Returns when the client adds money midway
Series XXI-B case study · set 2, case 2 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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A client account starts a year with ₹100 lakh. Immediately before a contribution at the exact midpoint of the year, its value is ₹120 lakh. The client then adds ₹80 lakh, so the account has ₹200 lakh immediately after the contribution. At year-end it is worth ₹180 lakh. There are no other cash flows, fees or taxes. For time-weighted return, calculate each half-year’s investment return excluding the contribution and link the two growth factors. For annual money-weighted return r, use the cash-flow equation 100(1+r) + 80(1+r)^0.5 = 180. The manager must explain why the client’s rupee experience and the linked investment return can differ.
All amounts and contract terms in this case are hypothetical.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A client account starts a year with ₹100 lakh. Immediately before a contribution at the exact midpoint of the year, its value is ₹120 lakh. The client then adds ₹80 lakh, so the account has ₹200 lakh immediately after the contribution. At year-end it is worth ₹180 lakh. There are no other cash flows, fees or taxes. For time-weighted return, calculate each half-year’s investment return excluding the contribution and link the two growth factors. For annual money-weighted return r, use the cash-flow equation 100(1+r) + 80(1+r)^0.5 = 180. The manager must explain why the client’s rupee experience and the linked investment return can differ.
All amounts and contract terms in this case are hypothetical.
Q1What is the first half-year investment return?
Option A. 100%
Why it is wrong: This uses the post-contribution account value.
Option B. 10%
Why it is wrong: This divides the half-year return by two unnecessarily.
Option C. 20% — Correct answer
Option D. 80%
Why it is wrong: This confuses the later contribution with investment growth.
Answer: C. (₹120 lakh/₹100 lakh − 1) × 100 = 20%. Remember: Value a subperiod before the external cash flow at its boundary.
Hint, shown before you answer in practice mode: Use the value immediately before the contribution.
XXIB-S2-C02-Q1easynumerical
Q2What is the second half-year investment return?
Option A. −10% — Correct answer
Option B. 50%
Why it is wrong: This compares year-end wealth with the pre-contribution value.
Option C. 80%
Why it is wrong: This treats the contribution as return.
Option D. −20%
Why it is wrong: This divides by the original opening value instead of ₹200 lakh.
Answer: A. (₹180 lakh/₹200 lakh − 1) × 100 = −10%. Remember: Use the post-flow value as the next subperiod’s opening base.
Hint, shown before you answer in practice mode: The second subperiod begins with ₹200 lakh after contribution.
XXIB-S2-C02-Q2easynumerical
Q3What is the full-year time-weighted return?
Option A. 10%
Why it is wrong: This adds 20% and −10% without compounding.
Option B. 8% — Correct answer
Option C. 80%
Why it is wrong: This treats external money as investment growth.
Option D. 5%
Why it is wrong: This is the simple average of the half-year rates.
Answer: B. (1.20 × 0.90 − 1) × 100 = 8%. Remember: Link subperiod returns geometrically.
Hint, shown before you answer in practice mode: Link 1.20 and 0.90.
XXIB-S2-C02-Q3mediumnumerical
Q4What is the account’s total rupee investment profit over the year?
Option A. ₹80 lakh
Why it is wrong: This counts the client’s contribution as profit.
Option B. ₹0 — Correct answer
Option C. −₹20 lakh
Why it is wrong: This ignores first-half growth.
Option D. ₹8 lakh
Why it is wrong: This applies the time-weighted return to opening assets despite the cash flow.
Answer: B. Closing wealth ₹180 lakh − opening capital ₹100 lakh − contribution ₹80 lakh = ₹0. Remember: External contributions are not investment gains.
Hint, shown before you answer in practice mode: Subtract all client capital from closing wealth.
XXIB-S2-C02-Q4mediumnumerical
Q5What annual money-weighted return solves the supplied cash-flow equation?
Option A. −10%
Why it is wrong: This is only the second-half return.
Option B. 8%
Why it is wrong: This is the time-weighted return, not the cash-flow IRR.
Option C. 20%
Why it is wrong: This is only the first-half return.
Option D. 0% — Correct answer
Answer: D. At r = 0, 100(1+0) + 80(1+0)^0.5 = 180. More money was exposed to the losing half-year, so the client’s money-weighted result differs from the linked 8%. Remember: Money-weighted return reflects the size and timing of external cash flows.
Hint, shown before you answer in practice mode: Test the rate at which both invested sums grow into ₹180 lakh.
XXIB-S2-C02-Q5hardnumerical
Explaining active return by allocation and selection
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