Textbook

If you’ve ever heard the phrase “a dollar received today is worth more than a dollar received tomorrow,” you’re hearing a statement on the time value of money. This is because of **opportunity cost**, which represents the wasted opportunity to invest money.

For example, let’s assume we’re analyzing $1,000 to be received today versus receiving the same $1,000 one year later in an environment where a bank savings account earns only 1% annually. The $1,000 received today can be placed in the savings account and begin earning interest immediately. Even with just a 1% return, the account would earn $10 over the year (assuming interest doesn’t compound monthly). After one year, the investor would have $1,010 in the bank account. Now, compare it to the other scenario - waiting one full year to receive $1,000. The choice should be clear - even with just a small return, receiving money today is more valuable than waiting to receive the same sum of money.

An investor can determine the current value of future money received through **discounted cash flow** tools. By performing a **present value** calculation, an investor is “discounting” future cash flows. Let’s first establish the formula:

$PV=(1+DR)_{n}FV where:PVFVDRn =present value=future value=discount rate=# of years $

Let’s break down the components of this formula, then work through some numbers to better understand this topic. **Future value** is the amount of return (money) to be received in the future. The **discount rate** represents the average rate of return in the market. This is an important factor as it demonstrates the missed opportunity a person experiences if they must wait to receive money in the future. For example, it can be assumed the investor is missing out on a 5% return if the average rate of return in the market is 5%. The ‘**n**’ in the formula refers to the number of years the investor must wait to receive the future return.

*Series 65 test questions on discounted cash flow tend to be conceptual, although it’s possible you’re required to do a present value calculation. If this occurs, the calculation itself is typically simple.*

Let’s work through this example:

An investor is considering the purchase of a $1,000 par, 2-year, 5% corporate debenture currently trading at 97. The rate of return in the market is 6%. What is the present value of the debenture?

With the information provided in the question, we can calculate the bond’s present value. This is a two-year bond, so we’ll need to do two present value calculations - one for the return received after one year, and another for the return received after two years.

**Present value - year 1**

This bond pays a 5% coupon, which is always based on the bond’s par value ($1,000). Therefore, this bond will pay $50 of annual interest to the investor. In the first year of ownership, this is the only return the investor will gain. Let’s do the first year’s present value calculation:

$PV=(1+DR)_{n}FV $

$PV=(1+0.06)_{1}$50 $

$PV=1.06$50 $

$PV=$47.17$

If the investor must wait a full year to receive $50 when the average rate of return in the market is 6%, then the future return is only worth $47.17 in “today dollars.” Here’s another way to think about it - if the investor had $47.17 today and obtained an average 6% return, they would earn a return of roughly $2.83 ($47.17 x 6%). Earning $2.83 on an original investment of $47.17 results in a total of $50 after one year ($47.17 + $2.83). That’s why $50 received after one full year is considered equivalent to $47.17 today. It’s all about the missed opportunity!

**Present value - year 2**

The bond will pay another $50 in the second year, plus the investor will also receive the $1,000 par value at maturity. With this bond trading at a discount, the investor officially “earns” the discount at maturity. Bottom line - the investor receives $1,050 at the end of year two due to the combination of interest and par value. Let’s do the second year’s present value calculation:

$PV=(1+DR)_{n}FV $

$PV=(1+0.06)_{2}$1,050 $

$PV=1.06_{2}$1,050 $

$PV=1.1236$1,050 $

$PV=$934.50$

If the investor must wait two full years to receive $1,050 when the average rate of return in the market is 6%, then the future return is only worth $934.50 in “today dollars.” Here’s another way to think about it - if the investor had $934.50 today and obtained an average 6% return (compounded over two years), they would earn a return of roughly $115.50 (represents a compounded 6% return on $934.50 over two years). Earning $115.50 on an original investment of $934.50 results in a total of $1,050 after one year ($934.50 + $115.50). That’s why $1,050 received after two full years is considered equivalent to $934.50 today. Again, it’s all about the missed opportunity!

**Putting it all together**

To determine the total present value of the bond, we will now add the two years of present value we just calculated:

$Total PV=Year 1 PV + Year 2 PV$

$Total PV=$47.17 + $934.50$

$Total PV=$981.67$

From a pure “time value of money” perspective, the present value of the bond is $981.67. We discounted the future cash flow from this bond back to its value in today’s dollars. By doing so, we have an indicator of the bond’s value. We’ll learn more about this in a future chapter, but we can utilize this information to determine whether the bond is a good or bad deal at its current market price. Here’s a quick clue - it might be underpriced!

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