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Venture Capital Problem Set

David Liu8/3/26About 4 min

Venture Capital Problem Set

Question #1

Step 1: Terminal Value (2030 Exit)

Revenue = $6.5M, P/R = 14

VN=$6.5M×14=$91MV_N = \$6.5\text{M} \times 14 = \$91\text{M}

Series A (March 2025)

  • Investment: $1.5M
  • ROI: 50% p.a. over 5 years (2025–2030)
  • Required terminal value for TVC:

VIN=$1.5M×(1+0.5)5=$1.5M×7.59375=$11.39MV_{IN} = \$1.5\text{M} \times (1 + 0.5)^5 = \$1.5\text{M} \times 7.59375 = \$11.39\text{M}

  • Terminal ownership %:

%Terminal=$11.39M$91M=12.52%\%_{\text{Terminal}} = \frac{\$11.39\text{M}}{\$91\text{M}} = 12.52\%

Series B (March 2027)

  • Investment: $7M
  • ROI: 40% p.a. over 3 years (2027–2030)
  • Required terminal value:

VIN=$7M×(1+0.4)3=$7M×2.744=$19.21MV_{IN} = \$7\text{M} \times (1 + 0.4)^3 = \$7\text{M} \times 2.744 = \$19.21\text{M}

  • Terminal ownership %:

%Terminal=$19.21M$91M=21.11%\%_{\text{Terminal}} = \frac{\$19.21\text{M}}{\$91\text{M}} = 21.11\%

Series C (March 2028)

  • Investment: $8.5M
  • ROI: 30% p.a. over 2 years (2028–2030)
  • Required terminal value:

VIN=$8.5M×(1+0.3)2=$8.5M×1.69=$14.37MV_{IN} = \$8.5\text{M} \times (1 + 0.3)^2 = \$8.5\text{M} \times 1.69 = \$14.37\text{M}

  • Terminal ownership %:

%Terminal=$14.37M$91M=15.79%\%_{\text{Terminal}} = \frac{\$14.37\text{M}}{\$91\text{M}} = 15.79\%

Retention and Dilution

  • Series A Retention:

    RetentionA=100%−21.11%−15.79%=63.10%\text{Retention}_A = 100\% - 21.11\% - 15.79\% = 63.10\%

  • Series B Retention:

    RetentionB=100%−15.79%=84.21%\text{Retention}_B = 100\% - 15.79\% = 84.21\%

  • Series C Retention:

    RetentionC=100%\text{Retention}_C = 100\%

Required Ownership at Investment

  • Series A:

    %Acquired=12.52%63.10%=19.84%\%_{\text{Acquired}} = \frac{12.52\%}{63.10\%} = 19.84\%

  • Series B:

    %Acquired=21.11%84.21%=25.07%\%_{\text{Acquired}} = \frac{21.11\%}{84.21\%} = 25.07\%

  • Series C:

    %Acquired=15.79%\%_{\text{Acquired}} = 15.79\%

Share Calculations

post-$ serA=1.5M/19.84%=7.5M

pre-$ serA=7.5-1.5M=6M

Pre-Series A Shares:

  • Founders: 350K + 75K + 75K = 500K shares
  • Cathy’s SAFE converts at $4M post-money cap:

    %Cathy=$400K$4M=10%⇒Shares=10%1−10%×500K=55,556 shares\%_{\text{Cathy}} = \frac{\$400K}{\$4M} = 10\% \quad \Rightarrow \quad \text{Shares} = \frac{10\%}{1 - 10\%} \times 500K = 55,556 \text{ shares}

  • Total pre-Series A shares: 500K + 55,556 = 555,556 shares

Series A:

New Shares=19.84%1−19.84%×555,556=137,503 shares\text{New Shares} = \frac{19.84\%}{1 - 19.84\%} \times 555,556 = 137,503 \text{ shares}

Price/Share=$1.5M137,503=$10.918\text{Price/Share} = \frac{\$1.5M}{137,503} = \$10.918

Post-Money Val=$1.5M/19.84%=$7.56MPre-Money Val=$7.56M−$1.5M=$6.06M\text{Post-Money Val} = \$1.5M / 19.84\% = \$7.56M \quad \text{Pre-Money Val} = \$7.56M - \$1.5M = \$6.06M

Series B:
Total shares before Series B: 555,556 + 137,503 = 693,059

New Shares=25.07%1−25.07%×693,059=231,881 shares\text{New Shares} = \frac{25.07\%}{1 - 25.07\%} \times 693,059 = 231,881 \text{ shares}

Price/Share=$7M232,258=$30.19\text{Price/Share} = \frac{\$7M}{232,258} = \$30.19

Post-Money Val=$7M/25.07%=$27.93MPre-Money Val=$27.93M−$7M=$20.93M\text{Post-Money Val} = \$7M / 25.07\% = \$27.93M \quad \text{Pre-Money Val} = \$27.93M - \$7M = \$20.93M

Series C:
Total shares before Series C: 693,059 + 231,881 = 924,940

New Shares=15.79%1−15.79%×924,940=173,433 shares\text{New Shares} = \frac{15.79\%}{1 - 15.79\%} \times 924,940 = 173,433 \text{ shares}

Price/Share=$8.5M173,433=$49.01\text{Price/Share} = \frac{\$8.5M}{173,433} = \$49.01

Post-Money Val=$8.5M/15.79%=$53.83MPre-Money Val=$53.83M−$8.5M=$45.33M\text{Post-Money Val} = \$8.5M / 15.79\% = \$53.83M \quad \text{Pre-Money Val} = \$53.83M - \$8.5M = \$45.33M

Final Answers for Q1a & Q1b

Series A (2025)
  • % Acquired: 19.84%
  • New Shares: 137,503
  • Price/Share: $10.91
  • Pre-Money: $6.06M
  • Post-Money: $7.56M
Series B (2027)
  • % Acquired: 25.07%
  • New Shares: 231,881
  • Price/Share: $30.19
  • Pre-Money: $20.93M
  • Post-Money: $27.93M
Series C (2028)
  • % Acquired: 15.79%
  • New Shares: 173,433
  • Price/Share: $49.01
  • Pre-Money: $45.33M
  • Post-Money: $53.83M

Question #2

Terminal Price/Share (2030):

Total Shares=924,940+173,433=1,098,373⇒Price/Share=$91M1,099,658=$82.85\text{Total Shares} = 924,940 + 173,433 = 1,098,373 \quad \Rightarrow \quad \text{Price/Share} = \frac{\$91M}{1,099,658} = \$82.85

  • Ken’s Value:

    350,000×$82.75=$28.96M⇒ROI=($28.96M$30K)1/6−1=214.4% p.a.350,000 \times \$82.75 = \$28.96M \quad \Rightarrow \quad \text{ROI} = \left(\frac{\$28.96M}{\$30K}\right)^{1/6} - 1 = 214.4\% \text{ p.a.}

  • Other Founders:

    75,000×$82.75=$6.21M⇒ROI=($6.21M$10K)1/6−1=192.1% p.a.75,000 \times \$82.75 = \$6.21M \quad \Rightarrow \quad \text{ROI} = \left(\frac{\$6.21M}{\$10K}\right)^{1/6} - 1 = 192.1\% \text{ p.a.}

  • Cathy’s Value:

    55,556×$82.75=$4.6M⇒ROI=($4.6M$400K)1/6−1=50.3% p.a.55,556 \times \$82.75 = \$4.6M \quad \Rightarrow \quad \text{ROI} = \left(\frac{\$4.6M}{\$400K}\right)^{1/6} - 1 = 50.3\% \text{ p.a.}

Difference in Returns: Ken’s higher ownership (350K vs. 75K) leads to a slightly higher ROI.

Question #3

If $17M were raised in Series A at 50% p.a.:

\text{Required Terminal Ownership} = \frac{\$17M \times (1.5)^5}{\$91M} = 141.86\% \quad \text{(Impossible, >100%)}

Ken realized this would require giving away >100% ownership, making it infeasible.

Question #4

incorrect calculation of total shares at exit, impacting percent acquired values found. new shares, price/share, pre-money and post money valuations should change as well

Including 10% Option Pool

Adjust Terminal Shares:

Option Pool=10%1−10%×1,099,658=122,184 shares\text{Option Pool} = \frac{10\%}{1-10\%} \times 1,099,658 = 122,184 \text{ shares}

Total shares at exit: 1,099,658+122,184=1,221,8421,099,658 + 122,184 = 1,221,842

Revised Terminal Price/Share:

$91M1,221,842=$74.48\frac{\$91M}{1,221,842} = \$74.48

Revised Answers for Q1a & Q1b

We can seen the Terminal Value for the former investors and founder is 90% of origin.

V_N=$91M*(1-10\%)=81.9M

Series A (2025):

  • % Acquired: 19.84% (adjusted for dilution)
  • New Shares: 137,931 (unchanged)
  • Price/Share: $10.88 (unchanged)
  • Pre-Money Valuation: $6.06M (unchanged)
  • Post-Money Valuation: $7.56M (unchanged)

Series B (2027):

  • % Acquired: 25.07% (adjusted for dilution)
  • New Shares: 232,258 (unchanged)
  • Price/Share: $30.14 (unchanged)
  • Pre-Money Valuation: $20.93M (unchanged)
  • Post-Money Valuation: $27.93M (unchanged)

Series C (2028):

  • % Acquired: 15.79% (adjusted for dilution)
  • New Shares: 173,913 (unchanged)
  • Price/Share: $48.88 (unchanged)
  • Pre-Money Valuation: $45.33M (unchanged)
  • Post-Money Valuation: $53.83M (unchanged)

Revised Answer for Q2

  • Ken’s Shares (350,000):

    350,000×$74.48=$26.07M⇒CAGR=($26.07M$30,000)1/6−1=104.2% p.a.350,000 \times \$74.48 = \$26.07\text{M} \quad \Rightarrow \quad \text{CAGR} = \left(\frac{\$26.07\text{M}}{\$30,000}\right)^{1/6} - 1 = \mathbf{104.2\% \text{ p.a.}}

  • Other Founders (75,000 each):

    75,000×$74.48=$5.59M⇒CAGR=($5.59M$10,000)1/6−1=100.1% p.a.75,000 \times \$74.48 = \$5.59\text{M} \quad \Rightarrow \quad \text{CAGR} = \left(\frac{\$5.59\text{M}}{\$10,000}\right)^{1/6} - 1 = \mathbf{100.1\% \text{ p.a.}}

  • Cathy’s Shares (55,556):

    55,556×$74.48=$4.14M⇒CAGR=($4.14M$400,000)1/6−1=43.9% p.a.55,556 \times \$74.48 = \$4.14\text{M} \quad \Rightarrow \quad \text{CAGR} = \left(\frac{\$4.14\text{M}}{\$400,000}\right)^{1/6} - 1 = \mathbf{43.9\% \text{ p.a.}}

Question #5

Q5: rates of return exponent incorrect

Step 1: Adjust Investment Periods

  • Series A: 7 years (2025–2032)
  • Series B: 5 years (2027–2032)
  • Series C: 4 years (2028–2032)

Step 2: Recalculate TVC’s ROI

  • Terminal value remains $91M.

  • Series A:

    ROI=($74.48$10.88)1/7−1=27.3% p.a.\text{ROI} = \left(\frac{\$74.48}{\$10.88}\right)^{1/7} - 1 = \mathbf{27.3\% \text{ p.a.}}

  • Series B:

    ROI=($74.48$30.14)1/5−1=19.8% p.a.\text{ROI} = \left(\frac{\$74.48}{\$30.14}\right)^{1/5} - 1 = \mathbf{19.8\% \text{ p.a.}}

  • Series C (Increased to $10.5M):

    New Shares=$10.5M$48.88=214,810 shares\text{New Shares} = \frac{\$10.5\text{M}}{\$48.88} = 214,810 \text{ shares}

    ROI=($74.48$48.88)1/4−1=11.2% p.a.\text{ROI} = \left(\frac{\$74.48}{\$48.88}\right)^{1/4} - 1 = \mathbf{11.2\% \text{ p.a.}}

Question #6

Q6: rates of return exponent incorrect

Step 1: Priority Payout for Series B/C

  • Series B: Recovers $7M first.
  • Series C: Recovers $8.5M first.
  • Remaining Proceeds:

    $91M−$7M−$8.5M=$75.5M\$91\text{M} - \$7\text{M} - \$8.5\text{M} = \$75.5\text{M}

Step 2: Proportional Distribution of Remaining $75.5M

  • TVC’s Series B:

    232,2581,221,842×$75.5M=$14.35M⇒Total=$7M+$14.35M=$21.35M\frac{232,258}{1,221,842} \times \$75.5\text{M} = \$14.35\text{M} \quad \Rightarrow \text{Total} = \$7\text{M} + \$14.35\text{M} = \$21.35\text{M}

    ROI=($21.35M$7M)1/5−1=25.1% p.a.\text{ROI} = \left(\frac{\$21.35\text{M}}{\$7\text{M}}\right)^{1/5} - 1 = \mathbf{25.1\% \text{ p.a.}}

  • TVC’s Series C:

    214,8101,221,842×$75.5M=$13.27M⇒Total=$8.5M+$13.27M=$21.77M\frac{214,810}{1,221,842} \times \$75.5\text{M} = \$13.27\text{M} \quad \Rightarrow \text{Total} = \$8.5\text{M} + \$13.27\text{M} = \$21.77\text{M}

    ROI=($21.77M$8.5M)1/4−1=26.4% p.a.\text{ROI} = \left(\frac{\$21.77\text{M}}{\$8.5\text{M}}\right)^{1/4} - 1 = \mathbf{26.4\% \text{ p.a.}}

Step 3: Impact on Founders and Cathy

  • Remaining for Common Shareholders:

    $75.5M−$14.35M−$13.27M=$47.88M\$75.5\text{M} - \$14.35\text{M} - \$13.27\text{M} = \$47.88\text{M}

  • Ken’s Value:

    350,0001,221,842×$47.88M=$13.73M\frac{350,000}{1,221,842} \times \$47.88\text{M} = \$13.73\text{M}

  • Cathy’s Value:

    55,5561,221,842×$47.88M=$2.18M\frac{55,556}{1,221,842} \times \$47.88\text{M} = \$2.18\text{M}

David Liu · AI Systems & Infrastructure
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