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Present Value of Bonds Payable; Premium Mason Co. issued $260,000 of four-year, 13% bonds with interest...

Present Value of Bonds Payable; Premium

Mason Co. issued $260,000 of four-year, 13% bonds with interest payable semiannually, at a market (effective) interest rate of 11%.

Determine the present value of the bonds payable, using the present value tables in Exhibit 4 and Exhibit 5. Round to the nearest dollar.
$

Expert Solution

If r is the interest rate prevailing in the market, c is the coupon rate on the bond, t is the time periods occurring over the term of the bond and F is the face value of the bond, the present value of interest payments is calculated using the following formula:

Present Value of Interest Payments = c × F × 1 ? (1 + r)^-t/r

The present value of the face value (i.e. the maturity value) is calculated as follows:

Present Value of Face Value of a Bond = F/(1+r)^t

Therefore, the price of a bond is given by the following formula:

Present Value of Interest Payments= c × F × [1 ? (1 + r)^-t] / r + F/ (1 + r)^t

Since the interest is paid semiannually the bond interest rate per period is 6.5% (= 13% ÷ 2), the market interest rate is 5.5% (= 11% ÷ 2) and number of time periods are 8 (= 2 × 4). Hence, the present value payable will be

Present value of bond = 6.5% × 260000 × [1-(1+5.5%)^-8]/5.5% + 260000/(1+5.5%)⁸

= 16900 × [1-1/1.535]/5.5% + 260000/1.535

= 16900 × 6.34 + 169381

= 107146 + 169491

= 276637

Answer may vary a little due to calculation beyond 3 decimal places.

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ekkarill92 answered 1 year ago

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