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Present Value of Notes Receivable
  
[Key Concept]
Present value of notes receivable
          = Present value of face amount + Present value of interest payments

Present value calculation is based on market interest rate.
 
[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]
yd-01.gif (845 bytes) Market interest rate = 12%
          r = 0.12 (per annual period),  
          n = 2 (annual periods)

yd-01.gif (845 bytes) 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.

yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) Discount on note receivable
          = Face amount - Present value
          = $200,000 - $159,440 = $40,560

yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) 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]
yd-01.gif (845 bytes) Market interest rate = 12%
          r = 0.12 (per annual period),  
          n = 2 (annual periods)

yd-01.gif (845 bytes) 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.
 
yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) Discount on note receivable
          = Face amount - Present value
          = $200,000 - $193,242 = $6,758
 
yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) 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

yd-01.gif (845 bytes) 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
 

 
Tables for PV and FV Factors

 
Table of Future Value Factors for a Single Present Amount (pdf)
 Table of Present Value Factors for a Single Future Amount (pdf)
 Table of Future Value Factors for an Ordinary Annuity (pdf)
 Table of Present Value Factors for an Ordinary Annuity (pdf)
 How to derive PV and FV factors (pdf)


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