Market Price of Bonds Payable
[Key Concept]
Price of bonds = Present value of principal + Present value of interest payments
Interest to be paid each period is determined by coupon rate (stated interest rate) for that period.
Present value calculation is based on market interest rate.
[Exercise 1]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 12%. What will be the price of bonds issued by Company A?
[Solution to Exercise 1]
Market interest rate = 12%
Market interest rate for a semiannual period = 12% / 2 = 6%
r = 0.06 (per semiannual period),
n = 10 (semiannual periods)
Present value of principal
= $500,000 x Present value factor for a single payment (6%, 10 periods)
= $500,000 x 0.5584
= $279,200
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Present value of interest payments
= Interest payment each semiannual period
x Present value factor for an ordinary annuity (6%, 10 periods)
= ($500,000 x 5%) x 7.3601
= $184,002
Price of bonds
= Present value of principal + Present value of interest payments
= $279,200 + $184,002
= $463,202
The bonds will be sold at a $36,798 discount from the face amount.
($500,000 - $463,202 = $36,798)
[Exercise 2]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 8%. What will be the price of bonds issued by Company A?
[Solution to Exercise 2]
Market interest rate = 8%
Market interest rate for a semiannual period = 8% / 2 = 4%
r = 0.04 (per semiannual period),
n = 10 (semiannual periods)
Present value of principal
= $500,000 x Present value factor for a single payment (4%, 10 periods)
= $500,000 x 0.6756
= $337,800
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Present value of interest payments
= Interest payment each semiannual period
x Present value factor for an ordinary annuity (4%, 10 periods)
= ($500,000 x 5%) x 8.1109
= $202,773
Price of bonds
= Present value of principal + Present value of interest payments
= $337,800 + $202,773
= $540,573
The bonds will be sold at a $40,573 premium over the face amount.
($540,573 - $500,000 = $40,573)
Amortization of Discount on Bonds
[Exercise 3]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 12%.
As explained in Exercise 1, the price of bonds is $463,202, and bonds will be sold at $36,798 discount from the face amount of $500,000.
Calculate the amortization of discount on bonds using effective interest method.
[Solution to Exercise 3]
Date Interest paid Effective interest rate for semiannual period Interest expense Amortization of discount Present value of bonds
1/1/2006 $463,202
7/1/2006 $25,000 6% $27,792 $2,792 $465,994
1/1/2007 $25,000 6% $27,960 $2,960 $468,954
7/1/2007 $25,000 6% $28,137 $3,137 $472,091
1/1/2008 $25,000 6% $28,325 $3,325 $475,416
7/1/2008 $25,000 6% $28,525 $3,525 $478,941
1/1/2009 $25,000 6% $28,736 $3,736 $482,678
7/1/2009 $25,000 6% $28,961 $3,961 $486,639
1/1/2010 $25,000 6% $29,198 $4,198 $490,837
7/1/2010 $25,000 6% $29,450 $4,450 $495,287
1/1/2011 $25,000 6% $29,713 $4,713 $500,000
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Effective interest rate = Market interest rate = 12%
Effective interest rate for a semiannual period = 12% / 2 = 6%
Interest expense
= Present value of bonds at the beginning of the period
x Effective interest rate for the period
[1/1/2006 - 7/1/2006] --> $463,202 x 6% = $27,792
[7/1/2006 - 1/1/2007] --> $465,994 x 6% = $27,960
Amortization of discount on bonds
= Interest expense - Interest paid
[1/1/2006 - 7/1/2006] --> $27,792 - $25,000 = $2,792
[7/1/2006 - 1/1/2007] --> $27,960 - $25,000 = $2,960
Ending present value of bonds
= Beginning present value of bonds
+ Amortization of discount on bonds
[1/1/2006 - 7/1/2006] --> $463,202 + $2,792 = $465,994
[7/1/2006 - 1/1/2007] --> $465,994 + $2,960 = $468,954
Amortization of Premium on Bonds
[Exercise 4]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 8%.
As explained in Exercise 2, the price of bonds is $540,573, and bonds will be sold at $40,573 premium over the face amount of $500,000.
Calculate the amortization of premium on bonds using effective interest method.
[Solution to Exercise 4]
Date Interest paid Effective interest rate for semiannual period Interest expense Amortization of premium Present value of bonds
1/1/2006 $540,573
7/1/2006 $25,000 4% $21,623 $3,377 $537,196
1/1/2007 $25,000 4% $21,488 $3,512 $533,684
7/1/2007 $25,000 4% $21,347 $3,653 $530,031
1/1/2008 $25,000 4% $21,201 $3,799 $526,232
7/1/2008 $25,000 4% $21,049 $3,951 $522,282
1/1/2009 $25,000 4% $20,891 $4,109 $518,173
7/1/2009 $25,000 4% $20,727 $4,273 $513,900
1/1/2010 $25,000 4% $20,556 $4,444 $509,456
7/1/2010 $25,000 4% $20,378 $4,622 $504,834
1/1/2011 $25,000 4% $20,166 $4,834 $500,000
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Effective interest rate = Market interest rate = 8%
Effective interest rate for a semiannual period = 12% / 2 = 4%
Interest expense
= Present value of bonds at the beginning of the period
x Effective interest rate for the period
[1/1/2006 - 7/1/2006] --> $540,573 x 4% = $21,623
[7/1/2006 - 1/1/2007] --> $537,196 x 4% = $21,488
Amortization of premium on bonds
= Interest paid - Interest expense
[1/1/2006 - 7/1/2006] --> $25,000 - $21,623 = $3,377
[7/1/2006 - 1/1/2007] --> $25,000 - $21,488 = $3,512
Ending present value of bonds
= Beginning present value of bonds
- Amortization of premium on bonds
[1/1/2006 - 7/1/2006] --> $540,573 - $3,377 = $537,196
[7/1/2006 - 1/1/2007] --> $537,196 - $3,512 = $533,684
[Key Concept]
Price of bonds = Present value of principal + Present value of interest payments
Interest to be paid each period is determined by coupon rate (stated interest rate) for that period.
Present value calculation is based on market interest rate.
[Exercise 1]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 12%. What will be the price of bonds issued by Company A?
[Solution to Exercise 1]
Market interest rate = 12%
Market interest rate for a semiannual period = 12% / 2 = 6%
r = 0.06 (per semiannual period),
n = 10 (semiannual periods)
Present value of principal
= $500,000 x Present value factor for a single payment (6%, 10 periods)
= $500,000 x 0.5584
= $279,200
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Present value of interest payments
= Interest payment each semiannual period
x Present value factor for an ordinary annuity (6%, 10 periods)
= ($500,000 x 5%) x 7.3601
= $184,002
Price of bonds
= Present value of principal + Present value of interest payments
= $279,200 + $184,002
= $463,202
The bonds will be sold at a $36,798 discount from the face amount.
($500,000 - $463,202 = $36,798)
[Exercise 2]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 8%. What will be the price of bonds issued by Company A?
[Solution to Exercise 2]
Market interest rate = 8%
Market interest rate for a semiannual period = 8% / 2 = 4%
r = 0.04 (per semiannual period),
n = 10 (semiannual periods)
Present value of principal
= $500,000 x Present value factor for a single payment (4%, 10 periods)
= $500,000 x 0.6756
= $337,800
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Present value of interest payments
= Interest payment each semiannual period
x Present value factor for an ordinary annuity (4%, 10 periods)
= ($500,000 x 5%) x 8.1109
= $202,773
Price of bonds
= Present value of principal + Present value of interest payments
= $337,800 + $202,773
= $540,573
The bonds will be sold at a $40,573 premium over the face amount.
($540,573 - $500,000 = $40,573)
Amortization of Discount on Bonds
[Exercise 3]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 12%.
As explained in Exercise 1, the price of bonds is $463,202, and bonds will be sold at $36,798 discount from the face amount of $500,000.
Calculate the amortization of discount on bonds using effective interest method.
[Solution to Exercise 3]
Date Interest paid Effective interest rate for semiannual period Interest expense Amortization of discount Present value of bonds
1/1/2006 $463,202
7/1/2006 $25,000 6% $27,792 $2,792 $465,994
1/1/2007 $25,000 6% $27,960 $2,960 $468,954
7/1/2007 $25,000 6% $28,137 $3,137 $472,091
1/1/2008 $25,000 6% $28,325 $3,325 $475,416
7/1/2008 $25,000 6% $28,525 $3,525 $478,941
1/1/2009 $25,000 6% $28,736 $3,736 $482,678
7/1/2009 $25,000 6% $28,961 $3,961 $486,639
1/1/2010 $25,000 6% $29,198 $4,198 $490,837
7/1/2010 $25,000 6% $29,450 $4,450 $495,287
1/1/2011 $25,000 6% $29,713 $4,713 $500,000
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Effective interest rate = Market interest rate = 12%
Effective interest rate for a semiannual period = 12% / 2 = 6%
Interest expense
= Present value of bonds at the beginning of the period
x Effective interest rate for the period
[1/1/2006 - 7/1/2006] --> $463,202 x 6% = $27,792
[7/1/2006 - 1/1/2007] --> $465,994 x 6% = $27,960
Amortization of discount on bonds
= Interest expense - Interest paid
[1/1/2006 - 7/1/2006] --> $27,792 - $25,000 = $2,792
[7/1/2006 - 1/1/2007] --> $27,960 - $25,000 = $2,960
Ending present value of bonds
= Beginning present value of bonds
+ Amortization of discount on bonds
[1/1/2006 - 7/1/2006] --> $463,202 + $2,792 = $465,994
[7/1/2006 - 1/1/2007] --> $465,994 + $2,960 = $468,954
Amortization of Premium on Bonds
[Exercise 4]
On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 8%.
As explained in Exercise 2, the price of bonds is $540,573, and bonds will be sold at $40,573 premium over the face amount of $500,000.
Calculate the amortization of premium on bonds using effective interest method.
[Solution to Exercise 4]
Date Interest paid Effective interest rate for semiannual period Interest expense Amortization of premium Present value of bonds
1/1/2006 $540,573
7/1/2006 $25,000 4% $21,623 $3,377 $537,196
1/1/2007 $25,000 4% $21,488 $3,512 $533,684
7/1/2007 $25,000 4% $21,347 $3,653 $530,031
1/1/2008 $25,000 4% $21,201 $3,799 $526,232
7/1/2008 $25,000 4% $21,049 $3,951 $522,282
1/1/2009 $25,000 4% $20,891 $4,109 $518,173
7/1/2009 $25,000 4% $20,727 $4,273 $513,900
1/1/2010 $25,000 4% $20,556 $4,444 $509,456
7/1/2010 $25,000 4% $20,378 $4,622 $504,834
1/1/2011 $25,000 4% $20,166 $4,834 $500,000
Interest payment each semiannual period
= $500,000 x 5%
= $25,000
(Coupon rate for a semiannual period = 10% / 2 = 5%.)
Effective interest rate = Market interest rate = 8%
Effective interest rate for a semiannual period = 12% / 2 = 4%
Interest expense
= Present value of bonds at the beginning of the period
x Effective interest rate for the period
[1/1/2006 - 7/1/2006] --> $540,573 x 4% = $21,623
[7/1/2006 - 1/1/2007] --> $537,196 x 4% = $21,488
Amortization of premium on bonds
= Interest paid - Interest expense
[1/1/2006 - 7/1/2006] --> $25,000 - $21,623 = $3,377
[7/1/2006 - 1/1/2007] --> $25,000 - $21,488 = $3,512
Ending present value of bonds
= Beginning present value of bonds
- Amortization of premium on bonds
[1/1/2006 - 7/1/2006] --> $540,573 - $3,377 = $537,196
[7/1/2006 - 1/1/2007] --> $537,196 - $3,512 = $533,684
