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					 Future Value of Single Amount

Known amount of
single payment or
   investment             Future Value



                + Interest =
Present Value of Single Amount

                     Known amount
                       of single
                      payment in
Present Value           future



           Discount by
           Interest Rate
           PRESENT VALUE COMPONENTS

PV     =       The equivalent value of a future amount
               discounted back to the present time.
FV      =      the equivalent value of a present amount
                         invested over a period of time
n       =      time period (# of compounding periods)
r       =      interest rate corresponding to # periods
Annuity =      series of equal payments
Frequency of Compounding = number of times per year interest is
                                compounded


   Annually = 1
 Semiannually = 2
   Quarterly = 4
                Present Value of a Single Sum

Example 1: Would you rather have $1,000 today or receive $1,400
three years from now. The going rate of interest is 10%.



                   P.V. of $1 @ 10% for 3 years = .751



     Present Value of                         Known Payment =
    Known Payment= ?                               1400


                     Year 1      Year 2       Year 3


                  + Interest @ 10% per year
                Present Value of $1
(n)    2%      4%      6%      8%     10%     12%     15%

1     0.980   0.962   0.943   0.926   0.909   0.893   0.870
2     0.961   0.925   0.890   0.857   0.826   0.797   0.756
3     0.942   0.889   0.840   0.794   0.751   0.712   0.658
4     0.924   0.855   0.792   0.735   0.683   0.636   0.572
5     0.906   0.822   0.747   0.681   0.621   0.567   0.497
6     0.888   0.790   0.705   0.630   0.564   0.507   0.432
7     0.871   0.760   0.665   0.583   0.513   0.452   0.376
8     0.853   0.731   0.627   0.540   0.467   0.404   0.327
Present Value of a Single Amount Example – Using Formulas


                 PV = Future * (1 + r)-n
                                 or
                  PV = Future value
                         (1 + r)n


                    Plugging in from the prior
                           problem…

                      (1 + r)-n = (1 + 0.1)-3
                            = 0.751!!!
Three years from now ABC Co. will need $100,000 to repay a debt.
How much should ABC invest today earning 10% APR, compounded
semiannually?


 R=

 N=

 FV =

 PV =

 Freq =
Purchase equipment for a contract price of $50,000 on Jan. 1, 2007.
The lump sum payment is due on Dec. 31. 2008. The fair market value
of the equipment is not readily determinable, but the implicit interest
rate is 9%.

 R=

 N=

 FV =

 PV =

 Freq =
                              ANNUITIES

•   A series of equal periodic payments over a period of time
•   Related to the calculation of interest (to be received or paid)
            • Some bonds may require TWO P.V calculations
•   Retirement benefits from pensions

Ordinary Annuity - Payment or receipt made at end of each period.

If payment or receipt begins immediately, then the present value of the
first payment is simply the value stipulated



An amount, if presently invested at a compound interest, would provide
for a series of equal payments at the end of each period.
Would you rather have $25,000 today or receive three equal payments
of $9,000 at the end of each year. Assume the interest rate is10% and
is compounded annually.
R=

N=

PMT =

PV =

Freq =
Sampson Company just purchased a piece of equipment and financed
this purchase with a loan from the bank. Sampson must make annual
loan payments of $13,000 at the end of each year for the next five years.
Interest is compounded annually on the loan at a rate of 7%. What is the
cost of the equipment?

  R=

  N=

  PMT =

  PV =

  Freq =
                  Annuities: Additional Note
• Though one can and should use annuity tables when solving time
  value problems with a series of equal payments, an alternate exists

• Annuities are simply a stream of fixed payments on a determinable
  date (i.e. end of the year for ordinary annuities)

• To solve without an annuity table, we must simply evaluate each
  sum payment separately (discounted back to the present)

• That is, we can state the present value of an annuity as

        (P.V. of first payment) + (P.V. of second payment) + ….
                         (P.V. of the nth payment)
        Graphically, you can envision it this way…

                 Year 1               Year 2               Year 3




                P.V. = PMT*present value factor (r, 3)



P.V. of first             P.V. of second                 P.V. of third
 payment                     payment                      payment
   N=1                         N=2                          N=3
      Compound Interest Computations



 Present                        Future
value of a                     value of a
  single                         single
 amount                         amount


 Present                       Future
value of an                  value of an
 annuity                      annuity
           And now for the challenge!!!!

Management is considering purchasing a new
machine for a cost of $15,000. It is estimated that
the machine will generate positive net cash flows of
$3,000 per year for six years and will be sold for
salvage at the end of that time for $1,000. Assuming
that the company demands a minimum of an 8%
return on their investments, determine if
management should purchase the machine by
finding the present value of the future cash flows.
                         Current Liabilities

• Those obligations that will be met within a year’s time

• Recorded on the books at face value
        • because they are due in the coming year, there is no need to
          discount the payment by an interest rate (i.e. find a P.V.)

• They represent funding for short-term needs within the firm

• Classification remains important for two liquidity ratios in particular that
  involve current liabilities

                       Current Assets
Current Ratio =
                      Current Liabilities

Quick Ratio       =
                       Current Assets            ; assets are exclusive of
                      Current Liabilities          inventory and prepaids
                            Partial Balance Sheet

                                             • Accounts Payable
Liabilities and Stockholders’ Equity             - trade accounts with suppliers,
                                                    short-term, non-contractual
Current Liabilities                               - can be offered with discounts for
Accounts Payable                       XXX          early payment (2/20 n40)
Notes Payable                          XXX
Current maturities of                        • Notes Payable
Long-term debt                         XXX        - contractual agreement, with
Income taxes payable                   XXX
                                                    stipulated dates and firm
Accrued expenses and
Other                                  XXX          amounts (e.g. bank loans)
Total Current Liabilities              XXX        - may record a discount, but
                                                    different from accounts payable

                                             • Current Maturities of LTD
                                                   - Long-term debt may be due in a
                                                     series of payments, once these
                                                     payments come due, must
                                                     reclassify portion of LTD
  Recording the ISSUANCE of a Note Payable

 • Initially our couple writes a Note (or IOU) to another entity/creditor
 • This establishes an obligation as well as financing
    DR         Cash                               10,000
    CR           Note payable                              10,000

               Recording INTEREST EXPENSE
• Depending on the date that the note matures in relation to the
  fiscal year end or reporting date of the company, we may or
  may not need adjustment

         i.    If the life of the note overlaps the report date, then adjustment
               is necessary
         ii.   If the life of the note does not overlap with the report date, no
               adjustment is necessary, interest is recorded at MATURITY
         When to record Adjustment, or at Maturity

                           Life of the Note


             Reporting Period 1        Reporting Period 2


• Here, the life of the note overlaps with the end of reporting period one, we
  would need to record any interest expense as of the end of period one

           Life of the Note


           Reporting Period 1        Reporting Period 2

• Here, the life of the note is contained within the period, and no adjustment
  is necessary, we simply include the interest expense when we record the
  note’s maturity
Consider a $10,000 note, issued September 1, 2007, at a
rate of 9%. The note matures on February 28, 2008, when
the firm must pay back both interest and principal. The
company’s reporting period ends December 31, 2007.

 What is the journal entry at December 31st?




 What is the journal entry at February 28th?




 How would these entries have changed if the firm’s reporting period
 ended March 31st?
       Short-term Notes Issued at a Discount
• Sometimes lending institutions will discount the note at its issuance
  rather than charging interest. For example, instead of attaching a
  9% rate of interest to the prior note, we deduct the total interest from
  the face value of the note.




• The discount is recorded under DISCOUNT on NOTES PAYABLE, it
  is a contra-account associated with Notes Payable
• Like accumulated depreciation and ADA, it decreases the value of
  our notes when present on the balance sheet.
• To record the discount, we use the following entry
       DR       Cash                              9,550
                Discount on Notes Payable           450
       CR          Notes Payable                          10,000
              Effective Rates with Note Discounts

• Even though we discounted the note with a 9% interest rate. The
  company is only obtaining access to funds of $9,550.

• For this money, we’re effectively paying $450 for the discount, and
  facing an effective interest rate of 4.7% (450/9550) rather than 4.5%
  (450/10,000).

              Current Maturities of Long-term Debt

•   As portions of long-term debt come due, we must simply reclassify it.
•   Assume we had $20,000 of long-term debt, of which $2,000 will
    mature in the coming year, we would record the following entry:

         DR      Long-term Debt                           2,000
         CR        Current Portion of Long-term Debt              2,000
    Taxes Payable (and “other accrued liabilities)
•   Though most company have December 31st year-ends, taxes are not
    paid until March or April 15th depending on the business type.
•   Though we have not paid the taxes, we must accrue a liability under
    the accrual basis of accounting

                 DR       Tax Expense              XXX
                 CR         Taxes Payable                   XXX

•   Other liability accounts that we’ve examined that would be classified
    as current include:
                   » Wage Expense/Wages Payable
                   » Salaries Expense/Salaries Payable
                   » Interest Expense/Interest Payable
                    Contingent Liabilities
• Due to the conservative nature of accounting, we must recognize or
  disclose information related to contingent liabilities.
• A contingent liability implies an obligation that may arise in the future
  by the triggering of some condition or event (e.g. lawsuits)

Recognize – include on our financial statements (balance sheet)
        • Under GAAP, when the liability is probably AND reasonably
          estimated, we recognize it
Disclose – record it in the footnotes to the financial statements
        • Under GAAP, when the liability is either improbable OR its
          cost is uncertain, we disclose it IF its occurrence is
          reasonably probable


Because of the conservatism principle contingent ASSETS
  are NOT recorded or even disclosed until the condition
                    or event has past.

				
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