TIME VALUE OF MONEY

Prepared by J. Wu

Oct. 2014

The Time-Value-of-Money Concept

• Used Car: immediate cash payment of $22,500?

6% financing option with $395 monthly payment?

• Retirement plan: how much must you invest to establish a fund

sufficient to pay for your retirement in 45 years if you’re 20 years old now?

• Mortgage Loan: How much to pay for interest?

How much to pay for principal?

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Accounting Issues Associated With PV & FV Techniques

• Valuation Of Long-term Notes Receivable & Payable • Bonds Pricing & Amortization Of Bond Premiums Or

Discounts • Valuation & Accounting For Long-term Capital Leases • Accounting For Pension Funds • Analyzing Investment Alternatives • Mortgages Schedules & Periodic Payments On Long-term

Purchase Contracts • Business Valuation In Mergers & Acquisitions • Impairment Of Long Term Assets • Estimating The Fair Value Of Intangible Assets

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Computing the Amount of Interest

• What is Interest?

• Simple Interest

• Compound Interest

(1 )

FV=Futrue Value

PV=Present Value

CI=Compound Interest

i=Interest Rate Per Compounding Period

n=Number of Compounding Period

nFV PV i

CI FV PV

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Future and Present Value Techniques

• Future Value of a Single Payment

(Table I)

• Present Value of a Single Payment

(Table II)

(1 ) Where

FV = Futrue Value

P = Principal Amount To Be Accumulated

i = Interest Rate Per Period

n=Number of Periods

nFV P i

1 Where

(1 )

PV = Present Value

A = Accumulated Amount To Be Discounted

i = Interest Rate Per Period

n=Number of Periods

nPV A

i

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Future and Present Value Techniques (continued)

• Future Value of an Ordinary Annuity

(Table III)

• Present Value of an Ordinary Annuity

(Table IV)

(1 ) 1 Where

FV = Future Value of an Ordinary Annuity

R = Annuity Payment To Be Accumulated

i = Interest Rate Per Period

n=Number of Periods

niFV RAnord i

Anord

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(1 ) Where

PV = Present Value of an Ordinary Annuity

R = Annuity Payment To Be Discounted

i = Interest Rate Per Period

n=Number of Periods

n

Anord

Anord

iPV R

i

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Future and Present Value Techniques (continued)

• Future Value of an Annuity Due

(Table V)

• Present Value of an Annuity Due

(Table VI)

(1 ) 1

1 1 Where

Future Value of an Annuity Due

FV Future Value of an Ordinary Annuity

R = Annuity Payment To Be Accumulated

i = Interest Rate Per Period

n=Numb

Andue Anord

Andue

Anord

niFV FV i R i

i

FV

er of Periods

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(1 )1 1 Where

Present Value of an Annuity Due

PV Present Value of an Ordinary Annuity

R = Annuity Payment To Be Accumulated

i = Interest Rate Per Per

n

Andue Anord

Andue

Anord

iPV PV i R i

i

PV

iod

n=Number of Periods7

Future and Present Value Techniques (continued)

• Business (Financial) Calculator

HP10B or the TI BA Plus

• Excel Spreadsheet Functions

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Business Applications

• Example 1—Future Value of a Single Payment Marywhether Company loans its president, Celia Phillips, $45,000 to purchase a car. Marywhether accepts a note due in four years with interest at 10% compounded semiannually. How much cash does Marywhether expect to receive from Phillips when the note is paid at maturity?

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Business Applications (continued)

• Example 2—Present Value of a Single Payment Edgemont Enterprises holds a note receivable from a regular customer. The note is for $22,000, which includes principal and interest, and is due to be paid in exactly two years. The customer wants to pay the note now, and both parties agree that 10% is a reasonable annual interest rate to use in discounting the note. How much will the customer pay Edgemont Enterprises today to settle the obligation? ($18,181)

10

Business Applications (continued)

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Business Applications (continued)

• Example 4—Future Value of an Annuity Boswell Co. owes an installment debt of $1,000 per quarter for five years. The creditor has indicated a willingness to accept an equivalent single payment at the end of the 5-year period instead of the series of equal payments made at the end of each quarter. If the money is worth 16% compounded quarterly, what is the equivalent single payment at the end of the contract period? ($29,778)

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Business Applications (continued)

• Example 5—Present Value of an Annuity Mary Sabin, proprietor of Sabin Appliance, received two offers for her last deluxe-model refrigerator. Jerry Sloan will pay $6,500 in cash. Elise Jensen will pay $7,000 consisting of a down payment of $1,000 and 12 monthly payments of $500. If the installment interest rate is 24% compounded monthly, which offer should Sabin accept? ($6,500 vs. $6,288)

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Business Applications (continued)

• Example 6—Determining the Number of Periods Rocky Mountain Survey Company wants to purchase new equipment at a cost of $100,000. The company has $88,850 available in cash but does not want to borrow the other $11,150 for the purchase. If the company can invest the $88,850 today at an interest rate of 12% compounded quarterly, how many years will it be before Rocky Mountain will have the $100,000 it needs to buy the equipment? (1 year)

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Business Applications (continued)

• Example 7—Determining the Interest Rate The Hughes family wishes to purchase a used grand piano. The cost of the piano one year from now will be $5,800. If the family can invest $5,000 now, what annual interest rate must they earn on their investment to have $5,800 at the end of one year? (16%)

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Business Applications (continued)

• Example 8—Determining the Amount of Payment Provo 1st National Bank is willing to lend a customer $75,000 to buy a warehouse. The note will be secured by a 5-year mortgage and carry an annual interest rate of 12%. Equal payments are to be made at the end of each year over the 5-year period. How much will the yearly payment be? ($20,286)

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Business Applications (continued)

• Example 9—Calculating Annuity-Due Values for Future Amounts Porter Corporation desires to accumulate funds to retire a $200,000 bond issue at the end of 15 years. Funds set aside for this purpose can be invested to yield 8%. What annual payment, starting immediately, would provide the needed funds? ($6,821)

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Business Applications (continued)

• Example 10—Calculating Annuity-Due Values for Present Values Utah Corporation has completed negotiations to lease equipment with a fair market value of $45,897. The lease contract specifies semiannual payments of $3,775 for 10 years beginning immediately. At the end of the lease, Utah Corporation may purchase the equipment for a nominal amount. What is the implicit annual rate of interest on the lease purchase? (12%)

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t • The FASB’s conceptual framework allows for various measurement

attributes, one of which is discounted present values.

• Further attention: In February 2000, the FASB released Statement of Financial Accounting Concepts No. 7, “Using Cash Flow Information and Present Value in Accounting Measurement.”

• The FASB has addressed the following issues:

– Under what circumstances an amount should be recognized in financial statements based on the present value of estimated future cash flows;

– When it is appropriate to use the effective interest method in accounting allocations over the life of an asset or liability;

– When the interest element involved with present-value-based measurements should be recognized as interest revenue or expense;

– How to reflect uncertainty in the calculation of present values.

• The application of the present value & future value techniques in the computation of fair values for accounting purposes is illustrated in the Fair Value Module in the textbook. 19