# (present value). ```Reporting and Interpreting
Liabilities
Chapter 09
Part 2 – Long-Term Liabilities and Present Value
Techniques
McGraw-Hill/Irwin
Long-Term Liabilities
Creditors often require the borrower to pledge
specific assets as security for the long-term
liability.
Maturity = 1 year or less
Maturity &gt; 1 year
Current
Liabilities
Noncurrent
Liabilities
Long-Term Notes Payable and Bonds
Relatively small debt needs
can be filled from single
sources.
Banks
Insurance
Companies
Pension
Plans
Long-Term Notes Payable and Bonds
Significant debt needs are
often filled by issuing bonds to
the public.
Bonds
Cash
Present Value Concepts
\$1,000 invested
today at 10%.
In 1 year it will
be worth
\$1,100.
In 5 years it will
be worth
\$1,610!
Money can grow over time, because it can
earn interest.
Present Value Concepts
The growth is a mathematical function of
four variables:
1. The value today (present value).
2. The value in the future (future value).
3. The interest rate.
4. The time period.
Present Value of a Single Amount
The present value of a single amount is the
worth to you today of receiving that amount
some time in the future.
Present
Value
Future
Value
Interest compounding periods
Today
Future
Calculating the Present Value of a
Single Amount
• Need:
1. The Appropriate Interest Rate (i) Use these to
determine the PVF\$
2. The number of periods (n)
3. Future Value you wish to determine its
present value
• Multiply the PVF\$ (Present Value Factor of a \$)
times the future value
Calculating the PVF\$ and PVFA
Present Value Factor for a single amount
PVF\$ = 1/(1 + i)^n
Present Value Factor for An Annuity Formula
PVFA = (1-PVF\$)/i
Present Value of a Single Amount
How much do we need to invest today at 10%
interest, compounded annually, if we need
\$1,331 in three years?
a. \$1,000.00
The required future amount is \$1,331.
b. \$ 990.00
i = 10% &amp; n = 3 years
c. \$ 751.30
Using the present value of a single amount
d. \$ 970.00
table, the factor is .7513.
\$1,331 &times; .7513 = \$1,000 (rounded)
Present Values of an Annuity
An annuity is a series of
consecutive equal periodic
payments.
Today
Present Values of an Annuity
What is the value today of a series of
payments to be received or paid out in the
future?
Payment 1
Present
Value
Today
Payment 2
Interest compounding periods
Payment 3
Calculating the Present Value of an
Annuity
• Need:
1. The Appropriate Interest Rate (i)
2. The number of periods (n)
3. Annual payment
Use these to
determine the PVFA
• Multiply the PVFA (Present Value Factor of an
Annuity) times the annual payment
Calculating the PVF\$ and PVFA
Present Value Factor for a single amount
PVF\$ = 1/(1 + i)^n
Present Value Factor for An Annuity Formula
PVFA = (1-PVF\$)/i
Present Values of an Annuity
What is the present value of receiving \$1,000 each
year for three years at an interest rate of 10%,
compounded annually?
a. \$3,000.00
b. \$2,910.00
The consecutive equal payment amount is
\$1,000.
c. \$2,700.00
i = 10% &amp; n = 3 years
d. \$2,486.90
Using the present value of an annuity
table, the factor is 2.4869.
\$1,000 &times; 2.4869 = \$2,486.90
Try AP9-6 (page 500-501)
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