Final answer:
The current price of Sail Fish Corporation's bonds with semi-annual payments of $40, a par value of $1,000, and a required yield to maturity of 8%, would be approximately $940.00, as it is the closest price when rounding to the nearest dollar based on the present value calculations.
Step-by-step explanation:
To determine the current price of the Sail Fish Corporation's bonds that make semi-annual payments of $40 and mature in 4 years with a par value of $1,000, we must discount the cash flows at the investors' required yield to maturity of 8%. The bond pays interest semi-annually, which means there are 8 total payments remaining (2 payments per year for 4 years). The present value of the interest payments and the par value must be calculated separately and then summed to find the total current price.
The present value (PV) of the interest payments is calculated using the formula: 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 total number of periods. Then, the present value of the par value is calculated as PV = F / (1 + r)^n, where F is the future value of the bond (par value).
At an 8% annual rate (or 4% semi-annual), for 8 periods, the present value of the interest payments is:
PVinterest = $40 × [1 - (1 + 0.04)^-8] / 0.04 = $280.92
And the present value of the par value is:
PVpar = $1,000 / (1 + 0.04)^8 = $675.56
The current price of the bond is the sum of PVinterest + PVpar:
Current Price = $280.92 + $675.56 = $956.48
Thus, the bond would be priced closest to $940.00 on the market, taking into account that the bond prices are typically rounded to the nearest dollar.