Learning Outcome Statement
Calculate and interpret alternative investment returns both before and after fees.
On the exam: The question gives invested and committed capital, exit proceeds, fee rates, a hurdle convention, and a holding period, then asks for a gross or net holding-period return, multiple, or fee amount in a calculation or multiple-choice format.
An alternative investment can show a strong exit value, but the investor does not keep all of it. Gross return looks at the deal before fees. Net return follows the cash left after fees, which is what the investor actually earned.
Call the invested capital $P$. It is the capital actually put to work. Committed capital is the amount promised, so it is not the denominator here.
Call the exit proceeds $X$. Call total fees $F$. The comparison below separates profit-based returns from proceeds-based multiples.
| Measure | Numerator | Denominator |
|---|---|---|
| Gross holding-period return | $X-P$ | $P$ |
| Net holding-period return | $(X-F)-P$ | $P$ |
| Gross multiple | $X$ | $P$ |
| Net multiple | $X-F$ | $P$ |
The same invested amount sits in every denominator. A multiple says how many times invested capital comes back.
The gross holding-period return, $R_{\mathrm{gross}}$, measures profit before fees. The net holding-period return, $R_{\mathrm{net}}$, uses cash after $F$. The gross multiple, $M_{\mathrm{gross}}$, compares exit proceeds with $P$. The net multiple, $M_{\mathrm{net}}$, compares cash after fees with $P$.
$$ R_{\mathrm{gross}}=\frac{X-P}{P} \qquad R_{\mathrm{net}}=\frac{(X-F)-P}{P} $$
$$ M_{\mathrm{gross}}=\frac{X}{P} \qquad M_{\mathrm{net}}=\frac{X-F}{P} $$
Subtracting fees lowers the net numerator. A multiple keeps proceeds in the numerator, while a holding-period return subtracts the original capital first. Every denominator remains $P$, and the result is not annualized.
Fees change the cash flow, not the denominator. The annual management fee rate is $m$. The performance fee rate is $f$. The hurdle rate is $h$.
The holding period is $n$ years. The hurdle value is $H$. It is invested capital grown at the hurdle rate for the holding period. The performance fee base is $B$, the positive profit above $H$ under the stated waterfall convention.
Compound $P$ at $h$ for $n$ to set $H$. The fund charges management fees on $P$ each year and a performance fee on $B$ at exit under the stated waterfall.
$$ H=P(1+h)^n $$
$$ B=\max(X-H,0) \qquad F=P\cdot m\cdot n+B\cdot f $$
Compounding raises $H$ as $h$ or $n$ rises. The maximum operation makes $B$ zero when $X$ does not exceed $H$. The first term in $F$ is the management fee and the second is the performance fee. Both terms reduce the investor's net proceeds.
Worked example
You are an investor in an unlevered private equity fund. You are handed invested and committed capital, exit proceeds, fee rates, a hurdle convention, and a holding period. The question asks for gross and net holding-period returns, multiples, and fee amounts. The rate inputs below are decimals.
| Input | Value |
|---|---|
| Capital structure | Unlevered |
| Invested capital, $P$ | USD 10,000,000.00 |
| Committed capital | USD 15,000,000.00 |
| Exit proceeds, $X$ | USD 14,000,000.00 |
| Holding period, $n$ | 3 years |
| Management fee rate, $m$ | 0.02 per year |
| Performance fee rate, $f$ | 0.2 |
| Hurdle rate, $h$ | 0.08 per year |
Use the stated investor perspective. Exit proceeds are gross of fees. The fund charges management fees annually on invested capital and performance fees at exit on positive excess above the compounded hurdle, with no catch-up.
The bars show gross exit proceeds, return of capital, fee deductions, and net profit. Negative bars show amounts removed in the waterfall.
Loading diagram…
Read the bars from left to right as the fund moves from gross exit proceeds to investor profit. Returning capital removes the original USD 10,000,000.00, then the two fee deductions reduce what remains. The final positive amount is net profit, not net proceeds: add the returned capital to that profit to recover net proceeds. The table records each step numerically.
| Stage | Waterfall amount |
|---|---|
| Gross exit | USD 14,000,000.00 |
| Return capital | USD -10,000,000.00 |
| Management fee | USD -600,000.00 |
| Performance fee | USD -280,576.00 |
| Net profit | USD 3,119,424.00 |
- Calculate the hurdle value. Use the table inputs in $H=P(1+h)^n$ because the performance fee starts only above the hurdle. The result is USD 12,597,120.00.
- Calculate gross profit. Subtract invested capital from exit proceeds before any fees. The result is USD 4,000,000.00.
- Calculate gross return and multiple. Divide gross profit by $P$ to get $R_{\mathrm{gross}}=0.400000$. Divide $X$ by $P$ to get the gross multiple, $M_{\mathrm{gross}}=1.400000$.
- Calculate management fees. Multiply $P$ by $m$ and $n$ because the fund charges the annual fee on invested capital. The result is USD 600,000.00.
- Calculate the performance fee base. Subtract $H$ from $X$ because only positive excess clears the hurdle. The result is USD 1,402,880.00.
- Calculate performance fees. Multiply that base by $f$ under the stated exit convention. The result is USD 280,576.00.
- Add both fee amounts to get total fees of USD 880,576.00. Subtract total fees from exit proceeds to get net proceeds of USD 13,119,424.00. The resulting net profit is USD 3,119,424.00.
- Divide net profit by $P$ to get $R_{\mathrm{net}}=0.311942$. Divide net proceeds by $P$ to get $M_{\mathrm{net}}=1.311942$.
Use the net measures for the investor decision because they show cash retained after the stated fees.
Changed condition
Only exit proceeds change. Predict the direction before looking at the after column.
| Measure | Before | After |
|---|---|---|
| Exit proceeds | USD 14,000,000.00 | USD 16,000,000.00 |
| Performance fee | USD 280,576.00 | USD 680,576.00 |
| Net holding-period return | 0.311942 | 0.471942 |
The prediction is a larger performance fee and a higher net return because the hurdle value and management fee stay fixed. The extra proceeds create more excess above the hurdle, and that extra value outweighs the added performance fee.
Before reading on, calculate the after-case total fees.
Common error
You may use committed capital as the return denominator because it is the larger headline figure. The larger denominator makes the return look more conservative, so the choice feels right. The fact pattern separately identifies invested capital, and the fund bases both the return and fees on that invested amount. That exposes the mistake.
Calculator
The calculator's percent entry takes the hurdle rate as a percentage. Make the invested capital a negative cash outflow.
Check yourself
Practice
An unlevered investment has invested capital of USD 10,000,000.00, exit proceeds of USD 14,000,000.00, and total fees of USD 880,576.00. What is the net holding-period return?
Revision snapshot
Gross holding-period return equals $\frac{X-P}{P}$, meaning exit proceeds minus invested capital divided by invested capital. Net return subtracts management and performance fees before dividing by invested capital. Performance fee base is positive profit above the hurdle value, subject to the stated waterfall convention.
Use invested, not merely committed, capital. Label gross or net and levered or unlevered. On the exam, calculate the requested holding-period return, multiple, or fee amount from the stated convention.
Unlock the full lesson and continue reading
Signup to continue reading this lesson and unlimited access questions, flashcards, AI notes, and more