Chapter 3 Time Value of Money

1. Read problem thoroughly

• 1. Read problem thoroughly
• 2. Create a time line
• 3. Put cash flows and arrows on time line
• 4. Determine if it is a PV or FV problem
• 5. Determine if solution involves a single CF, annuity stream(s), or mixed flow
• 6. Solve the problem
• 7. Check with financial calculator (optional)

• Steps to Solve Time Value of Money Problems

Julie Miller will receive the set of cash flows below. What is the Present Value at a discount rate of 10%.

• Julie Miller will receive the set of cash flows below. What is the Present Value at a discount rate of 10%.

• 0 1 2 3 4 5

• $600 $600 $400 $400 $100

• PV0

• 10%

• Mixed Flows Example

1. Solve a “piece-at-a-time” by discounting each piece back to t=0.

• 1. Solve a “piece-at-a-time” by discounting each piece back to t=0.
• 2. Solve a “group-at-a-time” by first breaking problem into groups of annuity streams and any single cash flow groups. Then discount each group back to t=0.

• How to Solve?

• 0 1 2 3 4 5

• $600 $600 $400 $400 $100

• 10%

• $545.45
• $495.87
• $300.53
• $273.21
• $ 62.09

• $1677.15 = PV0 of the Mixed Flow

• “Piece-At-A-Time”

• 0 1 2 3 4 5

• $600 $600 $400 $400 $100

• 10%

• $1,041.60
• $ 573.57
• $ 62.10

• $1,677.27 = PV0 of Mixed Flow [Using Tables]

• $600(PVIFA10%,2) = $600(1.736) = $1,041.60
• $400(PVIFA10%,2)(PVIF10%,2) = $400(1.736)(0.826) = $573.57
• $100 (PVIF10%,5) = $100 (0.621) = $62.10

• “Group-At-A-Time” (#1)

• 0 1 2 3 4

• $400 $400 $400 $400

• PV0 equals
• $1677.30.

• 0 1 2

• $200 $200

• 0 1 2 3 4 5

• $100

• $1,268.00

• $347.20

• $62.10

• Plus

• Plus

• “Group-At-A-Time” (#2)

Use the highlighted key for starting the process of solving a mixed cash flow problem

• Use the highlighted key for starting the process of solving a mixed cash flow problem

• Press the CF key and down arrow key through a few of the keys as you look at the definitions on the next slide

• Solving the Mixed Flows Problem using CF Registry

• Source: Courtesy of Texas Instruments

Defining the calculator variables:

• Defining the calculator variables:
• For CF0: This is ALWAYS the cash flow occurring at time t=0 (usually 0 for these problems)
• For Cnn:* This is the cash flow SIZE of the nth group of cash flows. Note that a “group” may only contain a single cash flow (e.g., $351.76).
• For Fnn:* This is the cash flow FREQUENCY of the nth group of cash flows. Note that this is always a positive whole number (e.g., 1, 2, 20, etc.).

• * nn represents the nth cash flow or frequency. Thus, the first cash flow is C01, while the tenth cash flow is C10.

• Solving the Mixed Flows Problem using CF Registry