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Year 3 CF: 600 / (1.12)3 = 427.07
Year 4 CF: 800 / (1.12)4 = 508.41
Total PV = 178.57 + 318.88 + 427.07 +
Total
508.41 = 1,432.93
508.41
8 Example 6.3 Timeline
0 1 200 2 3 4 400 600 800 178.57
318.88
427.07
508.41
1,432.93
9 Multiple Cash Flows Using a
Multiple
Spreadsheet
Spreadsheet You can use the PV or FV functions in Excel to
You
find the present value or future value of a set of
cash flows
cash
Setting the data up is half the battle – if it is set
Setting
up properly, then you can just copy the
formulas
formulas
Click on the Excel icon for an example 10
10 Multiple Cash Flows – PV
Multiple
Another Example
Another You are considering an investment that will pay
You
you $1,000 in one year, $2,000 in two years and
$3000 in three years. If you want to earn 10%
on your money, how much would you be willing
to pay?
to PV = 1000 / (1.1)1 = 909.09
PV = 2000 / (1.1)2 = 1,652.89
PV = 3000 / (1.1)3 = 2,253.94
PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92 11
11 Decisions, Decisions Your broker calls you and tells you that he has this great investment
Your
opportunity. If you invest $100 today, you will receive $40 in one
year and $75 in two years. If you require a 15% return on
investments of this risk, should you take the investment?
investments Use the CF keys to compute the value of the investment
• CF; CF0 = 0; C01 = 40; F01 = 1; C02 = 75; F02 = 1
• NPV; I = 15; CPT NPV = 91.49 No – the broker is charging more than you would be willing
No
to pay.
to 12
12 Saving For Retirement You are offered the opportunity to put some
You
money away for retirement. You will receive
five annual payments of $25,000 each
beginning in 40 years. How much would you be
willing to invest today if you desire an interest
rate of 12%?
rate Use cash flow keys:
• CF; CF0 = 0; C01 = 0; F01 = 39; C02 = 25,000; F02 = 5;
NPV; I = 12; CPT NPV = 1,084.71
NPV; 13
13 Saving For Retirement Timeline
012 … 39 40 41 42 000 … 0 25K 25K 25K 43 44 25K 25K Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows years 1 – 39 are 0 (C01 = 0; F01 = 39)
The cash flows years 40 – 44 are 25,000 (C02 = 25,000;
F02 = 5)
14
14 Quick Quiz – Part I Suppose you are looking at the following possible cash
Suppose
flows: Year 1 CF = $100; Years 2 and 3 CFs = $200;
Years 4 and 5 CFs = $300. The required discount rate is
7%
7%
What is the value of the cash flows at...

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