[Exercise 1:
Non-Interest Bearing Note Receivable]
On January 1, 2011, Company A
sold its products to Company B and received a non-interest bearing
note with $200,000 face amount and due on December 31, 2012. At the time of issuance,
market interest rate is 12%. What is the present
value of the note receivable? |
[Solution to Exercise 1]
Market interest rate = 12%
r = 0.12 (per annual period),
n = 2 (annual periods)
Present value of face amount
= $200,000 x Present value factor for a single payment (12%,
2 periods)
= $200,000 x 0.7972
= $159,440
| |
Present value factor for a single payment (12%, 2 periods) = 0.7972
From
present
value of a single payment table
or Excel function --> " = PV (rate, nper, pmt, fv, type) "
--> " = PV (12%, 2, , 1, 0) "
--> 0.7972
Type = 0 or omitted, if payment is made at the end of period.
= 1,
if payment is made at the beginning of period. |
Present value of interest amount
= 0 (non-interest
bearing note)
Present value of note receivable
= Present value of face
amount + Present value of interest payments
= $159,440 + $0 =
$159,440
Discount on note receivable
= Face amount -
Present value
= $200,000 - $159,440 =
$40,560
Amortization of discount on note
receivable
--> Effective
interest method
| Date |
Interest received |
Effective interest rate for annual period |
Interest income |
Amortization of discount |
Present
value of note receivable |
|
1/1/2011 |
|
|
|
|
$159,440 |
|
12/31/2011 |
$0 |
12% |
$19,132 |
$19,232 |
$178,572 |
|
12/31/2012 |
$0 |
12% |
$21,428 |
$21,428 |
$200,000 |
Interest income
= Present value of note at the beginning of the period
x Effective interest rate for
the period
[1/1/2011 - 12/31/2011] --> $159,440 x
12% = $19,132
[1/1/2012 - 12/31/2012] --> $178,572 x
12% = $21,428
Amortization of discount on note
= Interest income - Interest received
[1/1/2011 - 12/31/2011] --> $19,232 - $0
= $19,232
[1/1/2012 - 12/31/2012] --> $21,428 - $0 =
$21,428
|
[Exercise 2:
Interest Bearing Note Receivable]
On January 1, 2011, Company A
sold its products to Company C and received a note with $200,000
face amount, 10% annual stated interest rate, and due on December
31, 2012. Interest is paid annually on December 31, each year. At the time of issuance,
market interest rate is 12%. What is the present
value of the note receivable? |
[Solution to Exercise
2]
Market interest rate = 12%
r = 0.12 (per annual period),
n = 2 (annual periods)
Present value of face amount
= $200,000 x Present value factor for a single payment (12%,
2 periods)
= $200,000 x 0.7972
= $159,440
| |
Present value factor for a single payment (12%, 2 periods) = 0.7972
From
present
value of a single payment table
or Excel function --> " = PV (rate, nper, pmt, fv, type) "
--> " = PV (12%, 2, , 1, 0) "
--> 0.7972
Type = 0 or omitted, if payment is made at the end of period.
= 1,
if payment is made at the beginning of period. |
Present value of interest amount
= $20,000 x Present value factor for an
ordinary annuity (12%,
2 periods)
= $20,000 x
1.6901
= $33,802
Annual interest amount = $200,000 x 10% stated interest rate
= $20,000
| |
Present value factor for an ordinary annuity (12%, 2 periods) =
1.6901
From
present
value of an ordinary annuity table
or Excel function --> " = PV (rate, nper, pmt, fv, type) "
--> " = PV (12%, 2, 1 , , 0) "
--> 1.6901
Type = 0 or omitted, if payment is made at the end of period.
= 1,
if payment is made at the beginning of period. |
Present value of note receivable
= Present value of face
amount + Present value of interest payments
= $159,440 + $33,802 =
$193,242
Discount on note receivable
= Face amount -
Present value
= $200,000 - $193,242 =
$6,758
Amortization of discount on note
receivable
--> Effective
interest method
| Date |
Interest received |
Effective interest rate for annual period |
Interest income |
Amortization of discount |
Present
value of note receivable |
|
1/1/2011 |
|
|
|
|
$193,242 |
|
12/31/2011 |
$20,000 |
12% |
$23,189 |
$3,189 |
$196,431 |
|
12/31/2012 |
$20,000 |
12% |
$23,569 |
$3,569 |
$200,000 |
Interest income
= Present value of note at the beginning of the period
x Effective interest rate for
the period
[1/1/2011 - 12/31/2011] --> $193,242 x
12% = $23,189
[1/1/2012 - 12/31/2012] --> $178,572 x
12% = $21,428
Amortization of discount on note
= Interest income - Interest received
[1/1/2011 - 12/31/2011] --> $23,189 -
$20,000 = $3,189
[1/1/2012 - 12/31/2012] --> $23,569 -
$20,000 = $3,569
|