Question

on December 31, 2018, when the market interest rate is 8%, Mcmann realty issues $500,000 of 5.25%, 10 year bonds payable. The bonds pay interest semiannually. The present value of the bonds at issuance amounts to what?

Answer 1

Semi annual interest payment = Par value of bonds x Stated interest rate x 6/12

= 500,000 x 5.25% x 6/12

= $13,125

Market interest rate = 8%

Semi annual Market interest rate = 4%

Maturity period of bonds = 10 years or 20 semi annual periods

Present value of principal to be received at the maturity = Par value of bonds x Present value factor (r%, n)

= 500,000 x Present value factor (4%, 20)

= 500,000 x 0.45639

= $228,195

Present value of interest to be paid periodically over the term of the bonds = Interest x Present value annuity factor (r%, n)

= x Present value annuity factor (4%, 20)

= 13,125 x 13.59033

= $178,373

Present value of bond = Present value of principal to be paid at the maturity + Present value of interest to be paid periodically over the term of the bonds

=228.195+178,373

= $406,568

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