A bond below face value
Series X-A case study · set 1, case 5 of 9 · 5 questions · 1 mark each
Question 1 of 5Case practice
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Dev considers a bond with face value ₹1,000, annual coupon rate 8% and current market price ₹950. Coupons are paid annually. For a separate one-year valuation check, assume exactly one coupon and the ₹1,000 principal remain, both payable in one year, with no default. The required annual return for that check is 10%. A longer-duration bond in the same discussion has modified duration 4. Use the first-order duration approximation for a 0.50 percentage-point yield increase, ignoring convexity and credit-spread changes. Dev should keep the current-yield, discounted-value and duration calculations separate.
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.
Dev considers a bond with face value ₹1,000, annual coupon rate 8% and current market price ₹950. Coupons are paid annually. For a separate one-year valuation check, assume exactly one coupon and the ₹1,000 principal remain, both payable in one year, with no default. The required annual return for that check is 10%. A longer-duration bond in the same discussion has modified duration 4. Use the first-order duration approximation for a 0.50 percentage-point yield increase, ignoring convexity and credit-spread changes. Dev should keep the current-yield, discounted-value and duration calculations separate.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What annual coupon does the ₹1,000 bond pay?
Option A. ₹76
Why it is wrong: This applies the coupon rate to market price.
Option B. ₹95
Why it is wrong: This applies a 10% rate to market price.
Option C. ₹100
Why it is wrong: This confuses required return with coupon rate.
Option D. ₹80 — Correct answer
Answer: D. ₹1,000 × 8% = ₹80 each year. Remember: Coupon rate and market yield use different bases.
Hint, shown before you answer in practice mode: Coupon interest is based on face value.
XA-S1-C05-Q1easynumerical
Q2What is the current yield at a ₹950 price, rounded to two decimals?
Option A. 8.00%
Why it is wrong: This is the coupon rate on face value.
Option B. 8.42% — Correct answer
Option C. 10.00%
Why it is wrong: This is the required return for the separate valuation check.
Option D. 5.26%
Why it is wrong: This measures the discount to face value as a fraction of price.
Answer: B. ₹80 ÷ ₹950 × 100 = 8.42%. This measure does not include the gain or loss at redemption. Remember: Current yield is an income yield, not a complete maturity return.
Hint, shown before you answer in practice mode: Current yield uses annual coupon divided by current price.
XA-S1-C05-Q2mediumnumerical
Q3What is the one-year bond’s value at the specified 10% required return?
Option A. ₹1,080.00
Why it is wrong: This is next year’s cash flow before discounting.
Option B. ₹950.00
Why it is wrong: The quoted market price is not automatically the discounted value.
Option C. ₹981.82 — Correct answer
Option D. ₹900.00
Why it is wrong: This subtracts 10% from face value and omits the coupon.
Answer: C. (₹1,000 + ₹80) ÷ 1.10 = ₹981.82. Remember: Bond value is the present value of its expected cash flows.
Hint, shown before you answer in practice mode: Discount the combined coupon and principal for one year.
XA-S1-C05-Q3mediumnumerical
Q4Using modified duration 4, what is the approximate price change for the stated yield increase?
Option A. A fall of 0.125%
Why it is wrong: This divides the yield change by duration.
Option B. A fall of 2% — Correct answer
Option C. A fall of 20%
Why it is wrong: This misreads 0.50 percentage point as 5 percentage points.
Option D. A rise of 2%
Why it is wrong: Bond price and yield move in opposite directions in this approximation.
Answer: B. Approximate percentage change = −4 × 0.005 × 100 = −2%. Remember: Duration is a local estimate of interest-rate sensitivity.
Hint, shown before you answer in practice mode: Multiply modified duration by the yield change in decimal form, with a minus sign.
XA-S1-C05-Q4mediumnumerical
Q5If Dev must sell before maturity and market yields rise, which risk is directly illustrated?
Option A. The face value must immediately change.
Why it is wrong: Market yields do not mechanically rewrite contractual face value.
Option B. A government guarantee is created.
Why it is wrong: The case provides no such guarantee.
Option C. The annual coupon must automatically increase.
Why it is wrong: The coupon is fixed in the case.
Option D. The selling price may fall even though the promised coupon is unchanged. — Correct answer
Answer: D. A fixed coupon does not lock in a resale price. Rising required yields generally reduce the value buyers will pay for fixed future cash flows. Remember: Holding a fixed coupon does not remove market-price risk.
Hint, shown before you answer in practice mode: Separate contractual payments from the price available in the market.
XA-S1-C05-Q5mediumapplication
Mutual fund units and a disclosed exit load
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