Question1.6 Consider two bonds, A and B. Both bonds presently sell at their par value of $1,000. Bond A will mature in 6 years while bond B will mature in 4 years. If the yields to maturity on the two bonds increase from 7% to 8% Both bonds remain par bonds Both bonds become discount bonds and bond A’s discount will be less than bond B Both bonds become premium bonds and bond A’s premium will be less than bond B Both bonds become premium bonds and bond A’s premium will be greater than bond B Both bonds become discount bonds and bond A’s discount will be greater than bond B ResetMaximum marks: 2.5 Flag question undefinedSingle choice
A
Both bonds remain par bonds
B
Both bonds become discount bonds and bond A’s discount will be less than bond B
C
Both bonds become premium bonds and bond A’s premium will be less than bond B
D
Both bonds become premium bonds and bond A’s premium will be greater than bond B
E
Both bonds become discount bonds and bond A’s discount will be greater than bond B

Question

Question1.6 Consider two bonds, A and B. Both bonds presently sell at their par value of $1,000. Bond A will mature in 6 years while bond B will mature in 4 years. If the yields to maturity on the two bonds increase from 7% to 8% Both bonds remain par bonds Both bonds become discount bonds and bond A’s discount will be less than bond B Both bonds become premium bonds and bond A’s premium will be less than bond B Both bonds become premium bonds and bond A’s premium will be greater than bond B Both bonds become discount bonds and bond A’s discount will be greater than bond B ResetMaximum marks: 2.5 Flag question undefinedSingle choice

A

Both bonds remain par bonds

B

Both bonds become discount bonds and bond A’s discount will be less than bond B

C

Both bonds become premium bonds and bond A’s premium will be less than bond B

D

Both bonds become premium bonds and bond A’s premium will be greater than bond B

E

Both bonds become discount bonds and bond A’s discount will be greater than bond B

BlackTom AI · Accepted Answer

When YTM exceeds the coupon rate, a bond sells below par; the longer the maturity, the more sensitive the price is to a change in yield.

1. Relevant concepts
- A bond priced at par implies its coupon rate equals the YTM (here 7%), so both bonds pay coupons of 7% × $1,000 = $70 annually.
- If YTM rises above the coupon rate (from 7% to 8%), bond prices fall below par (discount bonds).
- Price sensitivity to yield changes increases with maturity (duration/convexity): longer-maturity bonds experience larger price drops for a given change in yield.

2. Step-by-step reasoning
- Confirm coupon = $70 and initial price = $1,000 at YTM = 7% (given).
- Compute new prices at YTM = 8% using P = C × [1 − (1 + r)^−n]/r + F × (1 + r)^−n, where C = 70, F = 1000, r = 0.08, n = maturity in years.

3. Calculations (intermediate steps)
- For bond A (n = 6):
  - (1.08)^6 = 1.586874322944 → (1.08)^−6 = 1/1.586874322944 = 0.630169
  - Annuity factor = (1 − 0.630169)/0.08 = 0.369831/0.08 = 4.6228875
  - PV coupons = 70 × 4.6228875 = 323.6021
  - PV principal = 1000 × 0.630169 = 630.169
  - Price A = 323.6021 + 630.169 = 953.7711 → Discount = 1000 − 953.7711 = $46.23

- For bond B (n = 4):
  - (1.08)^4 = 1.36048896 → (1.08)^−4 = 0.734664
  - Annuity factor = (1 − 0.734664)/0.08 = 0.265336/0.08 = 3.3167
  - PV coupons = 70 × 3.3167 = 232.169
  - PV principal = 1000 × 0.734664 = 734.664
  - Price B = 232.169 + 734.664 = 966.833 → Discount = 1000 − 966.833 = $33.17

4. Why the correct answer is correct
- Since YTM (8%) > coupon rate (7%), both bonds trade at discounts. The longer-maturity bond A loses more value (≈$46.23) than bond B (≈$33.17) because price sensitivity to yield changes is greater for longer maturities.

5. Why other options are incorrect
- “Remain par” is wrong because YTM changed. “Become premium” options are wrong because premium requires YTM < coupon rate. The option stating A’s discount is less than B contradicts the numerical result showing A’s discount is greater.