Chapter 4.13® - Determining Present Value of Multiple Future Cash Flows – Homework Example

• 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

Question:

Suppose you are offered an investment that will pay you $200 in one year, $400 the next year, $600 the following year and $800 at the end of next year. You can earn 9% on such similar investments. That being said, what is the most you would be willing to pay for this investment? In other words, what is the present value of this investment?

Solution:

To solve this problem, we need to calculate the present value of each of these cash flows at 9%. Let’s deal with each one, one at a time:
Note: To solve this problem, we must use the present value discount factor explained in the time value of money chapter.

Below is the data summarized in tabular format and following it is the data shown on a pretty little graph:

Notice from this graph that for instance if at the end of Year 1 we receive a payment of $200 as cash flows, then the present value or discounted value of that cash flow at the end of the year is $183.49. Similarly, an investment that pays $400 at the end of the 2nd year is discounted for present value at $337 now. We can perform these calculations using our financial calculator, let’s actually do it to compare our results.

This graph shows the breakdown of the annual cash payments of $200 in the first year, $400 in the 2nd year, $600 in the third and so on and breaks down the present values of each of these cash flows in a graphical format.

i) Find Present Value of $200 at Year 1, 9% rate of return.

ii) Find Present Value of $400 at Year 2, 9% rate of return.

iii) Find Present Value of $600 at Year 3, 9% rate of return.

iv) Find Present Value of $800 at Year 4, 9% rate of return.