The Ness Company sells $5,000,000 of five-year,10% bonds at the start of the year.The bonds have an effective yield of 9%.Present value factors are below: $$\begin{array}{lcc}& \underline{10\%}& \underline{9\%}\\ \text{ PV \$1 factor 1 year }& 0.90909& 0.91743\\ \text{ PV \$1 factor 2 years }& 0.82645& 0.84168\\ \text{ PV \$1 factor 3 years }& 0.75131& 0.77218\\ \text{ PV \$1 factor 4 years }& 0.68301& 0.70843\\ \text{ PV \$1 factor 5 years }& 0.62092& 0.64993\end{array}$$
The bonds will sell for

A) $4,805,525.
B) $5,000,000.
C) $5,050,000.
D) $5,194,475.

To determine the selling price of the bonds, we calculate the present value of the bond's cash flows (interest payments and principal repayment) using the effective yield rate of 9% as the discount rate. The bond pays annual interest of 10% on the face value of $5,000,000, which equals $500,000 per year for 5 years, and repays the principal of $5,000,000 at the end of year 5.The present value of the interest payments (an annuity) is calculated using the present value of an annuity formula, which in this case involves summing the present value factors for the 9% column for years 1 through 5 and multiplying by the annual interest payment: PV_{interest} = $500,000 \times (0.91743 + 0.84168 + 0.77218 + 0.70843 + 0.64993) = $500,000 \times 3.88965 = $1,944,825 The present value of the principal repayment is calculated by multiplying the face value by the present value factor for a single sum for year 5 at 9%: PV_{principal} = $5,000,000 \times 0.64993 = $3,249,650 Adding these two present values together gives the selling price of the bonds: Selling\ Price = PV_{interest} + PV_{principal} = $1,944,825 + $3,249,650 = $5,194,475