Question

Your company plans to issue bonds later in the upcoming year. But with the economic uncertainty and varied interest rates, it is not clear how much money the company will receive when the bonds are issued. The company is committed to issuing 2,400 bonds, each of which will have a face value of $1,000, a stated interest rate of 10 percent paid annually, and a period to maturity of 10 years. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1) (Use appropriate factor(s) from the tables provided.) 

Required: 

.1. Compute the bond issue proceeds assuming a market interest rate of 10 percent. (When computing proceeds, round the present value of the face amount and of the annual interest payment to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the total proceeds to the total face value. (Round "Bond Issue Price as a Percentage" to 2 decimal places. )

2. Compute the bond issue proceeds assuming a market interest rate of 9 percent. (When computing proceeds, round the present value of the face amount and of the annual interest payment to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the total proceeds to the total face value. (Round "Bond Issue Price as a Percentage" to 2 decimal places.) 

3. Compute the bond issue proceeds assuming a market interest rate of 11 percent. (When computing proceeds, round the present value of the face amount and of the annual interest payment to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the total proceeds to the total face value. (Round "Bond Issue Price as a Percentage" to 2 decimal places.) 

Answer 1

Solution

1. Computation of the bond issue proceeds assuming a market interest rate of 10%:

Table or Calculator Function
Face value of bond issuance from future value	$2,400,000
Market Interest Rate	10%
Present value of proceeds from bond issue	$2,400,000
Bond issue price as a percentage of Face Value	100%

Computations:

Bonds face value = $2,400,000

Stated rate = 10%

Period, n = 10 years

Annual interest payments, hence period = 10 x1 = 10 years

Market interest rate = 10%

Present value of bond issue = FV x (P/F, 10%, 10)

= 2,400,000 x 0.3855

Present value of bond issue = 925,200

Add: present value of interest payments –

Annual interest = 2,400,000 x 10% = $240,000

Present value of interest payments = 240,000 x (P/A, 10%, 10)

= 240,000 x 6.145 = $1,474,800

Bond issue proceeds = present value of bond issue + present value of interest payments

= $925,200 + $1,474,800 = $2,400,000

Since, the stated rate of interest and market rate of interest are same, 10% for the bond issue, the bond is issued at par.

2. Computation of the bond issue proceeds assuming a market interest rate of 9%:

Table or Calculator Function
Face value of bond issuance from future value	$2,400,000
Market Interest Rate	9%
Present value of proceeds from bond issue	$2,554,080
Bond issue price as a percentage of Face Value	106.4%

Computations:

Bonds face value = $2,400,000

Stated rate = 10%

Period, n = 10 years

Annual interest payments, hence period = 10 x1 = 10 years

Market interest rate = 9%

Present value of bond issue = FV x (P/F, 9%, 10)

= 2,400,000 x 0.4224

Present value of bond issue = $1,013,760

Add: present value of interest payments –

Annual interest = 2,400,000 x 10% = $240,000

Present value of interest payments = 240,000 x (P/A, 9%, 10)

= 240,000 x 6.418 = $1,540,320

Bond issue proceeds = present value of bond issue + present value of interest payments

= $1,013,760 + $1,540,320 = $2,554,080

Since, the stated rate of interest, 10% is more than the market rate of interest, 9% for the bond issue, the bond is issued at premium.

Premium on Bonds Payable = 2,554,080 – 2,400,000 = $154,080

3. Computation of the bond issue proceeds assuming a market interest rate of 11%:

Table or Calculator Function
Face value of bond issuance from future value	$2,400,000
Market Interest Rate	11%
Present value of proceeds from bond issue	$2,258,640
Bond issue price as a percentage of Face Value	94.11%

Computations:

Bonds face value = $2,400,000

Stated rate = 10%

Period, n = 10 years

Annual interest payments, hence period = 10 x1 = 10 years

Market interest rate = 11%

Present value of bond issue = FV x (P/F, 11%, 10)

= 2,400,000 x 0.3522

Present value of bond issue = $845,280

Add: present value of interest payments –

Annual interest = 2,400,000 x 10% = $240,000

Present value of interest payments = 240,000 x (P/A, 11%, 10)

= 240,000 x 5.889 = $1,413,360

Bond issue proceeds = present value of bond issue + present value of interest payments

= $845,280 + $1,413,360 = $2,258,640

Since, the stated rate of interest, 10 is less than the market rate of interest 11%, the bond is issued at discount.

Discount on bonds payable = 2,400,000 – 2,258,640 = $141,360