1. Quant Topics PE IIRR, TVPI, DPI, RVPI, arithmetic, geometry returns PME, PME future value, excess return over PME Management, transaction, monitoring fee, offset, carry interest calculation, net of fee IRR, gross of fee IRR

2. IRR, TVPI, DPI, RVPI Return, PME

3. Calculate the following: 1. Interim IRR. 2. TVPI, DPI, RVPI. 3. Arithmetic and geometric returns. 4. Excess return assuming a PME return of 3%.

4. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5.

5. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million.

6. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5. What is the interim IRR?

7. CF0 = -50 CF1-3 = 0 CF4 = 20 CF5 = 195 Interim IRR = 34.73%

8. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5. Interim IRR = 34.73% What is TVPI, DPI, RVPI?

9. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5. Interim IRR = 34.73% What is TVPI, DPI, RVPI? TVPI = (20+30+165)/50 = 430% DPI = (20+30)/50 = 100% RVPI = 165/50 = 330%

10. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5. Interim IRR = 34.73%; TVPI = 430%; DPI = 100%; RVPI = 330%. What is the annual return? Arithmetic? Geometric?

11. Brighton Funds is a 5-year old private equity fund. Investors have put in a combined $50 million and have received distributions of $20 million at the end of year 4 and $30 million at the end of year 5. The net asset value (NAV) of the fund is estimated to be $165 million at the end of year 5. Interim IRR = 34.73%; TVPI = 430%; DPI = 100%; RVPI = 330%. What is the annual return? Arithmetic = 430% / 5 = 86% Geometric = (1+4.3)^0.2-1 = 39.6%

12. What is the excess return above PME return?

13. What is the PME as of the last year assuming a PME return of 3%?

15. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million. Calculate the interim IRR for Edge Capital.

16. Cash flow registry on your calculator: CF0 = -200; CF1-3 = 0; CF4 = 150; CF5 = 370 (= 60 + 310); IRR → CPT = 22.60%

17. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million. Calculate the interim IRR for Edge Capital. IIRR = 22.60%. What is TVPI, DPI, RVPI?

18. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million. Calculate the interim IRR for Edge Capital. IIRR = 22.60%. What is TVPI, DPI, RVPI? TVPI = (150+60+310)/200 = 260% DPI = (150+60)/200 = 105% RVPI = 310/200 = 155%

19. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million. Calculate the interim IRR for Edge Capital. IIRR = 22.60%; TVPI = 260%; DPI = 105%; RVPI = 155%. What is the annual return? Arithmetic? Geometric?

20. Edge Capital is a private equity fund that is five years old. Investor funds were $200 million at inception. Investors received distributions of $150 million after four years and $60 million after five years. The NAV of the fund at the end of year 5 is estimated to be $310 million. Calculate the interim IRR for Edge Capital. IIRR = 22.60%; TVPI = 260%; DPI = 105%; RVPI = 155%. What is the annual return? Arithmetic = 260% / 5 = 52% Geometric = (1+2.6)^0.2-1 = 29.2%

21. What is the excess return above PME return?

22. What is the PME as of the last year assuming a PME return of 3%?

24. I have invested in Wu Capital with the following cash flows. Year 1: 100m, Year 2: 150m, Year 3: 50m, Year 4: distrib 200m, Year 5: distrib 50m, contribution 50m, Year 6 distrib 100m, Year 7 NAV of 400m. IIRR?

25. IIRR = 23.43%

26. I have invested in Wu Capital with the following cash flows. Year 1: 100m, Year 2: 150m, Year 3: 50m, Year 4: distrib 200m, Year 5: distrib 50m, contribution 50m, Year 6 distrib 100m, Year 7 NAV of 400m. IIRR = 23.43% What is TVPI, DPI, RVPI?

27. I have invested in Wu Capital with the following cash flows. Year 1: 100m, Year 2: 150m, Year 3: 50m, Year 4: distrib 200m, Year 5: distrib 50m, contribution 50m, Year 6 distrib 100m, Year 7 NAV of 400m. IIRR = 23.43% What is TVPI, DPI, RVPI? TVPI = (200+50+100+400)/(100+150+50+50) = 214% DPI = (200+50+100)/(350) = 100% RVPI = 400/350 = 114%

28. I have invested in Wu Capital with the following cash flows. Year 1: 100m, Year 2: 150m, Year 3: 50m, Year 4: distrib 200m, Year 5: distrib 50m, contribution 50m, Year 6 distrib 100m, Year 7 NAV of 400m. IIRR = 23.43%; TVPI = 214%; DPI = 100%; RVPI = 114%. What is the annual return? Arithmetic? Geometric?

29. I have invested in Wu Capital with the following cash flows. Year 1: 100m, Year 2: 150m, Year 3: 50m, Year 4: distrib 200m, Year 5: distrib 50m, contribution 50m, Year 6 distrib 100m, Year 7 NAV of 400m. IIRR = 23.43%; TVPI = 214%; DPI = 100%; RVPI = 114%. What is the annual return? Arithmetic = 214% / 7 = 30.6% Geometric = (1+2.14)^(1/7)-1 = 17.76%

30. What is the excess return above PME return?

31. What is the PME as of the last year assuming a PME return of 3%?

35. Fees

36. Steps Make fee table Commitment fee total Management fee calculate and put in table Find leverage use Calc investment size Put in table Transaction fee in year of purchase Monitoring fee

37. Steps Offset transaction and monitoring fees against management fee and carry forward if needed Calc equity value at end –Calc investment value at end = cost less transaction fee compounded less monitoring fees compounded –Calc debt value at end = debt FV –Equity value = investment value – debt value

38. Steps Calc carry interest –Management fee total allocated by initial investment amount –Carry interest % x (Equity value – initial value - allocated management fee)

39. Blackwood Fund example p.221 450 million committed capital, 2 investments Investment 1 – 200 million, year 3 for 4 years Investment 2 – 250 million, year 4 for 4 years Leverage = 4x equity Debt 5%, investment return 12% Offset 80% of monitoring 100% transaction Management 3%, transaction 1%, monitoring 0.5%, carrying interest 20%

40. The Basil Fund, a leveraged buyout fund, has $100 million in committed capital and will make one major investment during its life. The investment is for $100 million, occurs at the end of year one, and will last two years. The investment will utilize leverage of three times the equity amount and the cost of the debt will be 7%. The return on the investment is 14% per year with cash flows to investors occurring only at the end of the two-year investment. Assume no taxes are incurred on distributions. The Basil Fund uses the following fee structure: Organizational Expense: $1 million (charged at fund inception) Management Fee: 3% (assessed annually based on committed capital) Monitoring Fee: 0.75% (assessed relative to the total purchase price, 80% of the fee offsets management fees) Transaction Fee: 0.5% (assessed relative to the total purchase price, 50% of the fee offsets management fees) Carried Interest: 20% (assessed annually on net-of-fees profits)

41. Part 1) The transaction fee charged by the Basil Fund is closest to: A) $500,000. B) $2,000,000. C) $1,000,000. D) $1,500,000. The correct answer was B) $2,000,000. Transaction fees are charged on the total purchase price. Leverage of three times the equity amount means that the fund used $300 million in debt and $100 million in equity for a total investment of $400 million. $400 million × 0.5% = $2 million.

42. Part 2) The total management fee charged by the Basil Fund, including organizational expenses, after accounting for monitoring and transaction fee offsets is closest to: A) $5.6 million. B) $8.1 million. C) $7.2 million. D) $4.2 million. Your answer: A was incorrect. The correct answer was C) $7.2 million. total management fees = organizational fees + management fees − monitoring fees − transaction fees total management fees = $1 million + ($3 million x 4 years) − ($3 million x 2 years x 80%) − ($2 million x 50%) total management fees = $1 million + $12 million − $4.8 million − $1 million total management fees = $7.2 million

43. Part 3) The IRR of the Basil Fund on a net-of-fee basis is closest to: A) 6.39%. B) 17.96%. C) 20.44%. D) 30.51%. The correct answer was C) 20.44%.

44. The cash flows for the fund are as follows: Year 0: Investors are charged an organization fee of $1 million and a management fee of $3 million (= 3% � $100 million). Net yearly cash flow: −$4 million Year 1: The $100 million investment occurs and a transaction fee of $2 million (= $400 million � 0.5% = $2 million) is incurred. Therefore, a total of $398 is actually invested. Management fees are reduced by 50% of the transaction fee, and therefore total $2 million [= $3 million − ($2 million � 50%)]. Net yearly cash flow: −$102 million Year 2: Monitoring fee of $3 million (=0.75% � $400 million) is incurred. Management fees are reduced by 80% of the monitoring, and therefore total $0.6 million [= $3 million − ($3 million � 80%)]. Net yearly cash flow: −$0.6 million

45. Year 3: Monitoring fee of $3 million (=0.75% � $400 million) is incurred. Management fees again total $0.6 million. Ending investment value = ($398 � 1.142) � (3 + 3 � 1.141) Ending investment value = $517.24 − $3.00 − $3.42= $510.82 Debt value = $300 � 1.072 = $343.47 Equity value = $510.82 − 343.47 = $167.35 Profit less management fees = (167.35 − 100 − 12) = $55.35 Carried interest = 55.35 � 0.20 = $11.07 Net yearly cash flow: $155.68 million IRR: CF0 = −$4 million; CF1 = −$102 million; CF2 = −$0.6 million; CF3 = $155.68 million; IRR = 20.44%