On April 15 2017 Mary purchased 60000 ABC Cos 12 20year bond

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

Solution

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