In: Accounting
On April 15, 2017, Mary purchased $60,000 ABC Co.'s 12% 20-year bonds at face amount with interest being paid on December 31 each year. ABC Co. has paid interest due on the bonds regularly. On April 15, 2021, market interest rated had risen 14% and Mary is considering selling.
A) Calculate the market value of Mary's bonds on April 15, 2021
Market interest rate = 14% (EAR)
15 days interest rate = [(1.14)^1/24 - 1] *100 = 0.5474%
Firstly, we will calculate the market value of Bond if bond is sold as on December 31,2021:
Maturity date of Bond = April 15, 2036
Interest received till December 31, 2035 = 14 years
Maturity amount is due on April 15, 2036 i.e. 14 years 3 months and 15 days = 14*24 + 3*2 + 1 = 343 periods
Annual coupon amount on bond = 60000*12% = 7200
Maturity value = 60000
Price of Bond as on December 31,2021 = 7200*Present value annuity factor(14%,14) + 60000*Present value interest factor(0.5474%,343)
= 7200*6.002 + 60000*0.1537 = 43214.4 + 9222 = 52436.4
Now we will calculate price of Bond as on April 15, 2021:
Interest to be received as on December 31,2021 = 7200
15 days period from April 15, 2021 to December 31,2021 = 1 + 8*2 = 1+16 = 17 periods
Price of Bond as on April 15,2021 = 7200*Present value interest factor(0.5474%,17) + 52436.4*Present value interest factor(0.5474%,17)
= 7200*0.9113 + 52436.4*0.9113 = 6561.36 + 47785.29 = 54346.65
Market value of Mary's bonds on April 15, 2021 = $54346.65