# Slide cash for annuity payments

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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 =
• 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

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

• 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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 views: 19 posted: 2/15/2011 language: English pages: 24