Chapter 4.14® - Calculating Present Value with Multiple Future Cash Flows – Example #2

• Part 4.1 - Time Value of Money, Future Values of Compounding Interest, Investing for more than 1 Period & Examination of Original Investment & Growth of Investment
• Part 4.2 - Compounding Interest Homework Problem & Time Value of Money Continued - Future Value Formula, Growth of $100 & Future Value Comparisons
• Part 4.3 - How to Use a Financial Calculator BAII Plus to Perform Time Value of Money & Present / Future Value Calculations
• Part 4.4 - Changing Advanced Function Keys (BGN, C/Y, P/Y), Converting from Nominal Interest to Effective Interest Rates using BAII Financial Calculator
• Part 4.5 - Examples of Interest Rate Calculations & Practice Questions #1 - #7
• Part 4.6 - Nominal to Effective Interest Rate Calculations & Practice Questions #8 - #16
• Part 4.7 - Present Value & Discounting – We Know the Future Value, how do we find the Present Value? Single Period Case & PV Discounting for Multiple Periods
• Part 4.8 - An Example of Present Value Discounting & Saving Up Money & Deriving the Basic Present Value Equation
• Part 4.9 - Determining the Discount Rate using Basic Present Value equation & Finding the Number of Accounting Periods
• Part 4.10 - Summary of Time Value Formulas & Calculations
• Part 4.11 - Discounted Cash Flow Valuations - Future Value of Multiple Cash Flows & Designing the Cash Flows Timeline
• Part 4.12 - Compound the Accumulated Balance Forward One Year at a Time - Discounted Cash Flow Valuation - Determining Present Value of Multiple Future Cash Flows & Designing a Financial Timeline
• Part 4.13 - Determining Present Value of Multiple Future Cash Flows – Homework Example
• Part 4.14 - Calculating Present Value with Multiple Future Cash Flows – Example #2
• Part 4.15 - Valuing Annuity Level Cash Flows – Present & Future Value of Annuities
• Part 4.16 - Calculating Annuity Payments using Annuity Present Value Factor – Example
• Part 4.17 - Accounting for Perpetuities & Using the Annuity Present Value Factor Formula
• Part 4.18 - Accounting for Growing Perpetuities & Simplified Formula for Present Value of Growing Perpetuity - Example of Growing Perpetuity on Rental Cash Flows

Suppose you are offered an investment that will make three $10,000 payments in the future (thus generating future cash flows). The first payment will occur four years from today. The second will occur five years from today and the third payment will occur in six years. If you can earn 13% on other investments, what is the most you would be willing to pay for this investment now? In other words, what is the future value of the cash flows today?

This problem is asking us to solve two problems:

a) Future Value of the cash flows in 6 years

To calculate the future value of individual cash flows, here are the calculations:

Note: We will use the future value discount factor to come up with the answers.

This tells us that the future value of these cash flows, at 13% rate of return is $34,069. Notice how the funds will have grown from 3 rounds of $10,000 contributions totalling $30,000 to $34,069. Thus, what is the investment gain achieved?

b) Present value of the future cash flows

From the value of the future cash flows in 6 years, we can easily calculate the present value using the present value discount factor below:

This tell us that in order to buy this investment, the most you would be willing to pay for this investment right now (present value) is $16,379.33 assuming a rate of return of 13%.

Alternatively, we could calculate the present value by looking at the cash flows one at a time.

Here are the results summarized in tabular and graphical format

This graph above shows the present value of the annual $10,000 contributions each year and tells us the present value is $6,133.19 in Year 4, $5,427.60 in Year 5 and $4,803.19 in Year 6. Notice as the years get older, the present value tends to get smaller.