Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 09 The Time Value of Money Block, Hirt, and Danielsen Copyright © 2014 McGraw-Hill

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.

09The Time Value of Money

Block, Hirt, and Danielsen

Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.


• Time value associated with money• Determining future value at given interest rate• Present value based on current value of funds

to be received• Determining yield on investment.• Compounding or discounting occurring on less

than annual basis

Chapter Outline

9-2


• Time value of money used to determine whether future benefits sufficiently large to justify current outlays

• Mathematical tools of time value of money used in making capital allocation decisions

Relationship to The Capital Outlay Decision

9-3


• Measuring value of amount allowed to grow at given interest over period of time• Assuming worth of $1,000 needs to be calculated

after 4 years at 10% interest per year1st year……$1,000 × 1.10 = $1,1002nd year.....$1,100 × 1.10 = $1,2103rd year……$1,210 × 1.10 = $1,3314th year……$1,331 × 1.10 = $1,464

Future Value – Single Amount

9-4



9-5


Future Value of $1(FVIF)

9-6



• In determining future value, following can be used: FV = PV × FVIF

Where FVIF = interest factor

• If $10,000 were invested for 10 years at 8%, future value would be:

FV = PV × FVIF (n = 10, i = 8%)

FV = $10,000 × 2.159 = $21,590

9-7


Present Value – Single Amount

9-8


Present Value of $1(PVIF)

9-9


Relationship of Present and Future Value

9-10


Interest Rate – Single Amount

9-11


Number of Periods – Single Amount

9-12


Future Value – Annuity

• Annuity• A series of consecutive payments or receipts

of equal amount

• Future value of an annuity• Calculated by compounding each individual

payment into the future and then adding up all of these payments

9-13


Future Value – Annuity

9-14


Compounding Process for Annuity

9-15


Future Value of an Annuity of $1(FVIFA)

9-16


Present Value – Annuity

9-17


Present Value of an Annuity of $1(PVIFA)

9-18


• Comparisons include• Relationship between present value and future value

• Inverse relationship exists between present value and future value of single amount

• Relationship between present value of single amount and present value of annuity

• Present value of annuity is sum of present values of single amounts payable at end of each period

• Relationship between future value and future value of annuity

• Future value of annuity is sum of future values of single amounts receivable at end of each period

Time Value Relationships

9-19


• Review of variables involved in time value of moneyFV/PV — Future/present value of moneyN — Number of yearsI — Interest or yieldA — Annuity value/payment per period in annuity

• Given first three variables and determining fourth variable, A (unknown )

Determining the Annuity Value

9-20


Annuity Equaling a Future Value

9-21


Annuity Equaling a Present Value

9-22


Relationship of Present Value to Annuity

Annual interest based on beginning balance for each year

9-23


Loan Amortization

• Mortgage loan to be repaid over 20 years at 8% interest

9-24


Loan Amortization Table

• Part of payments to mortgage company for interest payment, remainder applied to debt reduction

9-25


Six Formulas

9-26


• Compounding frequency• Certain contractual agreements may require

semiannual, quarterly, or monthly compounding periods

• In such cases N = No. of years × No. of compounding periods

during year I = Quoted annual interest / No. of compounding

periods during year

Compounding over Additional Periods

9-27


• Patterns of Payment• Problems may evolve around number of different

payment or receipt patterns• Not every situation involves single amount or

annuity• Contract may call for payment of different amount

each year over stated period or period of annuity

Compounding over Additional Periods

9-28


Compounding Frequency— Cases

• Case 1: Determine the future value of a $1,000 investment after 5 years at 8% annual interest compounded semiannually • Where n = 5 × 2 = 10; i = 8%/2 = 4%

FV = PV × (1 + i)n

FV = $1,000 × (1.04) 10 = $1,480.24

9-29


Compounding Frequency— Cases

9-30


• Assume a contract involving payments of different amounts each year for a three-year period

• To determine the present value, each payment is discounted to the present and then totaled

(Assuming 8% discount rate)

Patterns of Payment with a Deferred Annuity

9-31


• Situations involving combination of single amounts and annuity

• When annuity is paid sometime in future

Deferred Annuity

9-32


Deferred Annuity Case

• Assuming a contract involving payments of different amounts each year for three year period• Annuity of $1,000 paid at end of each year from fourth

through eighth year• To determine present value of cash flows at 8% discount

rate:

9-33


• To determine annuity:


9-34


• To discount $3,993 back to present, which falls at beginning of fourth period, discount back three periods at 8% interest rate


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9-36


Alternate Method to Compute Deferred Annuity

1. Determine present value factor of annuity for total time period, where n = 8, i = 8%, PVIFA = 5.747

2. Determine present value factor of annuity for total time period (8) minus deferred annuity period (5)

8 – 5 = 3; n = 3; i = 8%Value = 2.577

2. Subtract the value of step 2 from the value of step 1, and multiply by A

9-37


Alternate Method to Compute Deferred Annuity

4. $3,170 is same answer for present value of annuity as that reached by first method

5. Present value of five-year annuity is added to present value of inflows over first three years

9-38

Documents

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. 09 The Time Value of Money Block, Hirt, and Danielsen Copyright © 2014 McGraw-Hill