Two purchases at different mutual fund NAVs
Series X-A case study · set 3, case 4 of 9 · 5 questions · 1 mark each
Question 1 of 5Case practice
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Rhea invests ₹5,000 in a fund at NAV ₹50 on the first date and another ₹5,000 at NAV ₹25 on the second date. She receives all units without entry deductions. After the second purchase, the NAV is ₹40 and she checks her combined holding. There are no distributions, taxes or exit charges. The dates are deliberately not specified closely enough to calculate an annualised money-weighted return. Rhea wants to distinguish total cost, units, average cost per unit and the simple gain on contributed money. She should not assume that purchasing regularly guarantees a profit in every market outcome.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
Rhea invests ₹5,000 in a fund at NAV ₹50 on the first date and another ₹5,000 at NAV ₹25 on the second date. She receives all units without entry deductions. After the second purchase, the NAV is ₹40 and she checks her combined holding. There are no distributions, taxes or exit charges. The dates are deliberately not specified closely enough to calculate an annualised money-weighted return. Rhea wants to distinguish total cost, units, average cost per unit and the simple gain on contributed money. She should not assume that purchasing regularly guarantees a profit in every market outcome.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1How many units are bought with the first ₹5,000?
Option A. 125 units
Why it is wrong: This uses the later measurement NAV.
Option B. 100 units — Correct answer
Option C. 200 units
Why it is wrong: This uses the second purchase NAV.
Option D. 50 units
Why it is wrong: This divides by an incorrect NAV.
Answer: B. ₹5,000 ÷ ₹50 = 100 units. Remember: Each purchase creates units at its own applicable NAV.
Hint, shown before you answer in practice mode: Use ₹50 for the first purchase.
XA-S3-C04-Q1easynumerical
Q2How many units are held after both purchases?
Option A. 400 units
Why it is wrong: This uses the lower NAV for both purchases.
Option B. 300 units — Correct answer
Option C. 250 units
Why it is wrong: This uses the final NAV for both purchases.
Option D. 200 units
Why it is wrong: This ignores the first purchase or averages incorrectly.
Answer: B. First purchase: 100 units. Second: ₹5,000/₹25 = 200 units. Total = 300. Remember: Unequal NAVs mean equal contributions buy unequal unit quantities.
Hint, shown before you answer in practice mode: Add units, not NAVs.
XA-S3-C04-Q2mediumnumerical
Q3What is the average cost per unit, rounded to two decimals?
Option A. ₹37.50
Why it is wrong: This is the unweighted average of the two NAVs.
Option B. ₹33.33 — Correct answer
Option C. ₹40.00
Why it is wrong: This is the measurement NAV.
Option D. ₹25.00
Why it is wrong: This ignores the higher-cost first purchase.
Answer: B. ₹10,000 ÷ 300 = ₹33.33 per unit. Remember: Average unit cost is quantity-weighted through total cost divided by total units.
Hint, shown before you answer in practice mode: Divide total contributed money by total units.
XA-S3-C04-Q3mediumnumerical
Q4At NAV ₹40, what is the simple total gain as a percentage of contributed money?
Option A. 20% — Correct answer
Option B. 6.67%
Why it is wrong: This compares ₹40 with the arithmetic-average NAV.
Option C. 60%
Why it is wrong: This measures only the second purchase’s return.
Option D. −20%
Why it is wrong: This measures only the first purchase’s price movement.
Answer: A. 300 × ₹40 = ₹12,000. Gain = ₹2,000 on ₹10,000, or 20%. This is not annualised IRR. Remember: A simple gain on contributions is different from a timing-adjusted annual return.
Hint, shown before you answer in practice mode: Value all units at ₹40 and compare with total contributions.
XA-S3-C04-Q4mediumnumerical
Q5What can be concluded if the NAV later falls below ₹33.33, with nothing else changing?
Option A. The original purchase prices cease to matter for cost.
Why it is wrong: Historical contributions still determine total cost.
Option B. The holding would be worth less than its ₹10,000 total cost. — Correct answer
Option C. Regular purchases guarantee that it remains profitable.
Why it is wrong: Regular investing does not guarantee a gain.
Option D. The number of units automatically doubles.
Why it is wrong: NAV movements alone do not create new units.
Answer: B. With 300 units and a cost near ₹33.33 per unit, a lower NAV gives a value below the ₹10,000 invested. Remember: Rupee-cost averaging changes purchase patterns, not the possibility of loss.
Hint, shown before you answer in practice mode: Compare market NAV with the holding’s average cost per unit.
XA-S3-C04-Q5mediumapplication
An AIF commitment is larger than cash already called
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