Mod 8 Present Values andLong-Term Liabilities

PRESENT VALUES:• A dollar received today is worth much more than a

dollar to be received in 20 years. Why?– Inflation, risk of not receiving the dollar, and immediate

versus deferred spending• Two components determine the “time value” of

money:– interest (discount) rate– number of periods of discounting

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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.

• Accounts that often require PV calculations:– bonds payable and bond investments – long-term notes payable – Long-term leases– Employee pensions

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Types of Present Value Calculations

• PV of a single sum (PV1): discounting a future value of a single amount that is to be paid in the future (ex: face value of bonds payable).

• PV of an ordinary annuity (PVOA): 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 (ex: interest on bonds payable).

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Present Value of a Single Sum

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 the PV1:

1. Formula: PV1 = FV1 [1/(1+i)n]2. Tables: Table 1

PV1 Table

PV1 = FV1( ) i, n

3.Calculator (with time value functions)4.Spreadsheet

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Illustration 1: L.T. Notes Payable

• Long-term, usually issued to financial institutions.• May be interest bearing or non-interest bearing (we

will look at non-interest bearing).• Illustration 1: On January, 2, 2009, 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 today, if a 6 percent discount rate is assumed?

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Illustration 1 SolutionSee Table 1

PV1 Table 1

PV1 = FV1( ) i, n PV1 Table1 i=6%, n=5

Journal entry Jan. 2, 2009:

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2. Present Value of an Ordinary Annuity (PVOA)

An annuity is defined as equal payments over equal periods of time. An ordinary annuity assumes that each payment occurs at the end of each period.PVOA 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 PVOA:1. Formula: PVOA = A [1-(1/(1+i)n)] / i 2. Tables: see page A-2 (back of text), Table 2

PVOA Table

PVOA = A( ) i, n

3.Calculator (with time value functions)4.Spreadsheet

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Illustration 2: Long Term Notes Payable

• Illustration 2: 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 2 SolutionSee Appendix A, Table 2

PVOA Table

PVOA = A ( ) i, n PVOA Table

= i=6%, n=5

Journal entry Jan. 2, 2008:

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Bonds Payable

• Bonds payable are issued by a company (usually to the marketplace) to generate cash flow.

• The bonds represent a promise by the company to pay a stated interest each period (yearly, semiannually, quarterly), and pay the face amount of the bond at maturity.

• The marketplace values bonds by discounting the cash flows using the market rate of interest. This is also called the yield rate, discount rate, or effective rate.

• There are two types of cash flows with bonds: PVOA (for interest payments) and PV1(for payment of maturity value).

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Illustration 3: Bonds Payable (Discount)• On January 1, 2006, Corvette Corporation issues

$100,000 of its 5 year bonds which have an annual stated rate of 5%, and pay interest annually each December 31, starting December 31, 2006. The bonds were issued to yield 6% annually.

• Calculate the issue price of the bond:What are the cash flows and factors?(1) Face value at maturity =(2) Stated Interest =

Face value x stated rate x time period

Number of periods = n = 5 yrsDiscount rate = 6% per year

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Illustration 3 : Present Value Calculations

PV of interest annuity:

PVOA Table PVOA Table

PVOA = A( ) = i, n i = 6%, n=5

PV of face value:

PV1 Table PV1 Table

PV =FV1( ) = i, n I = 6%, n=5

Total issue price = Issued at a discount of $4,212 because the company was

offering an interest rate less than the market rate, and investors were not willing to pay as much for the lower interest rate.

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Illustration 3: Journal Entry

The journal entry to record the initial issue of the bond would be:

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Illustration 4: Bonds Payable(Premium)• On July 1, 2005, Mustang Corporation issues

$100,000 of its 5 year bonds which have an annual stated rate of 7%, and pay interest semiannually each June 30 and December 31, starting December 31, 2005. The bonds were issued to yield 6% annually.

• Calculate the issue price of the bond:What are the cash flows and factors?(1) Face value at maturity = $100,000(2) Stated Interest =

Face value x stated rate x time period 100,000 x .07 x 1/2 = $3,500

Number of periods = n = 5 yrs x 2 = 10Discount rate = 6% / 2 = 3% per period

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Illustration 4 - Solution

PV of interest annuity:

PVOA Table PVOA Table

PVOA = A( ) = 3,500 (8.53020) = $29,856 i, n i = 3%, n = 10

PV of face value:

PV1 Table PV1 Table

PV =FV1( ) = 100,000(0.74409)=$74,409 i, n i=3%, n=10

Total issue price = $104,265Issued at a premium of $4,265 because the company was offering an interest rate greater than the market rate, and investors were willing to pay more for the higher interest rate.

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Illustration 4: Journal Entry

The journal entry to record the initial issue of the bond would be:

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Illustration 5: Annuity Income

• Other present value applications include financial decisions. For example:

• 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%, then compare to the $1,000,000 settlement.

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Illustration 5 Solution

PVOA Table

PVOA = A ( ) i, n PVOA Table

= i=4%, n=20

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 ordinary annuity (FVOA): 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 [(1+i)n]2. Table 3

FV1 Table

FV1 = PV1( ) i, n

3.Calculator (with time value functions).4.Excel spreadsheet.

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Illustration 6: InvestmentHolliman 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=6%, n=10 FV1 Table

FV1 = = i=6%, n=10

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4. Future Value of an Ordinary Annuity (FVOA)FVOA 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 FVOA:1. Formula: FVOA = A [(1+i)n - 1] / i 2. Table 4

FVOA Table

FVOA = A( ) i, n

3.Calculator (with time value functions).4.Excel spreadsheets.

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Illustration 7: Future Value of InvestmentJane Smith wants to invest $10,000 at the end of each year for the next 20 years, for her retirement. What balance will she have at the end of 20 years (after the last deposit), assuming a 6% interest rate, compounded annually?

FVOA Table 4

FVOA = A ( ) = i=6%, n=20

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Illustration 8: Future Value of InvestmentJames Holliman wants to accumulate $200,000 at the end of 10 years, for his son’s education fund. What equal amount must he invest annually to achieve that balance, assuming a 6% interest rate, compounded annually?

FVOA Table

FVOA = A ( ) = i=6%, n=10

FVOA Table

= i=6%, n=10

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