Discounted cash flow

If you’ve heard the phrase, “a dollar received today is worth more than a dollar received tomorrow,” you’ve heard the basic idea behind the time value of money. The reason is opportunity cost: money you receive today can be invested, while money you receive later can’t earn returns during the waiting period.

For example, compare receiving $1,000 today versus receiving the same $1,000 one year from now, assuming a bank savings account earns 1% annually.

• If you receive $1,000 today, you can deposit it immediately. At 1% simple interest (assuming interest doesn’t compound monthly), you’d earn $10 over the year and have $1,010 after one year.
• If you wait one year to receive $1,000, you have $1,000 after one year.

Even with a small return, receiving money today is more valuable because it gives you the chance to earn interest or investment returns during the waiting period.

Discounted cash flow

An investor can estimate what future money is worth today using discounted cash flow tools. When you perform a present value calculation, you’re “discounting” future cash flows back into today’s dollars.

Here’s the formula:

$$\begin{gathered} \text{PV}=\frac{\text{FV}}{(1+\text{DR}{)}^n} \\ \begin{array}{rl}\text{where:}& \\ PV& =\text{present value}\\ FV& =\text{future value}\\ DR& =\text{discount rate}\\ n& =\text{\# of years}\end{array} \end{gathered}$$

Before we plug in numbers, it helps to be clear on what each piece means:

• Future value (FV) is the dollar amount you’ll receive in the future.
• Discount rate (DR) is the market rate of return you could reasonably earn elsewhere. It captures the opportunity cost of waiting.
• n is how many years you must wait to receive the future cash flow.

Series 66 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?

To find the bond’s present value, we discount each cash flow back to today. Because this is a two-year bond, there are two cash-flow points to discount:

• the coupon payment at the end of year 1
• the coupon payment plus principal repayment at the end of year 2

Present value - year 1
This bond pays a 5% coupon, and the coupon rate is always applied to the bond’s par value ($1,000). So the annual interest payment is $50.

In year 1, the only cash flow is that $50 coupon. Discount it one year at 6%:

$$\text{PV}=\frac{\text{FV}}{(1+\text{DR}{)}^n}$$

$$\text{PV}=\frac{\text{\$50}}{(1+\text{0.06}{)}^1}$$

$$\text{PV}=\frac{\text{\$50}}{1.06}$$

$$\text{PV}=\text{\$47.17}$$

Interpreting that result: if the market return is 6%, then $50 received one year from now is equivalent to $47.17 today. Another way to see it is that $47.17 invested at 6% grows to about $50 after one year.

Present value - year 2
At the end of year 2, the investor receives:

• another $50 coupon payment, and
• the $1,000 par value at maturity

So the year-2 cash flow is $1,050. Discount it two years at 6%:

$$\text{PV}=\frac{\text{FV}}{(1+\text{DR}{)}^n}$$

$$\text{PV}=\frac{\text{\$1,050}}{(1+\text{0.06}{)}^2}$$

$$\text{PV}=\frac{\text{\$1,050}}{1.06^2}$$

$$\text{PV}=\frac{\text{\$1,050}}{1.1236}$$

$$\text{PV}=\text{\$934.50}$$

Interpreting that result: if the market return is 6%, then $1,050 received two years from now is equivalent to $934.50 today. If you invested $934.50 at 6% for two years (compounded), it would grow to about $1,050.

Putting it all together
To get the bond’s total present value, add the present value of each year’s cash flow:

$$\text{Total PV}=\text{Year 1 PV + Year 2 PV}$$

$$\text{Total PV}=\text{\$47.17 + \$934.50}$$

$$\text{Total PV}=\text{\$981.67}$$

From a time value of money perspective, the bond’s present value is $981.67. This is the value today of the bond’s future cash flows, discounted at the market rate. We’ll build on this in a future chapter, but this present value can be compared to the bond’s current market price to judge whether it appears attractively priced.

Lottery example

A common real-world application of these ideas is a lottery payout. Winners typically choose between two options:

Annuity option - The full jackpot amount paid out over 30 years in annual installments.

Lump sum option - A reduced amount paid immediately (often around half the advertised jackpot).

To compare these options, you can use Time Value of Money (TVM) and Discounted Cash Flow (DCF) to find which choice has the higher present value.

• Because money received today can be invested, each future annuity payment is discounted back to today using an assumed rate of return (the discount rate).
• For example, suppose a $100 million jackpot offers either $50 million today or $3.33 million per year for 30 years. If a 5% discount rate gives the annuity a present value of about $51 million, then the annuity is worth more in today’s dollars than the $50 million lump sum.

In practice, investment potential, inflation, and taxes also affect the decision.