Module 6: Numeric Questions

For students

Last updated: 10/11/2025 09:53

The questions are based on or inspired by the following references:

• Berk & DeMarzo, Corporate Finance, 5th ed. (2020)
  
• Brealey & Myers, Principles of Corporate Finance, 13th ed. (2020)

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💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.

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⚠️ These exercises are powered by AI-assisted technologies and may contain occasional formatting or logic errors. Please report any issues you encounter so I can improve the experience.

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📙 Part 2 (Midterm to Final)

Module	Chapter	Slides	T/F	MCQ	Numeric	Long	Self-quiz
6	ch23	🎞️	✅	❓	🔢	📝	🧪

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Answer the following questions based on the discussions in class.

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Q1.

Ownership and Debt Financing

After Series A, founders own 59.0% and Series A investors own 41.0%.
Then the company raises R$ 11.788 million via debt (no equity issued).

What are the final ownership percentages for founders and Series A investors after the debt raise?

1a. Founders’ final ownership (%):

✅ Debt financing does not issue new shares. Founders remain at 59%.

1b. Series A investors’ final ownership (%):

✅ No new equity issued ⇒ Series A remains at 41%.

Q2.

Convertible Bond — Conversion Price

You own a bond with a face value of $1000 and a conversion ratio of 40.46. What is the conversion price?

Answer (conversion price, $):

✅ Conversion price = Face / Ratio = 1000 / 40.46 = $ 24.72.

Q3.

Debt Issuance with Placement Fee — Sizing to Target Net Proceeds

The company plans to raise R$ 11.34 million in net proceeds from a bond issue sold at par, but must pay a placement fee of 2% of the total face value issued.

Because the fee is deducted from the proceeds, the company must issue more than the target amount to achieve its goal.

1. How much face value (million R$) must be issued to net the target?

2. How much is the total fee paid (million R$)?

3a. Face to issue (R$ million):

✅ \(\text{Face} = \frac{\text{Target Net}}{1 - \text{fee}} =\) 11.57 million.

3b. Total fee (R$ million):

✅ Fee paid = Face × fee = 0.23 million.

Q4.

Convertible Bond — Conversion Ratio

You own a bond with a face value of $1000 and a conversion ratio of $26.27. What is the conversion ratio?

Answer (conversion ratio):

✅ Conversion ratio = Face / Price = 1000 / 26.27 = 38.06.

Q5.

Convertible Bond — Conversion Value vs. Straight Value (Premium/Discount)

A convertible bond can be exchanged for 19 shares. The stock trades at 35.55 and the bond trades at 1101.31.

1. What is the conversion value of the bond?
   
2. What is the conversion premium (bond price − conversion value)? Use a negative sign if discount.

1) Conversion value:

✅ Conversion value = 19 * 35.55 = 675.45.

2) Conversion premium:

✅ Premium = Bond price − Conversion value = 1101.31 − 675.45 = 425.86.

Q6.

Convertible Bond — Conversion Parity Price

A convertible bond trades at $1359.43 and can be converted into 24 shares. What is the conversion parity price?

Conversion parity price:

✅ Parity price = Bond price / Ratio = 1359.43 / 24 = 56.64.

Q7.

Convertible Bond — Immediate Conversion Gain (%)

A convertible bond can be converted into 19 shares. The stock is currently $40.93 and the bond trades at $1016.99. What is the Immediate conversion gain in percent?

Immediate conversion gain (%):

✅ Gain(%) = (100) = 100 × (777.67 − 1016.99) / 1016.99 = -23.53%.