2.3 Quantitative Foundations

Question 1

What’s the difference between Discrete and Continuous compounding?

Answer 1

Discretely compounded interest is calculated and added to the principal at specific intervals (e.g., annually, monthly, or weekly). Simple interest is discrete.
Continuous compounding uses a natural log-based formula to calculate and add back accrued interest at the smallest possible intervals.

Question 2

What’s the difference between simple and compound interest?

Answer 2

Simple interest is an interest rate computation approach that does not incorporate compounding.

Question 3

What is Logarithmic Return used for?

Answer 3

Continuous Compounding

Question 4

What is Return Computation Interval?

Answer 4

Smallest time interval for which returns are calculated, such as daily, monthly, or even annually

Question 5

Internal rate of return (IRR)

Answer 5

Discount rate that equates the present value of the costs (cash outflows) with the present value of the benefits (cash inflows)

Discount rate that makes the net present value (NPV) of an investment equal to zero.

Question 6

Interim IRR

Answer 6

IRR based on cash flows prior to the investment’s termination

Question 7

Since-inception IRR

Answer 7

Interim IRR that starts with the underlying investment’s initial cash flow (inception date).

Question 8

Lifetime IRR

Answer 8

All of the cash flows, realized or anticipated, occurring over the investment’s entire life, from its beginning to its termination.

Question 9

What are scale differences when it comes to IRR?

Answer 9

Scale differences are when investments have unequal sizes and/or timing of their cash flows.

Question 10

What are the limitations of IRR?

Answer 10

1. IRR cannot be used for complex cash flows: Borrowing or multiple signs.
2. Scale differences can be misleading
3. IRRs should not be averaged

Question 11

What is Modified IRR?

Answer 11

• DISCOUNTS all project cash OUTFLOWS into a PRESENT VALUE using a FINANCING rate
• COMPOUNDS all cash INFLOWS into a FUTURE VALUE using an assumed REVINVESTMENT rate

= Discount rate that sets the absolute values of that future value and that present value equal to each other

Question 12

Difference between IRR and MIRR

Answer 12

1. MIRR uses different discount rate for different types of cash flows
2. Incorporates cost of capital rate
3. Will always return a single result regardless of the sequence and direction of cash flows
4. MIRR considered way more accurate

Question 13

Disadvantage of MIRR

Answer 13

MIRR is driven by user-selected rates (RR and CC) that conceptually are unrelated to the project.

Question 14

Three ratios as Performance Measures

Answer 14

1. Distribution to Paid-In ratio (DPI): Distribution / Capital Drawn
2. Residual Value to Paid-in ratio (RVPI): NAV change ignoring distribution / Capital Drawn
3. Total Value to Paid-in ratio (TVPI): (Distribution + NAV Change) / Capital Drawn

*Note these do not take into consideration time value of money

Question 15

Public Market Equivalent

Answer 15

Publicly traded index that has similar exposure, finds the premium for private over public index. Private return calucalated using capital call, distribution and terminal value.

Question 16

J Curve

Answer 16

• Plots IRR on vertical axis and Time on horizontal axis
• Combination of early expense recognition, early loss recognition, and deferred gain recognition.

Question 17

What is a waterfall with regards to distribution?

Answer 17

Provision of the limited partnership agreement that specifies how distributions from a fund will be split and how the payouts will be prioritized. Specifically, the waterfall details what amount must be distributed to the LPs before the fund manager or GPs can take a share from the fund’s profits.

Question 18

Hard hurdle rate

Answer 18

Limits incentives to profits in excess of hurdle rate

1. Capital is returned to the LP until their investment has been repaid.
2. Profits are distributed only to the LP until the hurdle rate is reached.
3. Additional profits are split such that the fund manager receives an incentive fee only on the profits in excess of the hurdle rate.

Question 19

Soft hurdle rate

Answer 19

Earn an incentive fee on all profits, given that the hurdle rate has been achieved

1. Capital is returned to the LP until their investment has been repaid.
2. Profits are distributed only to the LP until the hurdle rate is reached.
3. Additional profits are split, with a high proportion going to the fund manager until the fund manager receives an incentive fee on all of the profits.

Question 20

Catch-up Provision

Answer 20

Permits manager to receive a large share of profits once the hurdle rate of return has been achieved and passed.

Catch-up rate: percentage of the profits used to catch up TO the incentive fee once the hurdle is met. Incentive of TOTAL PROFIT remains to be the ceiling.

Question 21

Is an IRR a dollar-weighted return or a time-weighted return?

Answer 21

Dollar

Question 22

What is the primary cause of the shape of the J-curve of interim private equity fund returns?

Answer 22

It is caused by a combination of early expense recognition, early loss recognition, and deferred gain recognition.

Question 23

An investment has two solutions for its IRR. What can be said about the investment and the usefulness of the two solutions?

Answer 23

two sign changes in the cash flow stream of the investment. None of the IRRs should be used.

Question 24

In which scenario will a clawback clause lead to payments?

Answer 24

A clawback clause, clawback provision or clawback option is designed to return incentive fees to LPs when early profits are followed by subsequent losses.

Question 25

Two investments are being compared to ascertain which investment would add the most value to a portfolio. Both investments have simplified cash flow patterns of an initial cost followed by positive cash flows. Why might the IRRs of the investment provide an unreliable indication of which investment adds more value?

Answer 25

The major challenge with comparing IRRs across investments is when investments have scale differences. Scale differences are when investments have unequal sizes and/or timing of their cash flows.

Question 26

An analyst computes the IRR of one alternative to be 20% and another to be 30%. When the analyst combines the cash flows of the two alternatives into a single investment, must the IRR of the combination be greater than 20% and less than 30%?

Answer 26

No. IRR of a portfolio of two investments is not generally equal to a value-weighted average of the IRRs of the constituent investments. If the cash flows from two investments are combined to form a portfolio, the IRR of the portfolio can vary substantially from an average of the IRRs of the two investments.