# Chapter 3 Time Value of Money

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9780273713654 pp03

## Steps in the Process

• Steps in the Process
• Step 1: Press CF key
• Step 2: Press 2nd CLR Work keys
• Step 3: For CF0 Press 0 Enter ↓ keys
• Step 4: For C01 Press 600 Enter ↓ keys
• Step 5: For F01 Press 2 Enter ↓ keys
• Step 6: For C02 Press 400 Enter ↓ keys
• Step 7: For F02 Press 2 Enter ↓ keys

## Steps in the Process

• Steps in the Process
• Step 8: For C03 Press 100 Enter ↓ keys
• Step 9: For F03 Press 1 Enter ↓ keys
• Step 10: Press ↓ ↓ keys
• Step 11: Press NPV key
• Step 12: For I =, Enter 10 Enter ↓ keys
• Step 13: Press CPT key
• Result: Present Value = \$1,677.15
• Solving the Mixed Flows Problem using CF Registry

## General Formula:

• General Formula:
• FVn = PV0(1 + [i/m])mn
• n: Number of Years m: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n
• PV0: PV of the Cash Flow today
• Frequency of Compounding

## Julie Miller has \$1,000 to invest for 2 Years at an annual interest rate of 12%.

• Julie Miller has \$1,000 to invest for 2 Years at an annual interest rate of 12%.
• Annual FV2 = 1,000(1 + [0.12/1])(1)(2) = 1,254.40
• Semi FV2 = 1,000(1 + [0.12/2])(2)(2) = 1,262.48
• Impact of Frequency

## Qrtly FV2 = 1,000(1 + [0.12/4])(4)(2) = 1,266.77

• Qrtly FV2 = 1,000(1 + [0.12/4])(4)(2) = 1,266.77
• Monthly FV2 = 1,000(1 + [0.12/12])(12)(2) = 1,269.73
• Daily FV2 = 1,000(1 + [0.12/365])(365)(2) = 1,271.20
• Impact of Frequency
• The result indicates that a \$1,000 investment that earns a 12% annual rate compounded quarterly for 2 years will earn a future value of \$1,266.77.
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 2(4) 12/4 –1,000 0
• 1266.77
• Solving the Frequency Problem (Quarterly)

## Press:

• Press:
• 2nd P/Y 4 ENTER
• 2nd QUIT
• 12 I/Y
• –1000 PV
• 0 PMT
• 2 2nd xP/Y N
• CPT FV
• Solving the Frequency Problem (Quarterly Altern.)
• The result indicates that a \$1,000 investment that earns a 12% annual rate compounded daily for 2 years will earn a future value of \$1,271.20.
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 2(365) 12/365 –1,000 0
• 1271.20
• Solving the Frequency Problem (Daily)

## Press:

• Press:
• 2nd P/Y 365 ENTER
• 2nd QUIT
• 12 I/Y
• –1000 PV
• 0 PMT
• 2 2nd xP/Y N
• CPT FV
• Solving the Frequency Problem (Daily Alternative)
• Source: Courtesy of Texas Instruments

## Effective Annual Interest Rate

• Effective Annual Interest Rate
• The actual rate of interest earned (paid) after adjusting the nominal rate for factors such as the number of compounding periods per year.
• (1 + [ i / m ] )m – 1
• Effective Annual Interest Rate

## Basket Wonders (BW) has a \$1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)?

• Basket Wonders (BW) has a \$1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)?
• EAR = ( 1 + 0.06 / 4 )4 – 1 = 1.0614 - 1 = 0.0614 or 6.14%!
• BWs Effective Annual Interest Rate

## Press:

• Press:
• 2nd I Conv
• 6 ENTER
• ↓ ↓
• 4 ENTER
• ↑ CPT
• 2nd QUIT
• Converting to an EAR
• Source: Courtesy of Texas Instruments

## 1. Calculate the payment per period.

• 1. Calculate the payment per period.
• 2. Determine the interest in Period t. (Loan Balance at t – 1) x (i% / m)
• 3. Compute principal payment in Period t. (Payment - Interest from Step 2)
• 4. Determine ending balance in Period t. (Balance - principal payment from Step 3)
• 5. Start again at Step 2 and repeat.

## Julie Miller is borrowing \$10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years.

• Julie Miller is borrowing \$10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years.
• Step 1: Payment
• PV0 = R (PVIFA i%,n)
• \$10,000 = R (PVIFA 12%,5)
• \$10,000 = R (3.605)
• R = \$10,000 / 3.605 = \$2,774
• Amortizing a Loan Example
• End of
• Year
• Payment
• Interest
• Principal
• Ending
• Balance
• 0
• \$10,000
• 1
• \$2,774
• \$1,200
• \$1,574
• 8,426
• 2
• 2,774
• 1,011
• 1,763
• 6,663
• 3
• 2,774
• 800
• 1,974
• 4,689
• 4
• 2,774
• 563
• 2,211
• 2,478
• 5
• 2,775
• 297
• 2,478
• 0
• \$13,871
• \$3,871
• \$10,000
• [Last Payment Slightly Higher Due to Rounding]
• Amortizing a Loan Example
• The result indicates that a \$10,000 loan that costs 12% annually for 5 years and will be completely paid off at that time will require \$2,774.10 annual payments.
• N
• I/Y
• PV
• PMT
• FV
• Inputs
• Compute
• 5 12 10,000 0
• –2774.10
• Solving for the Payment

## Press:

• Press:
• 2nd Amort
• 1 ENTER
• 1 ENTER
• Results:
• BAL = 8,425.90* ↓
• PRN = –1,574.10* ↓
• INT = –1,200.00* ↓
• *Note: Compare to 3-82
• Source: Courtesy of Texas Instruments

## Press:

• Press:
• 2nd Amort
• 2 ENTER
• 2 ENTER
• Results:
• BAL = 6,662.91* ↓
• PRN = –1,763.99* ↓
• INT = –1,011.11* ↓
• Year 2 information only
• *Note: Compare to 3-82
• Using the Amortization Functions of the Calculator
• Source: Courtesy of Texas Instruments

## Press:

• Press:
• 2nd Amort
• 1 ENTER
• 5 ENTER
• Results:
• BAL = 0.00 ↓
• PRN = – 10,000.00 ↓
• INT = –3,870.49 ↓
• Entire 5 Years of loan information
• (see the total line of 3-82)
• Using the Amortization Functions of the Calculator
• Source: Courtesy of Texas Instruments

## 2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.

• 2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.
• 1. Determine Interest Expense – Interest expenses may reduce taxable income of the firm.
• Usefulness of Amortization

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