Chapter 6: Time Value of Money Concepts

1
Chapter 6 Accounting and the Time Value of Money
2
Accounting Applications

• Notes
• Leases
• Pensions
• Long-term assets
• Sinking funds
• Business combinations
• Disclosures
• Installment contracts

3
Variables in Interest Computations

• Principal The amount borrowed or invested
• Interest rate A percentage of the outstanding
  principle.
• Time the number of years or fractional portion
  of a year that principal is outstanding.

4
Basic Time Diagram
5
Choosing an Interest Rate in Time Value
Measurements

• The appropriate interest rate depends on
• the pure rate of interest
• credit risk rate of interest
• expected inflation rate of interest
• The higher the credit risk, the higher the
  interest rate.

6
Choosing an Interest Rate in Time Value
Measurements

• the pure rate of interest -What the lender would
  charge if there were no possibilities of default
  and no expectation of inflation
• credit risk rate of interest The government has
  little or no credit risk (i.e,, risk of
  nonpayment) when it issues bonds. A business
  enterprise, however, depending upon its financial
  stability, profitability, etc., can have a low or
  a high credit risk.
• expected inflation rate of interest - Lenders
  recognize that in an inflationary economy, they
  are being paid back with less valuable dollars.
  As a result, they increase the interest rate to
  compensate for this loss in purchasing power.

7
Choosing an Interest Rate in Time Value
Measurements
8
Simple and Compound Interests

• Simple interest is determined on the principal
  only.
• principal x interest rate () x 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  withdrawn).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.

9
3 Options for Calculating These Amts
1.) Use the Compound Interest Tables 2.) Use
Formulas 3.) Use your Calculator
You do not need to know every method just use the
method that you are most comfortable with
10
1.) Compound Interest Tables
Five Tables in Chapter 6
Table 1 - Future Value of 1 Table 2 - Present
Value of 1 Table 3 - Future Value of an Ordinary
Annuity of 1 Table 4 - Present Value of an
Ordinary Annuity of 1
LO 3 Use appropriate compound interest tables.
11
2.) Compound Interest Formula

• Present Value Future Value (1/(1i)n)
• Future Value Present Value (1i)n
• FVF-OAn,i ((1i)n 1)/i
• PVF-OAn,i (1-(1/(1i)n)/i
• where i interest rate
• n number of periods

12
Interest Rates and Frequency Compounding
Assumed interest rate per year 12
13
Single Sum Problems

• Typically one of two types
• Computing a future value of a known single sum
  present value.
• Computing a present value of a known single sum
  future value.

14
Single Sum Problems Future Value of Single Sum

• Given
• Amount of deposit today (PV) 50,000
• Interest rate 11
• Frequency of compounding Annual
• Number of periods (5 years) 5 periods
• What is the future value of this single sum?
• (use Table 6-1 to determine the factor of
  1.68506)
• 50,000 x (1.68506) 84,253
• OR 50,000(1.11)5 84,252.91

15
Single Sum Problems Present Value of 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
• What is the present value of this single sum?
• (use Table 6-2 to determine the factor of .59345)
• 84,253 x (0.59345) 50,000

16
Annuity Computations

• An annuity requires that
• the periodic payments or receipts (rents) always
  be of the same amount,
• the interval between such payments or receipts be
  the same, and
• the interest be compounded once each interval.

17
Types of Annuities

• Annuities may be broadly classified as
• Ordinary annuities where the rents occur at the
  end of the period.
• Annuities due where rents occur at the beginning
  of the period.

18
Annuities Future Value of an Ordinary Annuity

• Given
• Deposit made at the end of each period 5,000
• Compounding Annual
• Number of periods Five
• Interest rate 12
• What is future value of these deposits?
• Use table 6-3 to derive the factor of 6.35285
• 5,000 x (6.35285) 31,764.25

19
Annuities Present 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
• What is the present value of these receipts?
• Use table 6-4 to derive the factor of
  3.60478 6,000 x (3.60478) 21,628.68

20
Annuities Future Value of an Annuity Due

• Given
• Deposit made at the beginning of each period
• 800
• Compounding Annual
• Number of periods Eight
• Interest rate 12
• What is the future value of these deposits?

21
Annuities Future Value of an Annuity Due

• First Step
• Convert future value of ordinary annuity factor
  to future value for an annuity due
• Ordinary annuity factor 8 periods, 12
  12.29969
• Convert to annuity due factor 12.29969 x 1.12
  13.77565
• Second Step
• Multiply derived factor from first step by the
  amount of the rent
• Future value of annuity due 800 x 13.77565
  11,020.52

22
Annuities Present Value of an Annuity Due

• Given
• Payment made at the beginning of each period
  4.8
• Compounding Annual
• Number of periods Four
• Interest rate 11
• What is the present value of these payments?

23
Annuities Future Value of an Annuity Due

• First Step
• Convert future value of ordinary annuity factor
  to future value for an annuity due
• Ordinary annuity factor 4 periods, 11 3.10245
• Convert to annuity due factor 3.10245 x 1.11
  3.44372
• Second Step
• Multiply derived factor from first step by the
  amount of the rent
• Present value of annuity due 4.8M x 3.44372
  16,529,856

24
Valuation of Long-Term Bonds

• Two Cash Flows
• Periodic interest payments (annuity).
• Principal paid at maturity (single-sum).
• Bonds current market value is the combined
  present values of the both cash flows.

1,000,000
70,000
70,000
70,000
70,000
70,000
70,000
. . . . .
0
1
2
3
4
9
10
LO 8 Solve present value problems related to
deferred annuities and bonds.
25
Valuation of Long-Term Bonds
Present Value
70,000
70,000
70,000
70,000
70,000
1,070,000
. . . . .
0
1
2
3
4
9
10
BE6-15 Arcadian Inc. issues 1,000,000 of 7
bonds due in 10 years with interest payable at
year-end. The current market rate of interest for
bonds is 8. What amount will Arcadian receive
when it issues the bonds?
LO 8 Solve present value problems related to
deferred annuities and bonds.
26
Valuation of Long-Term Bonds
PV of Principal
1,000,000 x .46319 463,190
Principal Payment
Factor
Present Value
PV of Interest
70,000 x 6.71008 469,706
Interest Payment
Factor
Present Value
27
Valuation of Long-Term Bonds
BE6-15 Arcadian Inc. issues 1,000,000 of 7
bonds due in 10 years with interest payable at
year-end.
Present value of Interest 469,706 Present value
of Principal 463,190 Bond current market value
932,896
LO 8 Solve present value problems related to
deferred annuities and bonds.