Chapter 6 Discounted Cash Flow Valuation 0
0 Chapter 6 Discounted Cash Flow Valuation
Chapter Outline Future and Present values of Multiple Cash Flows Valuing Level Cash Flows:Annuities and Perpetuities Comparing Rates:The Effect of Compounding Periods Loan Types and Loan Amortization
1 Chapter Outline n Future and Present Values of Multiple Cash Flows n Valuing Level Cash Flows: Annuities and Perpetuities n Comparing Rates: The Effect of Compounding Periods n Loan Types and Loan Amortization
Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows ■ Be able to compute loan payments Be able to find the interest rate on a loan Understand how loans are amortized or paid off Understand how interest rates are quoted 2
2 Key Concepts and Skills n Be able to compute the future value of multiple cash flows n Be able to compute the present value of multiple cash flows n Be able to compute loan payments n Be able to find the interest rate on a loan n Understand how loans are amortized or paid off n Understand how interest rates are quoted
Multiple Cash Flows-Future Value Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years.How much will be in the account in five years if the interest rate is 8%? FV=$100(1.08)4+$300(1.08)2=$136.05+$349.92= $485.97 3
3 Multiple Cash Flows – Future Value n Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? § FV = $100(1.08)4 + $300(1.08)2 = $136.05 + $349.92 = $485.97
Time Line 0 7 2 3 4 5 $100 $300 $349.92 $136.05 $485.97 4
4 Time Line $100 0 1 2 3 4 5 $300 $136.05 $349.92 $485.97
Present Value Example 5.3 Time Line 1 2 3 4 200 400 600 800 the interest rate is 12% 5
5 Present Value Example 5.3 Time Line 0 1 2 3 4 200 400 600 800 the interest rate is 12%
Multiple Cash Flows-PV Example 5.3 Find the PV of each cash flow and add them ▣Year1CF:$200/(1.12)1=$178.57 ▣Year2CF:$400/(1.12)2=$318.88 ▣Year3CF:$600/(1.12)3=$427.07 0 Year4CF:$800/(1.12)4=$508.41 Total PV=$178.57+318.88+427.07+ 508.41=$1,432.93 6
6 Multiple Cash Flows – PV Example 5.3 n Find the PV of each cash flow and add them q Year 1 CF: $200 / (1.12)1 = $178.57 q Year 2 CF: $400 / (1.12)2 = $318.88 q Year 3 CF: $600 / (1.12)3 = $427.07 q Year 4 CF: $800 / (1.12)4 = $508.41 q Total PV = $178.57 + 318.88 + 427.07 + 508.41 = $1,432.93
Present Value Example 5.3 Time Line 2 3 4 200 400 600 800 178.57←☐ 318.88 427.07 508.41 1,432.93 7
7 Present Value Example 5.3 Time Line 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93
Multiple Uneven Cash Flows-Using the Calculator Another way to use the financial calculator for uneven cash flows is to use the cash flow keys Texas Instruments BA-ll Plus Clear the cash flow keys by pressing CF and then 2nd CLR Work Press CF and enter the cash flows beginning with year 0. You have to press the "Enter"key for each cash flow ■ Use the down arrow key to move to the next cash flow The"F"is the number of times a given cash flow occurs in consecutive years Use the NPV key to compute the present value by [ENTER]ing the interest rate for I,pressing the down arrow,and then computing NPV 8
8 Multiple Uneven Cash Flows – Using the Calculator n Another way to use the financial calculator for uneven cash flows is to use the cash flow keys q Texas Instruments BA-II Plus n Clear the cash flow keys by pressing CF and then 2nd CLR Work n Press CF and enter the cash flows beginning with year 0. n You have to press the “Enter” key for each cash flow n Use the down arrow key to move to the next cash flow n The “F” is the number of times a given cash flow occurs in consecutive years n Use the NPV key to compute the present value by [ENTER]ing the interest rate for I, pressing the down arrow, and then computing NPV
Example:Spreadsheet Strategies You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows ■ Setting the data up is half the battle-if it is set up properly,then you can just copy the formulas Click on the Excel icon for an example 9
9 Example: Spreadsheet Strategies n You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows n Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas n Click on the Excel icon for an example