Module 6: Numeric Questions

For students

Last updated: 15/10/2025 13:51

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 1 (until Midterm)

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.

Tesouro Selic — Daily Compounding (Business Days)

Initial amount: R$ 11.915,02   |   Annual rate: 11.74%   |   Business days: 28

Using the 252-day convention, compute the gross amount (R$) at the end of the period.

Answer (R$): <input type=“number” id=“module6_num_q1” name=“module6_num_q1” step=“0.01” style=“width:220px;” data-correct-answer=1.2063^{4} data-tolerance=“25” />

✅ Using (V = P,(1+r)^{d/252}) gives approximately R$ 12.063 (tolerance ± R$ 25).

Q2.

Covenant Step-Up — Present Value of Incremental Coupons

Par: R$ 1000 | Base coupon: 9.90% | Step-up: 1.80% (yrs 3–5) | Discount rate: 8.10%

Compute the present value (R$) of the incremental coupons due to the step-up in years 3–5, discounted at the given rate.

PV of increment (R$):

✅ Increment per year: (R$ 18).
(PV = _{t=3}^{5} ) R$ 39.62.

Q3.

Debt Issuance with Placement Fee — Sizing to Target Net Proceeds

Target net proceeds: R$ 11.342 million | Placement fee: 1.85%

The company issues bonds at par and pays a placement fee (as a % of face).
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):

✅ ( = = ) 11.556 million.

3b. Total fee (R$ million):

✅ Fee paid = Face × fee = 0.214 million.

Q4.

Ownership and Debt Financing (No Dilution)

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?

4a. Founders’ final ownership (%):

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

4b. Series A investors’ final ownership (%):

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

Q5.

Convertible Bond — Conversion Price (Quiz-Utils Layout)

Q: You own a bond with a face value of $1000 and a conversion ratio of 40.46.

Answer (conversion price, $):

✅ Conversion price = Face / Ratio = 1000 / 40.46 = $ 24.72. (We accept rounded to the nearest dollar.)

Q6.

Convertible Bond — Conversion Ratio (Quiz-Utils Layout)

Q: You own a bond with a face value of $1000 and a conversion price of $26.27.

Answer (conversion ratio):

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

::: {.webex-box}

Q7.

::: {.question}

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

cat(sprintf(“A convertible bond can be exchanged for %d shares. The stock trades at \(%1.2f</b> and the bond trades at <b>\)%1.2f.”, ratio, stock_price, bond_price))

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.

::: {.question-block}

1) Conversion value (\():</strong></label> <input type="number" id="module6_num_q7a" name="module6_num_q7a" step="0.01" style="width:220px;" data-correct-answer=675.45 data-tolerance="0.5" /> </form> <div id="feedback-module6_num_q7a" class="feedback" data-status="" style="display:none;"> ✅ Conversion value = 19 × 35.55 = <strong>\) 675.45.

:::

2) Conversion premium ($):

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

:::