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The Joy of Net Present Value (NPV)

Episode 29 - 30 Mar 2016

In the previous episode, we explored the wonderful world of Present Value (PV).

In this episode, we'll put Present Value (PV) to work...

...with a little help from a spreadsheet.

Then we'll move on to an even more powerful concept: Net Present Value (NPV)

Is it better to be paid quarterly or monthly?

Present Value (PV) and Net Present Value (NPV) to the rescue!

Introduction

In the previous episode, we explored the wonderful world of Present Value.

Today, we're going to do one more thing with Present Value,

then we're going to move on to ask even more powerful concept:

  • Net Present Value (NPV)

Maths Ahead

I deliberately avoided maths and equations in the previous episode because I didn't want to maths to cloud the key principle of Present Value:

  • Income now is more valuable than income in the future

Now that we've established that principle, it's time for some gentle maths.

Here's the equation for Present Value:

                              Future Value
          Present value    =  ------------
                               (1 + R)^T

Notes:

  • R in the Discount Rate expressed as a decimal. So 10% would be 0.1
  • T is the number of time periods.

Let's just check that it all works for a very simple example:

  • a payment of £100 a year from now
  • an interest rate of 10% per annum

So:

  • the Future Value is 100
  • R is 0.1
  • T is 1

Which gives us

                                  100
          Present value    =  ------------
                              (1 + 0.1)^1


                                  100
          Present value    =  ------------
                                 (1.1)^1

                                  100
          Present value    =  ------------
                                  1.1


          Present value    =  90.909090909090

The present value is £90.91 to the nearest penny.

Time for a spreadsheet

That's enough mental arthritic for one day. Time crank up Excel.

I'll put the discount rate here

This is the future value - £100 The year is 1

Now for the present value equation '=' select this present value cell divide by open brackets one plus ... the Discount Rate

Close the brackets Raise it to the power of the time period... Which is this cell Hit enter And there we have our 90.91

Let's have some fun with this

Fist thing to do is lock this value to this cell And now I can drag this along one cell Change this to 2 And we get the present value of 100 paid two years from now

Next, select all of these cells and drag to the right

I'm a visual kind of guy, so I'm going to want to see a graph

I'd encourage you to play around with the number to see how it changes be graph.

Multiple payments

Let's take the complexity up a step and look at multiple payments.

You get a new job. At £120,000 per annum.

You can choose to be paid monthly or quarterly.

I'm guessing you'd prefer the first option.

Let's see if your instincts are backed up with cold hard maths.

I'll adjust the spreadsheet.

Instead of ten years, we want 12 months: add a couple of columns.

And we'll also need a discount rate for a month rather than a year.

Let's choose 1%. Not quite equivalent to 10% per annum... but it's a nice round number.

It gets entered as 0.01

120k a year is 10 k a month...

I copy that value across

We're interested in the total value, so let's add a sum here - 120,000 as expected

And we also what the sum of the Present Value of all the payments.

Now we need to compare that with being paid quarterly.

First, I'll copy these rows

And change the payments.

30,000 here, here and here.

Zero everywhere else

The Present value of the quarterly payments is £112,250.

The Present value of the monthly payments is £111,432.

Looks like your instincts were correct. Congratulations!

Net Present Value

Let's move on - I'm keen to get to today's main event: Net Present Value.

So far we've looked at income - money that comes to you.

What about money that you pay out?

Would you rather pay 10k now, our in 12 months time.

You're right.

It's better delay outgoings as a long as possible.

The present value of the future payment is reduced: the longer you delay the payment, the better it is for you.

The equation for this is... exactly the same.

If you pay £100 now... it costs you £100

If you can delay the payment for a year, the present value of the payment drops to £90.91.

(Sick of that number yet?)

I am, of course assuming a Discount Rate of - say it with me now - 10% per annum.

Investment Opportunity

Let's put this straight into action.

If I come to you with an investment opportunity which means that you pay me

  • £50 now, and
  • £50 in 3 months time

And I pay you back in two payments:

  • £60 in 10 months time
  • £60 in 12 months time

£100 out, £120 in. To mere mortals it might look like a good deal.

But you have Present Value superpowers. Not to mention the power of a spreadsheet.

Lets start with the income:

I'll add in a note here so that we can keep track.

Then I'll add in the income payments: £60 here, £60 there.

Now for the outgoings.

As I said, the equations are the same, so I can copy these rows, update the label.

Make sure it's using the right time period, clean up, and we're ready to enter the expenses.

Minus £50 here and minus £50 here.

We now have all the numbers we need to calculate the NET Present value for each month: the NET of each income and expense

I'll add another sum at the end of this row

This is the Net Present Value of the entire "deal": £9.03.

A positive NPV is a good thing, so my investment opportunity can be considered to be a good deal.

Assuming, that is that 1% is the correct Discount Rate.

But what if it isn't? What if the correct discount rate is 2%

If I change the discount rate to 0.02, the NPV drops below zero. It no longer looks like a attractive deal.

All of which begs the question:

  • "What is the correct discount rate?"

We'll jump onto that very question in the next episode.

Watch "The Joy of Net Present Value (NPV)" on YouTube.