# 3. Time value of Money and Present Values

The time value of money concept is core to income-based valuation. In this lesson, I explain it how works in practice and how it accounts for risk.

**Time value of money**

- Income-based valuation is based on a concept called the **time value of money**

- Concept states that the money is worth more the sooner it is received

- This is due to money's future earning potential

**Present Values**

- The current worth of a future sum of money or stream of cash flows given a specified rate of return

- PV = Present Value

- FV = Future value

- r = Discount rate

- N = Number of periods into the future

**Discount rates**

- The discount rate serves to reduce to value of future payments

- The higher the discount rate, the riskier the investment

Income based valuation relies heavily on a concept called the time value of money.

In previous courses we've touched on this topic, but in this lesson, I'm going to explain the time value of money in a lot more detail.

The time value of money concept simply states that money available at the present time is worth more than the same amount in future due to its potential earning capacity.

So in effect, any amount of money is worth more the sooner it is received.

To illustrate this point more clearly, let's say I have $10,000 and I want to lodge it in a savings account with an interest rate of 3%.

The US Government guarantees this investment, so in effect it’s risk free.

Next year, my $10,000 will be worth $10,300, and not the original amount, so my money today is worth more than the equivalent amount in a year's time.

The equation that governs this investment is $10,000 multiplied by one plus the interest rate is equal to $10,300.

If I now divide both sides by 1 plus R, I'll get an equation for present value.

$10,000 is my present value, $10,300 is my future value, and R is called the discount rate.

This equation allows me to convert future cash flows into their present day value.

It’s called discounting and is the fundamental basis for income based valuation.

Now let's take another example of a $12,000 payment I am due to receive in two years.

I'd like to know how much this is worth in the present day.

For payments two years away, we simply discount twice.

So our equation this time round will be our answer is equal to $12,000, which is our future value, multiplied by one, divided by one plus R, all to be squared, because the payment is two years away.

To find the correct answer, we must just decide on a discount rate.

If I’m guaranteed this money in two years, then 3% or the risk free rate, seems like a reasonable value for R.

So if I put this into the equation, I'll see that in today's money, my future payment is worth $11,311, but how should I account for this payment if it’s a lot riskier and it's not quite guaranteed? Well, a safe dollar is worth more than a risky dollar, so in our equation we'll either have to increase the discount rate or decrease the future value.

I don't want to change the future value, because that's still the same, so to account for riskiness we'll increase the discount rate.

So if I recalculate our present value for a 15% discount rate, you'll see that we now have a much lower present value of $9,074.

And this is how the time value of money accounts for risk.

If we have a future payment that's quite risky, we simply increase the discount rate, which will lower the present day value of this future payment.

The examples we’ve taken so far are for single payments that are going to be received in the future.

However, most investment projects involve multiple future payments.

In the next lesson, we'll build a model in Excel that will calculate the present value of 10 future cash flows for a wind farm that’s for sale, and still has 10 years of operating life remaining.

# Contents

#### 1. Why Learn About Valuation

4 mins

#### 8. Limitations of IRR

3 mins

#### 9. Payback Period

3 mins

#### 10. IRR Versus NPV

3 mins

#### 19. Cost-Based Valuation

3 mins