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**Financial Accounting, Seventh Edition**

Appendix C Time Value of Money Financial Accounting, Seventh Edition

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**Study Objectives Distinguish between simple and compound interest.**

Solve for future value of a single amount. Solve for future value of an annuity. Identify the variables fundamental to solving present value problems. Solve for present value of a single amount. Solve for present value of an annuity. Compute the present value of notes and bonds. Use a financial calculator to solve time value of money problems. 1. On the topic, “Challenges Facing Financial Accounting,” what did the AICPA Special Committee on Financial Reporting suggest should be included in future financial statements? Non-financial Measurements (customer satisfaction indexes, backlog information, and reject rates on goods purchases). Forward-looking Information Soft Assets (a company’s know-how, market dominance, marketing setup, well-trained employees, and brand image). Timeliness (no real time financial information)

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**Basic Time Value Concepts**

Time Value of Money In accounting (and finance), the term indicates that a dollar received today is worth more than a dollar promised at some time in the future.

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**Basic Time Value Concepts**

Nature of Interest Payment for the use of money. Excess cash received or repaid over the amount borrowed (principal). Variables involved in financing transaction: Principal (p) - Amount borrowed or invested. Interest Rate (i) – An annual percentage of the principal. Time (n) - The number of years or portion of a year that the principal is borrowed or invested.

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**Simple Interest Full Year Principal $4,000.00**

Interest computed on the principal only. ILLUSTRATION: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ withdraw assuming the investment earns simple interest? Full Year Principal $4,000.00 Annual interest rate % Annual Interest $200.00 SO 1 Distinguish between simple and compound interest.

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**Simple Interest – Multiple Years**

ILLUSTRATION continued: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ earn as interest through the end of the third year using simple interest calculations? Multiple Year Principal $4,000.00 Annual interest rate % Annual Interest $200.00 Duration in years 2011 interest $600.00 SO 1 Distinguish between simple and compound interest.

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**Compound Interest Principal $4,000.00**

ILLUSTRATION: Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ withdraw assuming the investment earns interest compounded annually? (Round to two decimal places.) Principal $4,000.00 Future value factor for 10 periods at 5% Annual Interest $6,515.56 SO 1 Distinguish between simple and compound interest.

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**Compound Interest Proof**

EOY 1 [Principal + (Principal × 5%)] $4,200.00 EOY 2 [Balance + (Balance × 5%)] $4,410.00 EOY 3 [$4, ($4, × 5%)] $4,630.50 EOY 4 [$4, ($4, × 5%)] $4,862.03 EOY 5 [$4, ($4, × 5%)] $5,105.13 EOY 6 [$5, ($5, × 5%)] $5,360.39 EOY 7 [$5, ($5, × 5%)] $5,628.41 EOY 8 [$5, ($5, × 5%)] $5,909.83 EOY 9 [$5, ($5, × 5%)] $6,205.32 EOY 10 [$6, ($6, × 5%)] $6,515.59 EOY – End of year SO 1 Distinguish between simple and compound interest.

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**Partial Year Interest Partial Year Principal $4,000.00**

Interest computed on the principal only. ILLUSTRATION: On April 1, 2011, Russ Holub invested $4,000 at 5% annual interest, and left the money invested without withdrawing any of the interest for 10 years. At the end of the 10 years, Russ withdrew the accumulated amount of money. What amount did Russ earn as interest in year 2011? Partial Year Principal $4,000.00 Annual interest rate % Annual Interest $200.00 9 months of 12 months /12 2011 interest $150.00 SO 1 Distinguish between simple and compound interest.

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**Compound Interest Computes interest on the principal and**

any interest earned that has not been paid or withdrawn. Most business situations use compound interest. With simple interest Russ earned $ through the end of the third year while he earned $ in the same duration using compound interest calculations. SO 1 Distinguish between simple and compound interest.

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**Future Value Concepts Future Value of a Single Amount**

The value at a future date of a given amount invested assuming compound interest. FV = p x (1 + i )n Illustration C-3 Formula for future value FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods SO 2 Solve future value of a single amount.

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**Future Value Concepts Future Value of a Single Amount**

The value at a future date of a given amount invested assuming compound interest. Exercise: Racine Company signed a lease for an office building for a period of 10 years. Under the lease agreement, a security deposit of $10,000 is made. The deposit will be returned at the expiration of the lease with interest compounded at 4% per year. What amount will Racine receive at the time the lease expires? SO 2 Solve future value of a single amount.

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**Future Value Concepts What table do we use? Present Value $10,000**

2 4 6 8 10 12 Exercise: Racine’s deposit of $10,000 will earn 4% per year, compounded annually, during the 10-year lease, what amount will Racine receive at the end of the lease? What table do we use? SO 2 Solve future value of a single amount.

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**Future Value Concepts What factor do we use? TABLE 1 Future Value of 1**

Interest: 4% 5% 6% 8% Periods 1 2 3 4 5 6 7 8 9 10 11 12 What factor do we use? SO 2 Solve future value of a single amount.

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**Present value x Future value factor = Future amount**

Future Value Concepts TABLE 1 Future Value of 1 Interest: 2% 4% 6% 8% Periods 1 2 3 4 5 6 7 8 9 10 11 12 $10,000 x = $14,802.40 Present value x Future value factor = Future amount SO 2 Solve future value of a single amount.

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**Compound Interest Proof**

EOY 1 [Principal + (Principal × 4%)] $10,400.00 EOY 2 [Balance + (Balance × 4%)] $10,816.00 EOY 3 [$10, ($10, × 4%)] $11,248.60 EOY 4 [$11, ($11, × 4%)] $11,698.50 EOY 5 [$11, ($11, × 4%)] $12,166.50 EOY 6 [$12, ($12, × 4%)] $12,653.20 EOY 7 [$12, ($12, × 4%)] $13,159.30 EOY 8 [$13, ($13, × 4%)] $13,685.70 EOY 9 [$13, ($13, × 4%)] $14,233.10 EOY 10 [$14, ($14, × 4%)] $14,802.40 EOY – End of year (Rounded at each step) SO 1 Distinguish between simple and compound interest.

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**Future Value Concepts What table do we use? Present Value $10,000**

2 4 6 8 10 12 Exercise: Racine’s deposit of $10,000 will earn 4% per year, compounded semiannually, during the 10-year lease, what amount will Racine receive at the end of the lease? What table do we use? SO 2 Solve future value of a single amount.

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**Future Value Concepts What factor do we use? 20 compounding periods**

TABLE 1 Future Value of 1 Interest: 2% 4% 6% 8% Periods 1 2 9 10 11 12 18 19 20 21 What factor do we use? 20 compounding periods 2% interest per period SO 2 Solve future value of a single amount.

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**Present value x Future value factor = Future amount**

Future Value Concepts TABLE 1 Future Value of 1 Interest: 2% 4% 6% 8% Periods 1 2 9 10 11 12 18 19 20 21 $10,000 x = $14,859.50 Present value x Future value factor = Future amount SO 2 Solve future value of a single amount.

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**Future Value Concepts Annuity requires the following:**

Periodic payments or receipts of the same amount, Same-length interval between payments or receipts, Compounding of interest each interval. The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them. SO 3 Solve for future value of an annuity.

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**Future Value Concepts Future Value of an Annuity**

Rents occur at the end of each period. No interest during 1st period. Present Value Future Value $20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 1 2 3 4 5 6 7 8 SO 3 Solve for future value of an annuity.

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**Present Value Payments (in thousands) Future value**

Future Value Concepts Present Value Payments (in thousands) Future value 0 $ ? Exercise: Chaffee Company issued $1,000,000, 10-year bonds and agreed to make annual sinking fund deposits of $75,000. The deposits are made at the end of each year into an account paying 6% annual interest. What amount will be in the sinking fund at the end of 10 years? What table do we use? SO 3 Solve for future value of an annuity.

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**Future Value Concepts What factor do we use? Table 2**

Value of an Annuity of 1 Interest 4% 5% 6% 8% Period 1 2 3 4 5 6 7 8 9 10 11 12 What factor do we use? SO 3 Solve for future value of an annuity.

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**Present value x Future value factor = Future amount**

Future Value Concepts Table 2 Value of an Annuity of 1 Interest 4% 5% 6% 8% Period 1 2 3 4 5 6 7 8 9 10 11 12 $75,000 x = $988,559.25 Present value x Future value factor = Future amount SO 3 Solve for future value of an annuity.

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**Present Value Concepts**

The present value is the value now of a given amount to be paid or received in the future, assuming compound interest. Present value variables: Dollar amount to be received in the future, Length of time until amount is received, and Interest rate (the discount rate). SO 4 Identify the variables fundamental to solving present value problems.

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**Present Value Concepts**

Present Value of a Single Amount PV = FV / (1 + i )n Illustration C-9 Formula for present value PV = present value of a single amount FV = future value of a single amount p = principal (or present value) i = interest rate for one period n = number of periods SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

Present Value of a Single Amount Multiply the present value factor by the future value. Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return? SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

Future Value $500,000 1 2 3 4 5 6 Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return? What table do we use? SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

TABLE 3 Present Value of 1 Interest 8% 9% 10% 11% Period 1 2 3 4 5 6 7 8 9 10 11 12 What factor do we use? SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

TABLE 3 Present Value of 1 Interest 8% 9% 10% 11% Period 1 2 3 4 5 6 7 8 9 10 $500,000 x = $310,460.00 Future value x Present value factor = Future amount SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

Future Value $500,000 1 2 3 4 5 6 Exercise: Gonzalez Company is considering an investment that will return a lump sum of $500,000 five years from now. What amount should Gonzalez Company pay for this investment in order to earn a 10% return if interest is compounded semiannually? What table do we use? SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

TABLE 3 Present Value of 1 Interest 4% 5% 6% 8% Period 1 2 3 4 5 6 7 8 9 10 11 12 What factor do we use? SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

TABLE 3 Present Value of 1 Interest 4% 5% 6% 8% Period 1 2 3 4 5 6 7 8 9 10 $500,000 x = $306,955.00 Future value x Present value factor = Future amount SO 5 Solve for present value of a single amount.

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**Present Value Concepts**

Present Value of an Annuity The value now of a series of future receipts or payments, discounted assuming compound interest. Present Value $100,000 100,000 100,000 100,000 100,000 100,000 1 2 3 4 19 20 SO 6 Solve for present value of an annuity.

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**Present Value Concepts**

$30,000 30,000 30,000 30,000 30,000 30,000 1 2 3 4 14 15 Exercise: Bosco Company is considering investing in an annuity contract that will return $30,000 annually at the end of each year for 15 years. What amount should Bosco Company pay for this investment if it earns a 6% return? What table do we use? SO 6 Solve for present value of an annuity.

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**Present Value Concepts**

TABLE 4 Present Value of an Annuity of 1 Interest 4% 5% 6% 8% Period: 1 2 3 7 8 9 10 14 15 16 17 What factor do we use? SO 6 Solve for present value of an annuity.

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**Present Value Concepts**

TABLE 4 Present Value of an Annuity of 1 Interest 4% 5% 6% 8% Period: 1 2 3 7 8 9 10 14 15 16 17 $30,000 x = $291,367.50 Receipt x Present value factor = Present value SO 6 Solve for present value of an annuity.

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**Present Value Concepts**

Present Value of a Long-term Note or Bond Two Cash Flows: Periodic interest payments (annuity). Principal paid at maturity (single-sum). 100,000 $5,000 5,000 5,000 5,000 5,000 5,000 2 4 6 8 18 20 SO 7 Compute the present value of notes and bonds.

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**Present Value Concepts**

$5,000 5,000 5,000 5,000 5,000 105,000 1 2 3 4 9 10 Exercise: Midwest Railroad Co. is about to issue $100,000 of 10-year bonds paying a 10% interest rate, with interest payable semiannually. The discount rate for such securities is 8%. How much can Midwest expect to receive from the sale of these bonds? SO 7 Compute the present value of notes and bonds.

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**Present Value Concepts - Interest**

TABLE 4 Present Value of an Annuity of 1 Interest 4% 5% 6% 8% Period: 1 2 3 8 9 10 11 12 18 19 20 $5,000 x = $67,951.65 Interest Payment x PV factor = Present value SO 7 Compute the present value of notes and bonds.

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**Present Value Concepts - Principal**

TABLE 3 Present Value of 1 Interest 4% 5% 6% 8% Period 1 2 3 8 9 10 11 12 18 19 20 $100,000 x = $45,639.00 Principal x Present value factor = Present value SO 7 Compute the present value of notes and bonds.

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**Present Value Concepts**

Exercise: Midwest Railroad Co. is about to issue $100,000 of 10-year bonds paying a 10% interest rate, with interest payable semiannually. The discount rate for such securities is 8%. How much can Midwest expect to receive from the sale of these bonds? Present value of principal $45,693.00 Present value of interest 67,951.65 Bond present value $113,590.65 Date Account Title Debit Credit Cash 113,590.65 Bonds Payable 100,000.00 Premium on Bonds Payable 13,590.65 SO 7 Compute the present value of notes and bonds.

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**Using Financial Calculators**

Illustration C-22 Financial calculator keys N = number of periods I = interest rate per period PV = present value (occurs at the beginning of the first period) PMT = payment (all payments are equal, and none are skipped) FV = future value (occurs at the end of the last period. SO 8 Use a financial calculator to solve time value of money problems.

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**Using Financial Calculators**

Interest Rate for an Investment Reba McEntire wishes to invest $19,000 on July 1, 2011, and have it accumulate to $49,000 by July 1, Use a financial calculator to determine at what exact annual rate of interest Reba must invest the $19,000. 10 49,000 ?? 19,000 9.94% SO 8 Use a financial calculator to solve time value of money problems.

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**Using Financial Calculators**

Present Value of an Annuity On June 1, 2011, Shelley Long purchases lakefront property from her neighbor, Joey Brenner, and agrees to pay the purchase price in seven payments of $16,000 each, the first payment to be payable June 1, (Assume that interest compounded at an annual rate of 7.35% is implicit in the payments.) What is the purchase price of the property? -16,000 7 ?? 85,186.34 7.35 SO 8 Use a financial calculator to solve time value of money problems.

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**Using Financial Calculators**

Useful Applications – Auto Loan Bill Schroeder owes a debt of $35,000 from the purchase of his new sport utility vehicle. The debt bears annual interest of 9.1% compounded monthly. Bill wishes to pay the debt and interest in equal monthly payments over 8 years, beginning one month hence. What equal monthly payments will pay off the debt and interest? 8 × 12 9.1 ÷ 12 35,000 SO 8 Use a financial calculator to solve time value of money problems.

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**Using Financial Calculators**

Useful Applications – Bonds On January 1, 2011, Cooke Corporation purchased 200 of the $1,000 face value, 8% coupon, 10-year bonds of Howe Inc. The bonds mature on January 1, 2021, and pay interest annually beginning January 1, Cooke purchased the bonds to yield 10.65%. How much did Cooke pay for the bonds? 10 10.65 ? 16,000 200,000 -168,323.64 SO 8 Use a financial calculator to solve time value of money problems.

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