Chapter 4.9® - Determining the Discount Rate using Basic Present Value equation & Finding the Number of Accounting Periods

• 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

We can determine the discount rate in an investment by using the basic present value equation. The equation is;

There are 4 parts to this equation: the present value (PV), the future value (FVt), the discount rate (r) and life of the investment (t). If we are given 3 of these factors, we can easily find the fourth one.

Let’s consider an example where we have $1,000 and we are offered to put it in investments that will double this money in 8 years, what is the rate of return we are getting? In other words, we are trying to find the rate of return given the present value, future value and # of periods (years). To calculate the discount rate, let’s plug these numbers in to an equation:

To solve this equation, we must take a 1/8th root from each side. To take the 8th root from each side, on your calculate, press 2 yx 0.125 = ?
Note: We come up with 0.125 because 1 / 8 equal 0.125

The 8th root turns out to be about 1.09, which implies that the rate of return is 9%

What if we do this calculation using our financial calculator? Here are the variables

Notice both methods bring us 9% as the rate of return.

Finding the Number of Periods

Suppose we need to buy a BMW 745i for $60,000 and currently we have $25,000 on hand. If we can earn 7% rate of return on this principal balance, how much time do we need to wait before we have $60,000? This answer involves solving for the last variable in the basic present value equation, number of periods. Let’s manipulate the present value equation to derive our answer.

Next we look at 2.24 in the Future Value of a Lump Sum table in the 7% column. The answer is 12 years, which is close to what our financial calculator will tell us.

If we do this calculation using our financial calculator, here are the numbers plugged in:

As you can see from our answer, we would need to wait 12.9 years for our original principal of $25,000 to grow to $60,000 at a rate of 7% interest compounded annually.