Final answer:
The current value of SJU Corp's 15-year bond can be calculated by discounting the future cash flows (coupon payments and face value) at the current market interest rate. Using the present value of an annuity formula for the coupon payments and the present value of a lump sum for the face value, we can determine its current price. One year ago, the market interest rate likely equaled the bond's coupon rate of 8% if it was issued at par value.
Step-by-step explanation:
To calculate the current value of SJU Corp's 15-year bond with semi-annual coupon payments, we need to find the present value of the future cash flows, discounted at the market interest rate of 7%. The bond pays an 8% annual coupon rate, which means semi-annual payments of $40 ($1,000 x 0.08 ÷ 2 = $40) over the remaining 14 years, plus the face value of $1,000 at maturity.
To find the present value, we use the formula for the present value of an annuity for the coupon payments and the present value of a lump sum for the face value.
The present value of an annuity formula is PV = PMT [(1 - (1 + r)-n) ÷ r], where PMT is the payment per period, r is the discount rate per period, and n is the number of periods. We have 28 periods left (14 years × 2), and the semi-annual discount rate is 3.5% (7% annual rate ÷ 2).
The present value of the coupon payments is then:
PVcoupons = $40 [(1 - (1 + 0.035)-28) ÷ 0.035]
The present value of the face value is the lump sum discounted for 28 periods at the semi-annual rate: PVface value = $1,000 × (1 + 0.035)-28
The bond's current value is the sum of the present value of the coupon payments and the present value of the face value.
Regarding the market interest rate one year ago, if we assume the bond was issued at par value ($1,000), the market interest rate would have matched the coupon rate of the bond, which is 8%.