Time Value of Money” principle states that it is only possible to compare or combine values that refer to the:

• A. Same risk level.
• B. Different points in time after adjusting for inflation.
• C. Same point in time.
• D. Different currencies after exchange rate conversion.

Solution & Explanation

A basic tenet of finance is that a dollar today is worth more than a dollar tomorrow. To compare or combine cash flows occurring at different times, we must first compound or discount them to bring them to the same point in time (e.g., all to present value $PV$ or all to future value $FV$).

Therefore, Option C is correct.

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Question 8: Cost of Capital Estimation

Which of the following statements is correct without limitations?

• A. For companies with publicly traded debt, the equity cost of capital should reflect the current debt market rate the company is paying.
• B. All of the statements are false.
• C. The CAPM is mainly used for assessing the debt cost of capital.
• D. Yield-to-maturity and debt-rating are two methods of calculating the debt cost of capital.

Solution & Explanation

• The cost of debt ($r_d$) represents the interest rate a company would have to pay if it issued new debt today.
• If the company has outstanding, actively traded bonds, we can use their Yield-to-Maturity (YTM) as an estimate for the cost of debt.
• Alternatively, if the debt is not actively traded, we can look up the company’s credit rating (debt-rating) and use the average yield of other bonds with the same rating and maturity.
• CAPM is used for the equity cost of capital, making C incorrect. Equity cost of capital is not directly set by the debt rate, making A incorrect.

Therefore, Option D is correct.

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Question 9: WACC Calculation

A company is financed with the following capital structure (market values). Corporate tax rate is 30%. Equity: 600 EUR m at 11.0%; Debt: 400 EUR m at 6.0% (pre-tax). What is the company’s WACC?

• A. 8.50%
• B. 6.92%
• C. 9.00%
• D. 8.28%

Solution & Explanation

Given parameters:

• Equity ($E$) = $600\text{ EUR m}$
• Debt ($D$) = $400\text{ EUR m}$
• Total Value ($V=E+D$) = $1000\text{ EUR m}$
• Cost of Equity ($r_E$) = $11\%=0.11$
• Cost of Debt ($r_D$) = $6\%=0.06$ (pre-tax)
• Corporate tax rate ($T_C$) = $30\%=0.30$

WACC Formula:
$\text{WACC}=\frac{E}{V}\times r_E+\frac{D}{V}\times r_D\times (1-T_C)$

Calculation:
$\text{WACC}=\left(\frac{600}{1000}\right)\times 0.11+\left(\frac{400}{1000}\right)\times 0.06\times (1-0.30)$
$\text{WACC}=0.60\times 0.11+0.40\times 0.06\times 0.70$
$\text{WACC}=0.0660+0.0168=0.0828=8.28\%$

The correct answer is 8.28% (Option D).

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Question 10: Modigliani-Miller with Corporate Taxes

According to Modigliani-Miller with corporate taxes, which statement is correct?

• A. With corporate taxes, the value of a levered firm equals the value of the unlevered firm plus the present value of the interest tax shield.
• B. Higher leverage lowers the WACC solely because equity holders demand a lower return as debt rises.
• C. With corporate taxes, total firm value is independent of the capital structure.
• D. In the absence of taxes, a firm can raise its total value simply by increasing leverage.

Solution & Explanation

• Modigliani-Miller Proposition I with corporate taxes states that because interest payments are tax-deductible, leverage creates a benefit (interest tax shield) that increases the value of the firm:
  $V_L=V_U+PV(\text{Interest Tax Shield})$
  Thus, Option A is correct.
• Option B is incorrect: as leverage increases, equity becomes riskier, so equity holders demand a higher return (not lower).
• Option C is incorrect: total firm value does depend on capital structure when taxes are present.
• Option D is incorrect: in the absence of taxes, total firm value is completely independent of capital structure.