Final answer:
The bonds issued by Smartglass Inc., with a lower coupon rate compared to the current yield to maturity, would sell at a discount to provide a competitive yield to investors.
Step-by-step explanation:
Smartglass Inc.'s bonds with a par value of $1,000 and an annual coupon rate of 4.5% should sell at a price that discounts the future coupon payments and the lump-sum principal repayment back to their present value at the current yield to maturity of 6.2%. To calculate this price, we would use the present value formula for an annuity to discount the annual coupon payments and the present value formula for a lump sum to discount the principal repayment. Since the bond's coupon rate is lower than the current yield to maturity, the bond will sell at a discount, meaning less than its face value.
The calculation is based on the understanding that when interest rates rise, existing bonds with lower interest payments become less attractive, and therefore, they must be sold at a discount to compete with new bonds that offer higher yields. This is because investors will always seek the best available return. Hence, if they can get a higher interest elsewhere, the bond price must adjust to deliver a comparable yield. This adjustment translates to a lower selling price.