Indian Institute of Management

Sirmaur

Private Equity & Venture Capital

“The Venture Capital Method – Valuation

Problem Set”

Submitted to
Prof. B B Chakrabarti

Section A
Group 15

Chandni Bhanushali MBA23115 8408810398

Devansh Parekh MBA23011 7977423429
Jacob Ponraj MBA23118 9943630916
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Question 1:

a. Calculating the Share of the Company Required

The future value (FV) of the company at Year 5 is calculated as:

FV = Net Income × P/E Ratio = 5M × 20 = 100M

The PV is discounted back to today using the required rate of return (r):

PV = FV / (1 + r)^5

For r = 50%: PV = 100M / (1 + 0.5)^5 = 100M / 7.59375 ≈ 13.17M

For r = 30%: PV = 100M / (1 + 0.3)^5 = 100M / 3.71293 ≈ 26.93M

The share required by the VC is:

Required Share = Investment / PV

For r = 50%: Required Share = 5M / 13.17M ≈ 37.96%

For r = 30%: Required Share = 5M / 26.93M ≈ 18.57%

b. Calculating the Shares Purchased and Price per Share

Given 1,000,000 shares outstanding, calculate the total shares after investment:

Total Shares = Pre-existing Shares / (1 - Required Share)

For r = 50%:

Total Shares = 1M / (1 - 0.3796) ≈ 1.61M

Shares Purchased = 1.61M - 1M = 0.61M

Price per Share = Investment / Shares Purchased = 5M / 0.61M ≈ 8.20

For r = 30%:

Total Shares = 1M / (1 - 0.1857) ≈ 1.23M

Shares Purchased = 1.23M - 1M = 0.23M

Price per Share = Investment / Shares Purchased = 5M / 0.23M ≈ 21.74

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c. Raising $12 Million Instead

If $12M is raised instead:

Required Share = Investment / PV

For r = 50%: Required Share = 12M / 13.17M ≈ 91.09%

For r = 30%: Required Share = 12M / 26.93M ≈ 44.57%

Price per share can be calculated using the same steps as in part (b).

Question 2:

Management should own at least 15% by Year 5. This adjusts the VC's required share today.

Adjusted Required Share = Required Share / (1 - Management Ownership)

For r = 50%: Adjusted Required Share = 37.96% / (1 - 0.15) ≈ 44.66%

For r = 30%: Adjusted Required Share = 18.57% / (1 - 0.15) ≈ 21.85%

Question 3:

If another $3M is raised at the beginning of Year 3, the required shares for each round are

calculated below.

a. Round 1 Investor's Share Today

For Round 2 investors (r = 30%), the PV of the company is calculated as:

PV = FV / (1 + r)^2 = 100M / (1 + 0.3)^2 = 100M / 1.69 ≈ 59.17M

Round 1 PV (r = 50%):

PV = FV / (1 + r)^5 = 100M / (1 + 0.5)^5 ≈ 13.17M

Round 1 Required Share = Investment / PV = 5M / 13.17M ≈ 37.96%

b. Round 2 Investor's Share

For Round 2 investors:

Required Share = Investment / PV

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Required Share = 3M / 59.17M ≈ 5.07%

Price per share for Round 2 investors can be calculated similarly based on total shares.

c. Delayed Financial Target to Year 7

If financial targets are delayed to Year 7, the PV is recalculated using a discount period of 7

years:

For Round 1 PV:

PV = FV / (1 + r)^7

This will reduce the PV for both rounds, increasing the required share for each round.

Question 4:

Benedicta proposed using participating preferred stock, a hybrid security that provides

benefits like:

1. Principal repayment upon conversion (like debt).

2. Equity upside through conversion into common shares.

Below are the detailed calculations and their effects.

a. Effect on Rate of Return and Effective Ownership

Participating preferred stock increases the effective rate of return because Benedicta receives

both her investment principal and equity upside. Assume the following:

- Investment: $5M

- FV of Company: $100M

- Required Rate of Return: 50%

To calculate Benedicta’s effective ownership under participating preferred:

1. Principal repayment: $5M

2. Equity value from shares: Calculate based on required share.

Required Share = Investment / PV = 5M / 13.17M ≈ 37.96%

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 Equity Value = FV × 37.96% = 100M × 0.3796 = 37.96M

3. Total Value = Principal Repayment + Equity Value = 5M + 37.96M = 42.96M

Effective Ownership:

Effective Ownership = Total Value / FV = 42.96M / 100M = 42.96%

b. Counter-offer Terms

Roger can counter by proposing either standard preferred stock or adjusting terms as follows:

1. Limit the equity upside by offering a lower conversion rate.

2. Adjust the price per share to reduce dilution.

c. Perceptions of Risk and Reward

Impact of Participating Preferred Stock:

- For Roger: Higher risk due to reduced upside potential and greater claims on the company’s

assets.

- For Benedicta: Lower risk and higher guaranteed returns through dual benefits.

Roger might perceive this as overprotective, while Benedicta views it as fair compensation

for early-stage risks.

Question 5:

Benedicta proposed standard preferred stock with 10% cumulative dividends, increasing her

effective claim at conversion.

a. Effect on Rate of Return and Ownership

Calculate cumulative dividends and their impact on effective ownership:

Dividends = Investment × (1 + Dividend Rate)^5 - Investment

For $5M investment:

Dividends = 5M × (1 + 0.1)^5 - 5M = 5M × 1.61051 - 5M = 3.05M

Total Claim = Investment + Dividends = 5M + 3.05M = 8.05M

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Effective Ownership = Total Claim / PV

For PV = 13.17M:

Effective Ownership = 8.05M / 13.17M ≈ 61.12%

Question 6

Henry seeks $100,000 in seed-stage funding for his venture, aiming to develop a prototype,

engage customers, and refine his business plan.

a. Approach to Fundraising

Henry should target:

1. Angel Investors or Friends and Family: These investors are more likely to take risks at this

stage.

2. Challenges:

- Lack of a proven business model.

- High uncertainty and limited validation.

- Difficulty justifying valuation.

b. Valuation and Deal Terms

Valuation Example:

Assume comparable startups are valued at $1M. Henry can offer:

- 10% equity for $100,000.

Preferred structures include:

- Convertible Notes: Delays valuation to a later stage.

- SAFE Agreements: Simplifies the process without immediate equity dilution.