Chapter 3 Time Value of Money

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

• Solving the Mixed Flows Problem using CF Registry

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.)

• Source: Courtesy of Texas Instruments

• 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.

• Steps to Amortizing a Loan

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* ↓

• Year 1 information only

• *Note: Compare to 3-82

• Using the Amortization Functions of the Calculator

• 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