The Joy of Present Value (PV)

As you know, a bird in the hand is worth two in the bush.

But is that two to the nearest whole number?

Or is it two to three decimal places?

Today we'll try to answer those questions using one the most useful concepts in accounting and finance:

Present Value

Alchemy

"A bird in the hand is worth two in the bush" is one of the cleverest sayings of all time.

In just 11 words it says so much.

There's an element of time: 'now' versus 'later'

And there's an element of risk or uncertainty: the certainty of what you have now, the uncertainty of what you may or may not have later.

Then, it an act of pure alchemy, it transmutes time and risk into worth. Aka money.

Income now vs. Income later

income now is worth more than income later.

If I give you £100 now... it's worth £100.

If I give you £100 **a year from now***... that's less valuable.

Why?

Well for one thing, you've missed out on a year of interest payments.

Take £100 and put it in the bank in an account that provides 10% interest

(I don't know of an account that offers such a good interest rate... but it keeps the maths simple.)

Anyway... Put £100 in the bank now... and this will grow to £100 + 10% = £110 a year for now.

We can say that £100 now has the same value as £110 a year from now

Present Value (PV)

Now this is where things get interesting:

We can run the calculation in the opposite direction to work out the Present Value of a future payment.

The £100 that I have promised to pay you a year from now has a present value of £90.91.

Because we're moving from a large number to a smaller one, we no longer talk about an interest rate.

Instead, we we talk about a Discount Rate.

We could say that

• "A payment of £100 a year from now may be discounted to a present value (pause to add 10% on screen) of £90.91 by applying a discount rate of 10%"

More succinctly:

• "£100 a year from now has a Present Value of £90.91 (at a discount rate of 10%)"

We can apply similar calculations to any point in the future

At year ten, the Present valve is just £38.55

Let's fill in the rest of the years.

At just over SEVEN years, the Present value of £100 drops to £50 - half of its initial value.

If we run the numbers again with £500, it still drops to 50% at just over seven years.

It will drop to 50% at just over seven years whatever the initial value: the 10% discount rate sees to that.

It doesn't matter if it's:

• £100...
• a monkey (£500) or... dare I say it...
• a bird.

Concluding remarks

A bird in the hand is worth two in the bush, assuming the bird is extracted 7.27254 years from now given a discount rate of 10%