Question

On December​ 31,

20182018​,

when the market interest rate is

1616​%,

McMann RealtyMcMann Realty

issues

$ 800 comma 000$800,000

of

14.2514.25​%,

1010​-year

bonds payable. The bonds pay interest semiannually. Determine the present value of the bonds at issuance. ​(Round all currency amounts to the nearest whole​ dollar.)

Answer 1

Computation the present value at issuance of bond is:

Present value at issuance of bond = Present value of face amount of bond + Present value of interest payment

= $171,640 + $559,633

= $731,273

Hence, the present value at issuance of bond is $731,273.

Working notes:

1.

Computation the semiannual periods is:

Semiannual periods = Number of years * 2

= 10 * 2

= 20

Hence, the semiannual periods is 20.

2.

Computation the semiannual interest rate is:

Semiannual interest rate = Market interest rate annually / 2

= 16% / 2

= 8%

Hence, the semiannual interest rate is 8%.

3.

Computation the value of interest payment is:

Value of interest payment = Value of face amount of bond * Interest rate * 1/2

= $800,000 * 14.25% * 1/2

= $114,000 * 1/2

= $57,000

Hence, the value of interest payment is $57,000.

4.

Computation the present value of face amount of bond is:

Present value of face amount of bond = Value of face amount of bond * [1 / (1 + Semiannual market interest rate) ^{Semiannual periods}]

= $800,000 * [1 / (1 + 0.08) ²⁰]

= $800,000 * [1 / (1.08) ²⁰]

= $800,000 * [1 / 4.660957]

= $800,000 * 0.21455

= $171,640

Hence, the present value of principal payment is $171,640.

5.

Computation the present value of interest payment is:

Present value of interest payment = Value of interest payment * [1 - (1 / (1 + Semiannual market interest rate) ^{Semiannual periods}) / Semiannual market interest rate]

= $57000 * [1 - (1 / (1 + 0.08) ²⁰) / 0.08]

= $57,000 * [1 - (1 / (1.08) ²⁰​​​​​​​) / 0.08]

= $57,000 * [1 - (1 / 4.660957​​​​​​​) / 0.08]

= $57,000 * [(1 - 0.21455) / 0.08]

= $57,000 * [0.78545 / 0.08]

= $57,000 * 9.81813

= $559,633

Hence, the present value of interest payment is $559,633.