Chapter 6: Time Value of Money Concepts

1
Intermediate Accounting
Kieso
,
Weygandt
, and
Warfield
Chapter 6 The Time Value of Money
2
Basic Time Value Concepts

• The time value of money is the relationship
  between time and money.
• A dollar earned today is worth more than a dollar
  earned in the future.
• This concept is used to choose among alternative
  investment proposals.

3
Accounting Applications

• The following are some of the applications of
  time value of money concept
• Valuing non-current receivables and payables
• Valuing assets and obligations to be capitalized
  under long term leases
• Measuring post retirement obligations and pension
  expense
• Measuring the liability from bonds payable

4
Choosing an Interest Rate in Time Value
Measurements

• The relevance and reliability of accounting
  information depends on the selection of
  appropriate interest rates.
• The interest rate in turn depends on
• the risk free rate of interest (2 - 4)
• credit risk rate of interest (0 - 5)
• expected inflation rate of interest (0 - ?)
• The higher the credit risk, the higher the
  interest rate.

5
Simple and Compound Interest

• Simple interest is determined on the principal
  only.
• principal interest rate () time
• Compound interest is determined on
• the principal, and
• any interest earned (and not withdrawn)
• Compound interest is the typical computation
  applied in most time value applications.

6
Annuity Terminology

• Annuity Series of equal payments, equally spaced
  through time.
• An annuity requires that
• the periodic payments or receipts always be
  of the same amount,
• the interval between such payments or
  receipts be the same, and
• the interest be compounded once each interval

7
Ordinary Annuity Vs. Annuity Due

• Ordinary Annuity Payments occur at the end of
  the period.
• Annuity Due Payments occur at the beginning of
  the period.

8
Compound Interest Tables in Time Value of Money
Measurements

• Future value of 1 1 deposited today and left
  to accumulate for a specified number of periods
  until a future date
• Present value of 1 Value today of 1 to be
  received at some specified future date
• Future value of an ordinary annuity of 1 1
  deposited end of each period and left to
  accumulate until a specified future date.
• (Continued on next slide)

9
Compound Interest Tables in Time Value
Measurements

• Present value of an ordinary annuity of 1
  Value today of 1 to be received at at the end
  of each period for a specified number of periods
• Present value of an annuity due of 1 Value
  today of 1 to be received at the beginning of
  each period for a specified number of periods

10
Interest Rates and Frequency of Compounding
Interest rate per year 12
11
Single Sum Problems Future Value of a Single
Sum

• Given
• Amount of deposit today 50,000
• Interest rate 11
• Frequency of compounding Annual
• Number of periods (5 years) 5 periods
• Determine the future value of this single
  sum. (Use Table 6-1)
• 50,000 (1.68506) 84,253

12
Single Sum ProblemsPresent Value of a Single Sum

• Given
• Amount of deposit end of 5 years 84,253
• Interest rate (discount) rate 11
• Frequency of compounding Annual
• Number of periods (5 years) 5 periods
• Determine the present value of this single sum.
  (Use Table 6-2)
• 84,253 (0.59345) 50,000

13
AnnuitiesFuture Value of an Ordinary Annuity

• Given
• Deposits made at the end of each period
  5,000
• Compounding Annual
• Number of periods Five
• Interest rate 12
• Determine the future value of these deposits.
• (Use Table 6-3)
• 5,000 (6.35285) 31,764.25

14
AnnuitiesPresent Value of an Ordinary Annuity

• Given
• Rental receipts at the end of each period
  6,000
• Compounding Annual
• Number of periods (years) 5
• Interest rate 12
• Determine the present value of these receipts.
• (Use Table 6-4)
• 6,000 (3.60478) 21,268.68

15
AnnuitiesFuture Value of an Annuity Due

• Given
• 800 Deposits at the beginning of each period
  
• Compounding Annual
• Number of periods Eight
• Interest rate 12
• Determine the future value of these deposits.
• No FV Annuity Due Table Provided

16
Annuities - Future Value of an Annuity Due
1. Ordinary annuity factor 8 periods, 12
12.29969 2. Convert to annuity due factor
12.29969 1.12 13.77565 (One years
compounding is missing from table) 3. Future
value of annuity due 800 13.77565
11,020.52
17
AnnuitiesPresent Value of an Annuity Due

• Given
• 4.8M Payments made at beginning of each
  period
• Compounding Annual
• Number of periods Four
• Interest rate 11
• Determine the present value of these payments.
• (Use Table 6-5)
• 4.8M (3.44371) 16,529,808

18
AnnuitiesFuture Value of a Deferred Annuity

• (Deferred Annuity Payments occur after a
  specified Number of periods have passed)
• Deposits made at end of fourth, fifth, and
  sixth periods 80,000 each period
• No deposits were made at end of the first,
  second, or the third periods.
• Compounding Annual
• Interest rate 12
• Number of periods 6
• Determine the future value of the deferred
  annuity.

19
AnnuitiesFuture Value of a Deferred Annuity
1. Deferred annuity is calculated like ordinary
annuity. (Use Table 6-3, 12, 3 periods) 2.
80,000 (3.37440) 269,952
20
AnnuitiesPresent Value of a Deferred Annuity

• Given
• Payments made at end of fifth through tenth
  periods (6 payments) 5,000 each period
• No payments were made at end of the first
  through the fourth periods (deferred periods
  4).
• Compounding Annual
• Interest rate 8
• Number of periods 10 total
• Determine the present value of the deferred
  annuity.

21
Annuities Present Value of a Deferred
Annuity(Table 6-4)
1. Present value of an ordinary annuity (10
periods) 6.71008 2. Less P.V. of an
ordinary annuity (deferred 4 periods)(3.31213) 3
. Present value of an annuity (6 periods)
3.39795 4. Present value of the deferred
annuity 5,000 3.39795 16,989.75