Consider the following two bonds. Bond A returns $1000 (coupon) per year for the first 9 years and $5000 (face value) in the 10th year, and Bond B returns $900 (coupon) per year for the first 19 years and $10000 in the 20th year. Compare the present values of the bonds when the interest rate r is 0.1 and 0.2.

Present value of bond A:

interest rate = 10%

PV of face value = $5,000/1.1¹⁰ = $1,927.72

PV of coupon payments = $1,000 x 5.7590 (PV annuity factor, 10%, 9 periods) = $5,759

present value = $7,686.72

interest rate = 20%

PV of face value = $5,000/1.2¹⁰ = $807.53

PV of coupon payments = $1,000 x 4.0310 (PV annuity factor, 20%, 9 periods) = $4,031

present value = $4,838.53

Present value of bond B:

interest rate = 10%

PV of face value = $10,000/1.2¹⁰ = $1,615.06

PV of coupon payments = $900 x 8.3649 (PV annuity factor, 10%, 19 periods) = $7,528.41

present value = $9,143.47

interest rate = 20%

PV of face value = $10,000/1.2²⁰ = $260.84

PV of coupon payments = $900 x 4.8435 (PV annuity factor, 20%, 19 periods) = $4,359.15

present value = $4,619.99

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