Module 1: Numeric Questions

For students

Last updated: 28/07/2025 15:46

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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📘 Part 1 (until Midterm)

Chapter	Slides	T/F	MCQ	Numeric	Long
ch23	🎞️	✅	❓	🔢	📝

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Answer the following questions based on the discussions in class.

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Post-money valuation and ownership

You founded your company with 0.055 million and received 1 million shares.
You later sold 0.75 million shares to angel investors.
Now a VC wants to invest 3 million in exchange for 2 million shares.

1. What is the post-money valuation (in million)?

✅ Post-money = (Total shares) × (Price per share)
= (3.75) × (1.5) = 5.625 million

2. What percentage of the firm will the VC own?

✅ VC Ownership = 2 / (3.75) × 100 = 53.333%

3. What is the value of your shares (in million)?

✅ Value = 1 × 1.5 = 1.5 million

Capital raised and founder dilution

A company raised capital in three rounds (values in millions USD):

Series A: Pre = 3.368, Post = 6.287

Series B: Pre = 38.243, Post = 77.473

Series C: Pre = 132.115, Post = 184.012

1. How much did the company raise in Series A?

✅ Raised = Post - Pre = 6.287 - 3.368 = 2.919 million

2. How much did the company raise in Series B?

✅ Raised = Post - Pre = 77.473 - 38.243 = 39.23 million

3. How much did the company raise in Series C?

✅ Raised = Post - Pre = 184.012 - 132.115 = 51.897 million

4. What % of shares did founders keep after Series A?

✅ % kept = Pre / Post = 3.368 / 6.287 = 53.571%

5. What % of shares did founders keep after Series B?

✅ % kept = A × B = (53.571%) × (49.363%) = 26.444%

6. What % of shares did founders keep after Series C?

✅ % kept = A × B × C = (53.571%) × … = 18.986%

Post-money valuation and VC ownership

You founded a firm three years ago. You started with $0.293 million, which gave you 1.308 million shares. You later sold 1.146 million shares to angel investors. Now, a VC firm wants to invest $5.574 million in exchange for 2.804 million new shares.

1. What is the post-money valuation (in million)?

✅ Post-money = Total shares × Price per share = (5.258) × (1.988) = 10.452 million

2. What percentage of the firm will the VC own?

✅ VC Ownership = 2.804 / (5.258) × 100 = 53.328%

Valuation and Ownership After Equity Issuance

Erica owns all 4 million shares of her company, CoralTech. A new partner is offering to invest 1.631 million in exchange for 1.5 million shares.

1. What is the post-money valuation (in million)?

✅ Post-money = (5.5) shares × $1.087 (1.631/ 1.5) = 5.978 million

2. What percentage of the company will the new partner own?

✅ Partner Ownership = 1.5 / 5.5 × 100 = 27.273%

Ownership After Two Funding Rounds

After a Series A round, the founders owned 63.3% of BetaVision.
Then, Series B investors contributed 4.04 million and received 27.9% of the company.

1. What is the founders’ final ownership (%)?

✅ Founders’ final ownership = (1 - 27.9%) × 63.3% = 45.6%

2. What is the Series A investors’ final ownership (%)?

✅ Series A ownership = (1 - 27.9%) × 36.7% = 26.5%

Convertible Note with Discount

Context:
Yara invested in a startup using a convertible note of $1.501 million, with a 20% discount.
When the company raised Series A at $1.32 per share, her note converted at the discounted price.

1. How many shares did Yara receive upon conversion?

✅ Shares = Note / Discounted Price = 1.501 million / 1.056 = 1.421 million shares

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