Final answer:
On January 2, 2013, E-Tech Initiatives Limited would report the $530,000, 10-year, 4 percent bonds as a long-term liability of $519,400 on their balance sheet if issued at 98. The present value calculations are essential to determine the worth of bonds in current terms, especially when market rates vary.
Step-by-step explanation:
E-Tech Initiatives Limited plans to issue $530,000, 10-year, 4 percent bonds, with interest payable annually. If these bonds are issued at 98, this means they are issued at 98% of their face value. Therefore, the amount reported on the balance sheet would be the face value of the bonds minus the discount at which they are issued. The calculation for the balance sheet value on January 2, 2013, just after issuance would be:
$530,000 (face value) × 0.98 (issue price as a percentage of face value) = $519,400
This implies that the bonds will be reported as a long-term liability of $519,400 on E-Tech Initiatives Limited's balance sheet the day after they are issued.
Moreover, considering a simple two-year bond issued for $3,000 at an interest rate of 8%, it would pay $240 in interest each year. To calculate the present value of this bond if the discount rate is 8%, you would discount each of the cash flows (interest and principal payments) back to their present value using the formula for present value. If the discount rate rises to 11%, then the present value of the bond would be lower due to the higher discount rate reducing the present values of future cash flows.
A bond's present value calculation is crucial when deciding the worth of a bond in today's terms, especially when there is a fluctuation in market interest rates. For instance, if a water company issued a $10,000 bond with a 6% interest rate and you are considering buying this bond one year before it matures at a time when the interest rates have risen to 9%, you would likely pay less than the face value of $10,000. The present value calculation would allow you to determine the fair value you should pay for the bond.