Chapter AC, Problem AC.6E

Computing Bond Issue Proceeds and Issue Price

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 2,000 bonds, each of which will have a face value of $1,000, a stated interest rate of 8 percent paid annually, and a period to maturity of 10 years.

Required:

1. 1. Compute the bond issue proceeds assuming a market interest rate of 8 percent. (Do not round until totaling the bond proceeds, at which point you should round the total bond proceeds to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the (rounded) total proceeds to the total face value.
2. 2. Compute the bond issue proceeds assuming a market interest rate of 7 percent. (Do not round until totaling the bond proceeds, at which point you should round the total bond proceeds to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the (rounded) total proceeds to the total face value.
3. 3. Compute the bond issue proceeds assuming a market interest rate of 9 percent. (Do not round until totaling the bond proceeds, at which point you should round the total bond proceeds to the nearest thousand dollars.) Also, express the bond issue price as a percentage by comparing the (rounded) total proceeds to the total face value.

To determine

To compute: The bond issue proceeds assuming a market interest rate of 8% and express it as a percentage by comparing the total proceeds to the total face value.

Answer to Problem AC.6E

The bond issue proceeds assuming a market interest rate of 8% is $1,999,993, and the total proceeds to the total face value is 100%.

Explanation of Solution

Compute the bond issue proceeds assuming a market interest rate of 8%.

Particulars	Amount ($)
Face Value (1)	$2,000,000
Present value factor(2)	0.46319
Present value of face amount(3)	$926,380
Face Value (1)	$2,000,000
Stated interest rate(4)	0.08
Annual Interest Payment(5)	$160,000
Present value factor(6)	6.71008
Present value of interest payments(7)	$1,073,613
Total Bond Proceeds(8)	$1,999,993

Table (1)

Therefore, the total bond proceeds, rounded to the nearest thousand is $2,000,000.

Working Notes:

Calculate the face value.

$\begin{array}{c}\text{Face value = Issue price }\times \text{ Number of bonds}\\ =\$2,000\times 1,000\\ =\$2,000,000\end{array}$ (1)

Calculate the present value factor.

Present value of $1 at 8% for 10 years is 0.46319 as per the Present Value Table.

(2)

Calculate the present value of face amount.

$\begin{array}{c}\text{Present value of face amount = Face value }\times \text{ Present value factor}\\ =\$2,000,000\times 0.46319\\ =\$926,380\end{array}$ (3)

Calculate the stated interest rate.

$\begin{array}{c}\text{Stated interest rate = }8\%\\ =\frac{8}{100}\\ =0.08\end{array}$ (4)

Calculate the annual interest payment.

$\begin{array}{c}\text{Annual Interest Payment = Face value }\times \text{ Stated interest rate}\\ =\$2,000,000\times 0.08\\ =\$160,000\end{array}$ (5)

Calculate the present value factor.

Present value of $1 at 8% for 10 years is 6.71008 as per the Present Value of Annuity Table.

(6)

Calculate the present value of interest payments.

$\begin{array}{c}\text{Present value of interest payments = Annual Interest Payment }\times \text{ Present value factor}\\ =\$160,000\times 6.71008\\ =\$1,073,613\end{array}$ (7)

Calculate the total bond proceeds.

$\begin{array}{c}\text{Total bond proceeds = }\left(\begin{array}{l}\text{Present value of face amount +}\\ \text{Present value of interest payments}\end{array}\right)\\ =\$926,380+\$1,073,613 \\ =\$1,999,993\end{array}$ (8)

Compute the bond issue proceeds percentage by comparing the total proceeds to the total face value.

Calculate the total bond proceeds percentage.

$\begin{array}{c}\text{Total bond proceeds percentage = }\frac{\text{Total bond proceeds}}{\text{Face Value of Bonds}}\times \text{100}\\ =\frac{\$2,000,000}{\$2,000,000}\times \text{100}\\ =100\%\end{array}$ (9)

Thus, the total bond proceeds percentage is 100%.

Conclusion

Therefore, the bond issue proceeds assuming a market interest rate of 8% is $1,999,993, and the total proceeds to the total face value is 100%.

To determine

To compute: The bond issue proceeds assuming a market interest rate of 7% and express it as a percentage by comparing the total proceeds to the total face value.

Answer to Problem AC.6E

The bond issue proceeds assuming a market interest rate of 7% is $2,140,473, and the total proceeds to the total face value is 107%.

Explanation of Solution

Compute the bond issue proceeds assuming a market interest rate of 7%.

Particulars	Amount ($)
Face Value (1)	$2,000,000
Present value factor (10)	0.50835
Present value of face amount (11)	$1,016,700
Face Value (1)	$2,000,000
Stated interest rate (4)	0.08
Annual Interest Payment (5)	$160,000
Present value factor (12)	7.02358
Present value of interest payments (13)	$1,123,773
Total Bond Proceeds (14)	$2,140,473

Table (1)

Therefore, the total bond proceeds, rounded to the nearest thousand is $2,140,000.

Working Notes:

Calculate the present value factor.

Present value of $1 at 7% for 10 years is 0.50835 as per the Present Value Table.

(10)

Calculate the present value of face amount.

$\begin{array}{c}\text{Present value of face amount = Face value }\times \text{ Present value factor}\\ =\$2,000,000\times 0.50835\\ =\$1,016,700\end{array}$ (11)

Calculate the present value factor.

Present value of $1 at 7% for 10 years is 7.02358 as per the Present Value of Annuity Table.

(12)

Calculate the present value of interest payments.

$\begin{array}{c}\text{Present value of interest payments = Annual Interest Payment }\times \text{ Present value factor}\\ =\$160,000\times 7.02358\\ =\$1,123,773 \end{array}$ (13)

Calculate the total bond proceeds.

$\begin{array}{c}\text{Total bond proceeds = }\left(\begin{array}{l}\text{Present value of face amount +}\\ \text{Present value of interest payments}\end{array}\right)\\ =\$1,016,700+\$1,123,773 \\ =\$2,140,473\end{array}$ (14)

Compute the bond issue proceeds percentage by comparing the total proceeds to the total face value.

Calculate the total bond proceeds percentage.

$\begin{array}{c}\text{Total bond proceeds percentage = }\frac{\text{Total bond proceeds}}{\text{Face Value of Bonds}}\times \text{100}\\ =\frac{\$2,140,000}{\$2,000,000}\times \text{100}\\ =107\%\end{array}$ (15)

Thus, the total bond proceeds percentage is 107%.

Conclusion

Therefore, the bond issue proceeds assuming a market interest rate of 7% is $2,140,473, and the total proceeds to the total face value is 107%.

To determine

To compute: The bond issue proceeds assuming a market interest rate of 9% and express it as a percentage by comparing the total proceeds to the total face value.

Answer to Problem AC.6E

The bond issue proceeds assuming a market interest rate of 9% is $1,871,646, and the total proceeds to the total face value is 93.60%.

Explanation of Solution

Compute the bond issue proceeds assuming a market interest rate of 9%.

Particulars	Amount ($)
Face Value (1)	$2,000,000
Present value factor (16)	0.42241
Present value of face amount (17)	$844,820
Face Value (1)	$2,000,000
Stated interest rate (4)	0.08
Annual Interest Payment (5)	$160,000
Present value factor (18)	6.41766
Present value of interest payments (19)	$1,026,826
Total Bond Proceeds (20)	$1,871,646

Table (1)

Therefore, the total bond proceeds, rounded to the nearest thousand is $1,872,000.

Working Notes:

Calculate the present value factor.

Present value of $1 at 9% for 10 years is 0.42241 as per the Present Value Table.

(16)

Calculate the present value of face amount.

$\begin{array}{c}\text{Present value of face amount = Face value }\times \text{ Present value factor}\\ =\$2,000,000\times 0.42241\\ =\$844,820\end{array}$ (17)

Calculate the present value factor.

Present value of $1 at 9% for 10 years is 6.41766 as per the Present Value of Annuity Table.

(18)

Calculate the present value of interest payments.

$\begin{array}{c}\text{Present value of interest payments = Annual Interest Payment }\times \text{ Present value factor}\\ =\$160,000\times 6.41766\\ =\$1,026,826 \end{array}$ (19)

Calculate the total bond proceeds.

$\begin{array}{c}\text{Total bond proceeds = }\left(\begin{array}{l}\text{Present value of face amount +}\\ \text{Present value of interest payments}\end{array}\right)\\ =\$844,820+\$1,026,826 \\ =\$1,871,646\end{array}$ (20)

Compute the bond issue proceeds percentage by comparing the total proceeds to the total face value.

Calculate the total bond proceeds percentage.

$\begin{array}{c}\text{Total bond proceeds percentage = }\frac{\text{Total bond proceeds}}{\text{Face Value of Bonds}}\times \text{100}\\ =\frac{\$1,871,646}{\$2,000,000}\times \text{100}\\ =93.60\%\end{array}$ (21)

Thus, the total bond proceeds percentage is 93.60%.

Conclusion

Therefore, the bond issue proceeds assuming a market interest rate of 9% is $1,871,646, and the total proceeds to the total face value is 93.60%.