1.3 Present Value of Multiple Cash Flows

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Del curso dictado por Yonsei University

Valuation for Startups Using Discounted Cash Flows Approach

106 calificaciones

Yonsei University

Valuation for Startups Using Discounted Cash Flows Approach

106 calificaciones

Curso 1 de 5 en SpecializationValuation and Financial Analysis For Startups

Discounted cash flow method means that we can find firm value by discounting future cash flows of a firm. That is, firm value is present value of cash flows a firm generates in the future. In order to understand the meaning of present value, we are going to discuss time value of money, first. That is, the value of $100 today is different from the value of $100 a year later. Then, what should be the present value of $100 that you are going to receive in 1 year? How about the value of $100 dollars that you are going to receive every year for next 10 years? How about forever? After taking this course, you are going to be able to find the present value of these types of cash flows in the future. Unlike most of finance courses, in this course, you are going to learn how to use excel to find present value of future cash flows. In addition to the present value, you are also going to learn how to find future value given investment; interest rate given investment and future cash flows, payments given interest rates, number of periods to wait given investment and interest rate, and so on. After learning the concept and how to find the time value of money, you are going to apply this to real world examples and company valuation. After taking this course, you will be ready to make an estimate of firm value by discounting its cash flows in the future.

De la lección

Time Value of Money (1)

Investing money is important decision because a dollar today is worth more than a dollar in the future. In this module, you will look at several methods for calculating future value as well as present value. After this module, you can solve challenging examples with excel.

Welcome Video1:26

1.1 Future Value9:16

1.2 Present Value6:50

1.3 Present Value of Multiple Cash Flows5:56

1.4 NPV of Multiple Cash Flows4:05

1.5 Present Value of Annuity3:56

Conoce a los instructores

Hyun Han Shin
Professor
School of Business

So far you have learned how to find the present value of future

lump sum cash flow.

Next, let's learn how to find present value of multiple cash flows.

That is cash flows are more than once in the future.

For example, you're supposed to receive $100 next year,

$200 in two years, and $300 in three years.

This kind of stream of cash flows is called multiple cash flows.

In order to find present value of multiple cash flows, you need to find present

value of each cash flow first and then sum the present values of each cash flow.

The general form of calculating PV of multiple cash flows is

the formula in the slide.

That is PV = CF1/(1+r) raised to the power

of 1 + cash flow in time 2 divided by the 1 + r,

raised to the power of 2 +, so and so, up to cash flow in time n

divided by 1 plus rate raised to the power of n years.

Let's take a look at an example.

Suppose you have an opportunity to invest in a business that will pay

you $100,000 in one year, $200,000 in two years,

$300,000 in three years, and $400,000 in four years.

You can earn 10% per year compounded annually on a mutual

fund that has similar risk.

That means that the discount rate,

you need to apply to this investment opportunity is 10%.

In order to find the present value of these cash flows,

you need to find the present value of each cash flow first.

We can present these cash flows in a diagram as it is shown in this slide.

First, let's find PV of CF in year 1 using Excel.

Why don’t you just start Excel in your computer and open Excel template.

Since we are looking for PV we are going to use template for PV.

In the template for PV, type in 100,000 for FV.

Next type in 10% for RATE, and 0 for PMT.

Next type in 1 for NPER.

Then you get PV of 90,909.09.

That is, $100,000 in 1 year, is equal to,

$90,909 as of today.

As you already learned, PV calculated in Excel is negative, but

you interpret that as a positive value.

Next, let's find PV of CF in Year 2.

We're going to use the same PV template.

What you need to do is to change the value for

FV from 100,000 to 200,000.

And the value for NPER from 1 to 2.

And you get PV of 165,289.26,

that is $200,000 in two years is

equal to $165,289 as of today.

Next, let's find PV of cash flow in time 3.

In the previous solution, you need to change FV from

200,000 to 300,000, and NPER from 2 to 3.

In the same template you need to change the value for

FV from $200,000 to $300,000.

And the value of NPER from 2 to 3.

And you get PV of 225,394.

That is $300,000 in 3 years is

equal to $225,394 as of today.

Next, let's find PV of cash flow in year 4.

In the same template you need to change the value for FV from 300,000

to 400,000 and the value of NPER from 3 to 4.

Then you get PV of 273,205.

That is $400,000 in year 4 is

equal to $273,205, as of today.

Now you need to add all PVs.

As you can see in this table,

PV of 4 years of cash flows is $754,798.

If you're asked to pay less than this amount of PV for the business,

then investment opportunities worth to take.

For example if the cost of investment is $700,000.

Your profit is $754,798 -

$700,000 of cost.

So the profit is $54,798 which

is called the Net Present Value or NPV for short.

NPV is what you really earn after considering the cost of capital of 10%.

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