Practice Question
Adobe Inc. issues bonds with a $1,000 face value and a 20-year maturity. The bond makes semi-annual coupon payments of $30 each until the end of year 10. After that, the bond makes semi-annual coupon payments of $40 each until maturity. However, due to cash restraints, the firm makes no coupon payments on the bond in year one, and instead pays these coupons at maturity. If investors require an 8% rate of return over the life of the bond, what is the bond’s value today?
Step 1: Identify Cash Flows
- Face Value \( F = 1{,}000 \)
- Coupon payments:
- Years 3–10: \( 30 \) semi-annually (8 payments)
- Years 11–20: \( 40 \) semi-annually (20 payments)
- Deferred coupon payments from Year 1 and 2 are paid at maturity
- Total periods = 40 (20 years × 2)
- Rate per period = 4% (8% annually ÷ 2)
Step 2: Present Value of Years 3–10 Coupon Payments
\[ PV_{3-10} = 30 \times \left( \frac{1 - (1 + 0.04)^{-8}}{0.04} \right) \times (1 + 0.04)^{-2} \]
Step 3: Present Value of Years 11–20 Coupon Payments
\[ PV_{11-20} = 40 \times \left( \frac{1 - (1 + 0.04)^{-20}}{0.04} \right) \times (1 + 0.04)^{-10} \]
Step 4: Present Value of Face Value and Deferred Coupons
\[ PV_{maturity} = \frac{1{,}000 + 60}{(1 + 0.04)^{40}} = \frac{1{,}060}{(1.04)^{40}} \]
Step 5: Add All Present Values
Total bond value ≈ $820.01
Conclusion:
The value of Adobe Inc.'s bond today is approximately $820.01, taking into account deferred coupons, stepped payments, and time value of money.