NISM PracticeNAV, units and returns: the calculations
Six small calculations account for most of the numerical marks in a mutual fund paper. Each takes under a minute once the formula is in your hand.
1. Net asset value per unit
NAV = (Market value of the scheme's assets − Liabilities) ÷ Number of units outstanding
Example. A scheme holds investments and other assets worth ₹105 crore, has liabilities and accrued expenses of ₹5 crore, and has 5 crore units outstanding. NAV = (105 − 5) ÷ 5 = ₹20.
Points to remember: assets are taken at market value, expenses are deducted before the NAV is declared, and the NAV changes every business day as market values change.
2. Units allotted
Units = Amount invested ÷ Applicable NAV
Example. ₹10,000 invested at an applicable NAV of ₹25 gets 10,000 ÷ 25 = 400 units. If statutory charges such as stamp duty apply on purchase, they are deducted from the amount first; use the rate given in the question.
3. Redemption value with exit load
Redemption price = NAV × (1 − Exit load %); Amount = Units × Redemption price
Example. NAV ₹50, exit load 1%, 200 units redeemed. Price = 50 × 0.99 = ₹49.50. Amount = 200 × 49.50 = ₹9,900. The exit load of ₹100 goes back into the scheme.
4. Absolute (simple) return
Absolute return = (End value − Beginning value) ÷ Beginning value × 100
Example. NAV rises from ₹20 to ₹23. Return = 3 ÷ 20 × 100 = 15%. This says nothing about how long it took.
5. Simple annualised return
For periods under a year, a return is sometimes annualised simply: Absolute return × 12 ÷ months (or × 365 ÷ days).
Example. The 15% above was earned in six months. Simple annualised return = 15 × 12 ÷ 6 = 30%. Treat such a figure with care: it assumes the same performance repeats.
6. Compound annual growth rate
CAGR = (End value ÷ Beginning value)^(1 ÷ years) − 1
Example. ₹10,000 becomes ₹14,400 in two years. End ÷ beginning = 1.44. The square root of 1.44 is 1.2. CAGR = 20%.
Check by compounding forward: 10,000 × 1.2 = 12,000; 12,000 × 1.2 = 14,400. Compare with the absolute return of 44% over the two years, and with half of that, 22%: the simple average overstates the true compounded rate.
| ₹100 becomes | In years | CAGR |
|---|---|---|
| ₹121 | 2 | 10% |
| ₹144 | 2 | 20% |
| ₹133.10 | 3 | 10% |
| ₹200 | about 7.2 | 10% |
The last row is the "rule of 72": at r% a year, money doubles in roughly 72 ÷ r years.
7. Rupee cost averaging in an SIP
Average cost per unit = Total amount invested ÷ Total units bought
Example. ₹1,000 a month for three months at NAVs of ₹10, ₹20 and ₹25.
| Month | NAV (₹) | Units bought |
|---|---|---|
| 1 | 10 | 100 |
| 2 | 20 | 50 |
| 3 | 25 | 40 |
Total units = 190 for ₹3,000. Average cost = 3,000 ÷ 190 = ₹15.79. The average of the three NAVs is ₹18.33. Because a fixed amount buys more units when the NAV is low, the average cost is always at or below the average NAV. That is all "rupee cost averaging" means; it does not guarantee a profit.
8. Risk-adjusted return: the Sharpe ratio
Sharpe ratio = (Scheme return − Risk-free return) ÷ Standard deviation of scheme returns
Example. Return 12%, risk-free rate 6%, standard deviation 10%. Sharpe = 6 ÷ 10 = 0.6. Between two schemes of the same category, the higher ratio gave more return per unit of risk.
Traps in the questions
- Absolute or annualised? Read which is asked.
- Exit load reduces what the investor receives; it is applied on the NAV at redemption.
- Dividends (income distribution) reduce the NAV by the amount paid out; total return must add them back.
- Period in months or days: convert consistently.
- CAGR needs the root, not division. A 44% gain over two years is 20% a year, not 22%.
Practise these in the Mutual Fund Distributors question set. All formulas are on the formula sheet.
Questions candidates ask
How is NAV calculated?
NAV per unit = (market value of the scheme's assets minus its liabilities) divided by the number of units outstanding.
What is the difference between absolute return and CAGR?
Absolute return is the total percentage gain over the whole period. CAGR is the yearly compounded rate that would produce that gain.
What does rupee cost averaging mean?
Investing a fixed amount regularly buys more units when prices are low and fewer when high, so the average cost per unit is at or below the average NAV.
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