Final answer:
The bonds will sell at a price determined by the present value of the semiannual interest payments and the face value to be repaid at maturity, discounted at the market yield rate of 4% (2% semiannually) over 40 periods (20 years). The semiannual interest payment is $2.5 million, and the present value of payments and face value will provide the selling price.
Step-by-step explanation:
The price at which the bonds sell can be determined by calculating the present value of the bond's cash flows, which include the semiannual interest payments and the face value that is repaid at maturity. The semiannual interest payment, or coupon payment, will be the face amount times the coupon rate divided by two (since interest is paid semiannually). Therefore, the bond will pay 5% of $100 million divided by two, which equals $2.5 million every six months.
To find the present value of these cash flows, we will use the market yield of 4% (since the market yield for bonds of similar risk and maturity is 4%). Because the payments are semiannual, we will use 2% (the 4% annual yield divided by 2) as the discount rate. Lastly, since the bond's term is 20 years, there will be 40 semiannual periods.
The present value of an annuity (the interest payments) can be 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 number of periods.
The present value of a lump sum (the face value repayment at maturity) can be calculated using the formula: PV = FV / (1 + r)^n where FV is the face value and other variables are as previously defined.
By summing the present value of the annuity and the present value of the lump sum, we can ascertain the price at which the bond would sell in the market.