Choosing between money today and staged payments
Series X-A case study · set 3, case 2 of 9 · 5 questions · 1 mark each
Question 1 of 5Case practice
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Asha can choose either ₹1,00,000 today or two certain receipts of ₹60,000, one at the end of year 1 and one at the end of year 2. Her comparison rate is 10% annually with annual compounding. There are no fees, taxes, default risk or other cash flows. If she receives money before the end of year 2, assume she can reinvest it at the same rate. The choice is mutually exclusive. Asha wants to compare the alternatives both in today’s rupees and at the end of year 2, using consistent dates rather than simply adding future amounts.
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.
Asha can choose either ₹1,00,000 today or two certain receipts of ₹60,000, one at the end of year 1 and one at the end of year 2. Her comparison rate is 10% annually with annual compounding. There are no fees, taxes, default risk or other cash flows. If she receives money before the end of year 2, assume she can reinvest it at the same rate. The choice is mutually exclusive. Asha wants to compare the alternatives both in today’s rupees and at the end of year 2, using consistent dates rather than simply adding future amounts.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What is the present value of the first ₹60,000 receipt?
Option A. ₹60,000
Why it is wrong: This does not discount the payment.
Option B. ₹54,545.45 — Correct answer
Option C. ₹66,000
Why it is wrong: This grows a future payment instead of discounting it.
Option D. ₹49,586.78
Why it is wrong: This discounts for two years instead of one.
Answer: B. ₹60,000 ÷ 1.10 = ₹54,545.45. Remember: Cash flows must be placed on a common valuation date.
Hint, shown before you answer in practice mode: The first receipt is one year away.
XA-S3-C02-Q1easynumerical
Q2What is the present value of both future receipts together?
Option A. ₹1,20,000
Why it is wrong: This adds future cash flows without discounting.
Option B. ₹99,173.55
Why it is wrong: This discounts both payments for two years.
Option C. ₹1,09,090.91
Why it is wrong: This discounts both payments for one year.
Option D. ₹1,04,132.23 — Correct answer
Answer: D. ₹60,000/1.10 + ₹60,000/1.10² = ₹1,04,132.23. Remember: Different payment dates require different discount factors.
Hint, shown before you answer in practice mode: Discount each payment for its own waiting period.
XA-S3-C02-Q2mediumnumerical
Q3At the 10% comparison rate, by how much is the staged-payment option more valuable today?
Option A. ₹4,132.23 — Correct answer
Option B. ₹0
Why it is wrong: The two present values are not equal.
Option C. ₹20,000
Why it is wrong: This compares undiscounted future receipts with today’s cash.
Option D. ₹9,090.91
Why it is wrong: This uses only a one-year discount for both payments.
Answer: A. ₹1,04,132.23 − ₹1,00,000 = ₹4,132.23. Remember: An offer’s advantage can be measured as a present-value difference.
Hint, shown before you answer in practice mode: Subtract the immediate offer from the future option’s present value.
XA-S3-C02-Q3mediumnumerical
Q4What is the end-of-year-2 value of taking the staged payments and reinvesting the first receipt?
Option A. ₹1,32,000
Why it is wrong: This gives both receipts a year of reinvestment.
Option B. ₹1,20,000
Why it is wrong: This ignores interest on the first receipt.
Option C. ₹1,21,000
Why it is wrong: This is the end value of ₹1,00,000 invested today.
Option D. ₹1,26,000 — Correct answer
Answer: D. ₹60,000 × 1.10 + ₹60,000 = ₹1,26,000. Remember: A future-value comparison should honour each payment’s actual reinvestment period.
Hint, shown before you answer in practice mode: The year-1 receipt grows once. The year-2 receipt arrives at the comparison date.
XA-S3-C02-Q4mediumnumerical
Q5What would happen to the present value of the staged payments if the comparison rate increased while amounts and dates stayed fixed?
Option A. It would fall, making the immediate payment relatively more attractive. — Correct answer
Option B. The future payment dates would move earlier.
Why it is wrong: The dates are fixed by the case.
Option C. It would rise because future money is discounted more.
Why it is wrong: A larger discount factor lowers present value.
Option D. It would remain unchanged because payments are certain.
Why it is wrong: Even certain payments have a time value.
Answer: A. The two fixed future receipts are discounted more heavily at a higher rate. Their current value falls relative to the unchanged ₹1,00,000 available today. Remember: Certainty of payment does not remove the opportunity cost of waiting.
Hint, shown before you answer in practice mode: A higher required return increases the divisor in present-value formulas.
XA-S3-C02-Q5mediumapplication
A high current yield with credit and liquidity risk
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