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1.
To Identify: If the market rate is 8%, will the bonds issue at face amount, a discount or a premium and calculate price of the bonds.
1.
Explanation of Solution
Bonds
Bonds are a kind of interest bearing notes payable, usually issued by companies, universities and governmental organizations. It is a debt instrument used for the purpose of raising fund of the corporations or governmental agencies. If selling price of the bond is equal to its face value, it is called as par on bond. If selling price of the bond is lesser than the face value, it is known as discount on bond. If selling price of the bond is greater than the face value, it is known as premium on bond.
Stated interest rate (9%) is greater than the market interest rate (8%) means, the bonds issue at a premium.
Working notes:
Calculate the present value of face value of principal.
| Particulars | Amount ($) |
|
Face | $41,000,000 |
| PV factor at an annual market rate of 4% for 40 periods (b) |
|
|
Present value of face value of principal
| $8,539,850.83 |
Note: The present value of $1 for 40 periods at 4% is 0.20829 (refer Table 2 in Appendix).
Calculate present value of interest payments.
| Particulars | Amount ($) |
| Interest payments amount (a) | $1,845,000 |
| PV factor at an annual market rate of 4% for 40 periods (b) | |
|
Present value of interest payments
| $36,517,667.81 |
Note: The Present value of an ordinary annuity of $1 for 40 periods at 4% is 19.79277 (refer Table 4 in Appendix).
Calculate the amount of interest payment.
Therefore, price of the bonds is $45,057,518.65.
2.
To Identify: If the market rate is 9%, will the bonds issue at face amount, a discount or a premium and calculate price of the bonds.
2.
Explanation of Solution
Bonds
Bonds are a kind of interest bearing notes payable, usually issued by companies, universities and governmental organizations. It is a debt instrument used for the purpose of raising fund of the corporations or governmental agencies. If selling price of the bond is equal to its face value, it is called as par on bond. If selling price of the bond is lesser than the face value, it is known as discount on bond. If selling price of the bond is greater than the face value, it is known as premium on bond.
Stated interest rate (9%) is equal to the market interest rate (9%) means, the bonds issue at a par.
Working notes:
Calculate the present value of face value of principal.
| Particulars | Amount ($) |
| Face value of bonds (a) | $41,000,000 |
| PV factor at an annual market rate of 4.5% for 40 periods (b) |
|
|
Present value of face value of principal
| $7,049,076.74 |
Note: The present value of $1 for 40 periods at 4.5% is 0.17193 (refer Table 2 in Appendix).
Calculate present value of interest payments.
| Particulars | Amount ($) |
| Interest payments amount (a) | $1,845,000 |
| PV factor at an annual market rate of 4.5% for 40 periods (b) |
|
|
Present value of interest payments | $33,950,923.26 |
Note: The Present value of an ordinary annuity of $1 for 40 periods at 4.5% is 18.40158 (refer Table 4 in Appendix).
Calculate the amount of interest payment.
Therefore, price of the bonds is $41,000,000.
3.
To Identify: If the market rate is 10%, will the bonds issue at face amount, a discount or a premium and calculate price of the bonds.
3.
Explanation of Solution
Bonds
Bonds are a kind of interest bearing notes payable, usually issued by companies, universities and governmental organizations. It is a debt instrument used for the purpose of raising fund of the corporations or governmental agencies. If selling price of the bond is equal to its face value, it is called as par on bond. If selling price of the bond is lesser than the face value, it is known as discount on bond. If selling price of the bond is greater than the face value, it is known as premium on bond.
Stated interest rate (9%) is equal to the market interest rate (10%) means, the bonds issue at a discount.
Working notes:
Calculate the present value of face value of principal.
| Particulars | Amount ($) |
| Face value of bonds (a) | $41,000,000 |
| PV factor at an annual market rate of 5% for 40 periods (b) |
|
|
Present value of face value of principal
| $5,823,872.97 |
Note: The present value of $1 for 40 periods at 5% is 0.14205 (refer Table 2 in Appendix).
Calculate present value of interest payments.
| Particulars | Amount ($) |
| Interest payments amount (a) | $1,845,000 |
| PV factor at an annual market rate of 5% for 40 periods (b) |
|
|
Present value of interest payments
| $31,658,514.32 |
Note: The Present value of an ordinary annuity of $1 for 40 periods at 5% is 17.15909 (refer Table 4 in Appendix).
Calculate the amount of interest payment.
Therefore, price of the bonds is $37,482,387.30.
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