Chapter 9, Part 2 Time Value of Money

1
Chapter 9, Part 2 Time Value of Money

• 1. Present Value of a Single Amount
• 2. Present Value of an Annuity
• 3. Future Value of a Single Amount
• 4. Future Value of an Annuity

2
Introduction

• The value of a dollar today will decrease over
  time. Why?
• Two components determine the time value of
  money
• interest rate (i) for discounting and
  compounding.
• number of periods (n) for discounting and
  compounding.
• For external financial reporting, we are
  concerned primarily with present value concepts.
• For investment decisions, we are also concerned
  with future value concepts.

3
Introduction

• Future Value concepts
• What amount do we need to invest today to
  accumulate a specific amount at retirement?
• What yearly amounts do we need to invest to
  accumulate a specific future amount in an
  education fund?
• Present Value concepts
• What is the value today of a payment coming some
  time in the future?
• What is the value today of a series of equal
  payments received each year for the next 20
  years?

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Present Value Concepts

• To record activities in the general ledger
  dealing with future cash flows, we should
  calculate the present value of the future cash
  flows using present value formulas or techniques.
• Types of activities that require PV calculations
• investment decisions
• long term notes payable and notes receivable
• bonds payable and bond investments

5
Types of Present Value Calculations

• PV of a single sum (PV1) discounting a future
  value of a single amount that is to be paid or
  received in the future.
• PV of an annuity (PVA) discounting a set of
  payments, equal in amount over equal periods of
  time, where the first payment is made at the end
  of each period.

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1.Present Value of a Single Sum (PV1)

• All present value calculations presume a discount
  rate (i) and a number of periods of discounting
  (n). There are 4 different ways you can calculate
  PV1
• 1. Formula PV1 FV1 1/(1i)n
• 2. Tables see page 370, Table 9-2
• PV1 Table
• PV1 FV1( )
• i, n
• 3.Calculator (if you have time value functions).
• 4.Excel spreadsheet.
• (Note we will use tables in class and on exams.)

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Illustration 1 Long Term Notes Payable

• May be interest bearing or non-interest bearing
  (we will look at non-interest bearing).
• May be serial notes (periodic payments) or term
  notes (balloon payments). We will look at balloon
  payments here (serial payments, or annuities,
  later).
• Illustration 1 On January, 2, 2008, Pearson
  Company purchases a section of land for its new
  plant site. Pearson issues a 5 year non-interest
  bearing note, and promises to pay 50,000 at the
  end of the 5 year period. What is the cash
  equivalent price of the land, if a 6 percent
  discount rate is assumed?

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Illustration1 Solution

• See page 370, Table 9-2
• PV1 Table
• PV1 FV1( )
• i, n
• PV1 Table
• PV1 ( )
• i6, n5
• Journal entry Jan. 2, 2008

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Illustration1 Solution, continued

• Journal entry, December 31, 2008, assuming
  Pearson uses the straight-line method to
  recognize interest expense (12,650 / 5)
• Carrying value on B/S at 12/31/2008?
• Carrying value on B/S at 12/31/2012?

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Illustration 2 Investment

• Holliman Company wants to accumulate 500,000 at
  the end of 10 years. What amount must it invest
  today to achieve that balance, assuming a 6
  interest rate, compounded annually?
• PV1 Table
• PV1 ( )
• i6, n10
• What if the interest is compounded semiannually?
• PV1 Table
• PV1 ( )

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2. Present Value of an Annuity (PVA)

• An annuity is defined as equal payments over
  equal periods of time. (Specifically, we are
  using an ordinary annuity, which assumes that
  each payment occurs at the end of each period.)
• PVA calculations presume a discount rate (i),
  where (A) the amount of each annuity, and (n)
  the number of annuities (or rents), which is
  the same as the number of periods of discounting.
  There are 4 different ways you can calculate
  PVA
• 1. Formula PVA A 1-(1/(1i)n) / i
• 2. Tables see page 372, Table 9-4 (We will use
  this.)
• PVA Table
• PVA A( )
• i, n
• 3.Calculator (if you have time value functions).
• 4.Excel spreadsheets.

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Illustration 3 Long Term Notes Payable

• Illustration 3 On January, 2, 2008, Pearson
  Company purchases a section of land for its new
  plant site. Pearson issues a 5 year non-interest
  bearing note, and promises to pay 10,000 per
  year at the end of each of the next 5 years.
  What is the cash equivalent price of the land, if
  a 6 percent discount rate is assumed?

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Illustration 3 Solution

• See page 372, Table 9-4
• PVA Table
• PVA A ( )
• i, n
• PVA Table
• PVA ( )
• i6, n5
• Journal entry Jan. 2, 2008

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Illustration 4 Annuity Income

• Illustration 4 On January, 2, 2008, Donna Smith
  won the lottery. She was offered an annuity of
  100,000 per year for the next 20 years, or
  1,000,000 today as an alternative settlement.
  Which option should Donna choose. Assume that
  she can earn an average 4 percent return on her
  investments for the next 20 years.
• Solution calculate the present value of the
  annuity at a discount rate of 4.

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Illustration 4 Solution

• See page 372, Table 9-4
• PVA Table
• PVA A ( )
• i, n
• PVA Table
• PVA ( )
• i4, n20
• Which should she choose?
• At approximately what interest (discount) rate
  would she choose differently? (Based on whole
  percentage rate.)

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Types of Future Value Calculations

• FV of a single sum (FV1) compounding a future
  value of a single amount that is to be
  accumulated in the future. Example
• projected future value of a savings bond.
• FV of an annuity (FVA) compounding the future
  value of a set of payments, equal in amount over
  equal periods of time, where the first payment is
  made at the end of the first period. Examples
• projected balance in a retirement account.
• amount of payments into retirement fund.

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3.Future Value of a Single Sum (FV1)

• There are 4 different ways you can calculate the
  FV1
• 1. Formula FV1 PV1 (1i)n
• 2. Tables see page 369, Table 9-1
• FV1 Table
• FV1 PV1( )
• i, n
• 3.Calculator (if you have time value functions).
• 4.Excel spreadsheet.
• (Note we will use tables in class and on exams.)

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Illustration 5 Investment

• Holliman Company wants to invest 200,000 cash it
  received from the sale of land. What amount will
  it accumulate at the end of 10 years, assuming a
  6 interest rate, compounded annually?
• FV1 Table
• FV1 PV1 ( )
• i, n
• FV1 Table
• FV1 ( )
• i6, n10

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4.Future Value of an Annuity (FVA)

• FVA calculations presume a compound rate (i),
  where (A) the amount of each annuity, and (n)
  the number of annuities (or rents), which is
  the same as the number of periods of compounding.
  There are 4 different ways you can calculate
  FVA
• 1. Formula FVA A (1i)n - 1 / i
• 2. Tables see page 371, Table 9-3 (We will use
  this.)
• FVA Table
• FVA A( )
• i, n
• 3.Calculator (if you have time value functions).
• 4.Excel spreadsheets.

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Illustration 6 Future Value of Investment

• Jane Smith wants to invest 10,000 each year for
  the next 20 years, for her retirement. What
  balance will she have at the end of 20 years,
  assuming a 6 interest rate, compounded annually?
• FVA Table
• FVA A ( )
• i, n
• FVA Table
• FVA ( )
• i6, n20

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Illustration 7 Future Value of Investment

• James Holliman wants to accumulate 200,000 at
  the end of 10 years, for his sons education
  fund. What equal amount must he invest annually
  to achieve that balance, assuming a 6 interest
  rate, compounded annually?
• FVA Table
• FVA A ( )
• i, n
• FVA Table
• ( )
• i6, n10