# Chapter 3 Time Value of Money

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• 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%

## 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
• 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

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