Pricing a two-year bond
Series XXI-B case study · set 1, case 4 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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A manager considers purchasing an ordinary fixed-rate bond with face value ₹1,000, annual coupon rate 8%, and exactly two years remaining to maturity. The next coupons arrive one and two years from today, and the principal is repaid with the second coupon. The required yield is 10% a year, compounded annually. There is no accrued interest, default, call option or transaction cost. For a separate small-yield-change estimate, the manager supplies a modified duration of 1.75 and instructs the analyst to ignore convexity. The analyst must distinguish coupon rate, current yield and required yield, and must report a first-order estimate as an approximation rather than an exact future price.
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 manager considers purchasing an ordinary fixed-rate bond with face value ₹1,000, annual coupon rate 8%, and exactly two years remaining to maturity. The next coupons arrive one and two years from today, and the principal is repaid with the second coupon. The required yield is 10% a year, compounded annually. There is no accrued interest, default, call option or transaction cost. For a separate small-yield-change estimate, the manager supplies a modified duration of 1.75 and instructs the analyst to ignore convexity. The analyst must distinguish coupon rate, current yield and required yield, and must report a first-order estimate as an approximation rather than an exact future price.
All amounts and contract terms in this case are hypothetical.
Q1What annual coupon cash flow does this bond pay?
Option A. ₹100
Why it is wrong: This uses the required yield as the coupon rate.
Option B. ₹80 — Correct answer
Option C. ₹160
Why it is wrong: This adds both future coupons.
Option D. ₹8
Why it is wrong: This applies the percentage incorrectly.
Answer: B. ₹1,000 × 8% = ₹80 each year. Remember: Coupon cash flows come from the contract, not the required market yield.
Hint, shown before you answer in practice mode: Apply the coupon rate to face value.
XXIB-S1-C04-Q1easynumerical
Q2What is the bond’s present price at the stated required yield?
Option A. ₹1,160
Why it is wrong: This adds future cash without discounting.
Option B. ₹1,000
Why it is wrong: This would be par, but coupon and required yield differ.
Option C. About ₹965.29 — Correct answer
Option D. ₹892.56
Why it is wrong: This omits the first coupon.
Answer: C. Price = 80/1.10 + 1,080/1.10² = ₹965.2893, or ₹965.29. Remember: A bond price is the present value of all promised cash flows under the assumed yield.
Hint, shown before you answer in practice mode: Discount ₹80 for one year and ₹1,080 for two years.
XXIB-S1-C04-Q2mediumnumerical
Q3What is the approximate current yield at that price?
Option A. 8.29% — Correct answer
Option B. 16.58%
Why it is wrong: This uses both coupons in a one-year income ratio.
Option C. 8.00%
Why it is wrong: This is the coupon rate on face value.
Option D. 10.00%
Why it is wrong: This is the required yield to maturity, not coupon divided by price.
Answer: A. ₹80 / ₹965.2893 × 100 = about 8.29%. It excludes the price change toward maturity. Remember: Current yield and yield to maturity measure different things.
Hint, shown before you answer in practice mode: Current yield uses one annual coupon divided by current price.
XXIB-S1-C04-Q3mediumnumerical
Q4For a 0.50-percentage-point rise in yield, what percentage price change does the duration approximation give?
Option A. About −1.75%
Why it is wrong: This corresponds to a one-percentage-point change.
Option B. About −0.875% — Correct answer
Option C. About −87.5%
Why it is wrong: This uses 0.50 rather than 0.005 for the yield change.
Option D. About +0.875%
Why it is wrong: Price and yield changes have opposite signs in this approximation.
Answer: B. Approximate proportional change = −1.75 × 0.005 = −0.00875, or −0.875%. Remember: Convert percentage-point yield changes to decimals before applying duration.
Hint, shown before you answer in practice mode: Use minus modified duration times the yield change expressed as a decimal.
XXIB-S1-C04-Q4mediumnumerical
Q5What is the approximate rupee price fall for that yield rise?
Option A. ₹8.45 — Correct answer
Option B. ₹80
Why it is wrong: This is the coupon, not the duration-based price change.
Option C. ₹0.875
Why it is wrong: This confuses a percentage with a rupee amount.
Option D. ₹16.89
Why it is wrong: This uses twice the stated yield move.
Answer: A. ₹965.2893 × 0.00875 = about ₹8.4463, or ₹8.45. This is a duration estimate, not exact repricing. Remember: Label approximations and their units clearly.
Hint, shown before you answer in practice mode: Multiply current price by the magnitude of the estimated percentage change.
XXIB-S1-C04-Q5hardnumerical
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