Question

dobbs company issues 5%, two-year bonds, on december 31, 2021, with a par value of $105,000 and semiannual interest payments. semiannual period-end unamortized discount carrying value (0) 12/31/2021 $ 6,100 $ 98,900 (1) 6/30/2022 4,575 100,425 (2) 12/31/2022 3,050 101,950 (3) 6/30/2023 1,525 103,475 (4) 12/31/2023 0 105,000

Answer 1

The present discounted value of a two-year bond is calculated using the present value formula. When a bond's interest rate and discount rate are equal, its present value equals its face value. If the discount rate increases, the present value of the bond decreases.

Step-by-step explanation:

The concept of present discounted value (PDV) is essential in determining the value of financial assets like stocks and bonds. For a bond, the present value is calculated by discounting the future coupon (interest) payments and the principal repayment back to their present value using a discount rate. This process helps investors determine what they should pay for the bond today given the future income stream it will generate.

Consider a two-year bond with a principal amount of $3,000 and an annual interest rate of 8%. It pays $240 in interest at the end of each year ($3,000 x 8%). The present value of these interest payments and the principal repayment can be calculated using the formula for present value:

PV = C / (1 + r)^t

Where PV is the present value, C is the cash flow in each period, r is the discount rate, and t is the time period.

At a discount rate of 8%, the bond's present value will be equal to its face value because the discount rate and the interest rate are the same. However, if the discount rate rises to 11%, the present value of the bond will decrease. This is because as the discount rate increases, the present value of future cash flows reduces.

Answer 2

The issue price of the bond is $105,000, and it carries a 5% coupon rate with semiannual interest payments. Dobbs Company issued these bonds at a discount, as indicated by the decreasing unamortized discount in the period-end carrying value. The discount amortization is reducing over time, reaching zero by the bond's maturity date.

Step-by-step explanation:

Dobbs Company issued 5%, two-year bonds on December 31, 2021, with a par value of $105,000. The company sells these bonds at a discount, which results in the initial carrying value being less than the par value. The semiannual interest payments are calculated based on the par value multiplied by the coupon rate, which in this case is 5%. The unamortized discount gradually decreases over time, getting closer to zero by the bond's maturity.

The semiannual amortization of the discount is the process of reducing the discount amount by an equal portion over each period until the bond matures. As the bond approaches maturity, the discount decreases until it fully amortizes to zero, aligning the carrying value with the bond's par value by the bond's maturity date.

The schedule provided displays the bond's carrying value at the end of each semiannual period and the corresponding unamortized discount. The unamortized discount reduces over time as portions of it are amortized, eventually converging to zero by the bond's maturity date, aligning the carrying value with the bond's par value. This method of amortization helps to account for the discount on bonds and systematically adjust it until it is completely eliminated by the bond's maturity.