Discounted Cash Flow

mge

I realise that Discounted Cash Flow has been covered before on this forum, but I have a specific question and would really appreciate some help in answering it:

I will take a capital investment project out of the Osborne book (Project Aye), and summarise some of the details:

Amount invested at Year 0: £20,000
Cumulative Cash Flow over 5 year length of project: £11,000 in
Net Present Value: £4,913 (assuming a rate of return of 10%).

The book goes on to say that as there is a positive NPV, this project will be of benefit to the organisation.

However, my thinking is this:

If the rate of return on capital is 10% (used when calculating NPV above) and we didn't invest in this capital project:

The return on the £20,000 would be:

Cumulative Cash Flow over 5 years (at 10% interest rate): £12,210 in
Net Present Value: £9,090

Looking at either of the figures, it seems as though it would be much better not to invest in this capital project than to invest in it.

SandyHood

Net Present Value means the amount over and above the cost of capital that the project will earn.
If capital costs us 10%, then we are effectively borrowing money for the project at 10% interest.
So, £20,000 is paid out now - paying out now means we don't discount it (or multiply by 1.00)
The first time any money comes in is a year from now (£8,000). So I guess you'd prefer the money now rather than wait a year. If we went to the bank and said, we've a promise of £8,000 in one year please can I borrow the money that it is equivalent to now, then the bank would work out how much now would be equivalent to £8,000 in a years time.
In this case £7,273 invested now at 10% would be worth £8,000 in a year's time.
We say that the present value of £8,000 receivable in one year is £7,273.
Similarly £12,000 in 2 years is worth £9,912 now
£5,000 £3,755
£4,000 £2,732
and £2,000 £1,242

Giving the NPV of £4,913

SandyHood

mge wrote: »

If the rate of return on capital is 10% (used when calculating NPV above) and we didn't invest in this capital project:

The return on the £20,000 would be:

Cumulative Cash Flow over 5 years (at 10% interest rate): £12,210

Absolutely true
If you put £20,000 in the bank at 10% APR and didn't touch it for 5 years you could withdraw £32,210 and £12,210 would be the interest.

But what is the discounted value, afterall the discounted value of the Project Aye is £4,913.

Well look at the interest you earn, the interest rate is exactly the same as the cost of capital so all the interest disappears when you apply the discounting.

PGM

SandyHood wrote: »

Well look at the interest you earn, the interest rate is exactly the same as the cost of capital so all the interest disappears when you apply the discounting.

Leaving you with a NPV of 0.

mge

Many thanks for your replies. Once more it is very much appreciated. I now understand where my thinking is flawed.

However, I'm still not absolutely certain why the NPV would be 0.

Year 1: £2000 interest earned. DCF= £2000 x 0.909 = £1818 in
Year 2: £2200 interest earned. DCF= £2200 x 0.826 = £1818 in
Year 3: £2420 interest earned. DCF= £2420 x 0.751 = £1818 in
Year 4: £2662 interest earned. DCF= £2662 x 0.683 = £1818 in
Year 5: £2928 interest earned. DCF= £2928 x 0.621 = £1818 in

Total DCF from interest = £9090 in

Also:
Year 0: £20,000 investment. DCF = £20,000 x 1.000 = £20,000 out.
Year 5: £20,000 investment amount back in. DCF = £20,000 x 0.621 = £12,420 in

This still leaves an NPV of £1510

SandyHood

mge wrote: »

Many thanks for your replies. Once more it is very much appreciated. I now understand where my thinking is flawed.

However, I'm still not absolutely certain why the NPV would be 0.

Year 1: £2000 interest earned. DCF= £2000 x 0.909 = £1818 in
Year 2: £2200 interest earned. DCF= £2200 x 0.826 = £1818 in
Year 3: £2420 interest earned. DCF= £2420 x 0.751 = £1818 in
Year 4: £2662 interest earned. DCF= £2662 x 0.683 = £1818 in
Year 5: £2928 interest earned. DCF= £2928 x 0.621 = £1818 in

Total DCF from interest = £9090 in

Also:
Year 0: £20,000 investment. DCF = £20,000 x 1.000 = £20,000 out.
Year 5: £20,000 investment amount back in. DCF = £20,000 x 0.621 = £12,420 in

This still leaves an NPV of £1510

Stop and think
Borrow £20,000 at a cost of capital
And then invest it
You have discounted the interest but what about the capital

You have not treated the two alterrnatives in the same way

If you put £20,000 into the bank today then you have £22,000 in the bank in one year
but if you discount that £22,000 to the present value you must x by 0.909 which is £20,000 ( I know the sum gives you £19,998 but the 0.909 is a rounded factor)
So the value after one year is exactly what it was before the year started.

The Project Aye investment values the whole cash flow each year and then discounts it.

Even if you say that your £20,000 stays invested for 5 years then you need to say "what is the present value of the £20,000 I get back 5 years from now?"
It isn't £20,000 - that is how much £20,000 is worth today.
If I have to wait 5 years it is only worth £20,000 x 0.621 = £12,420

So the value invested £20,000 has a present value of £12,420 because we have to wait 5 years before we see it again.
Additionally, you list the interest as increasing but it is also a cash flow.
If you earn £2,000 in year 1 AND this is your cash flow, then your interest in year 2 cannot be based on investing £22,000 as there is only £20,000 to earn interest on.

So you have a choice,

1. Take £2,000 each year as a cash flow, or
2. Take all the interest in year 5 £32,210.20

If you wait until year 5 then discount it, you'll have a £2,210.20 cash flow x 0.621 = £20,000 (or using the factor to 3 decimal places £20,002.53).

If you take the cash each year the calculation would be:
Year 1: £2000 interest earned. DCF= £2000 x 0.909 = £1818 in
Year 2: £2000 interest earned. DCF= £2000 x 0.826 = £1652 in
Year 3: £2000 interest earned. DCF= £2000 x 0.751 = £1502 in
Year 4: £2000 interest earned. DCF= £2000 x 0.683 = £1366 in
Year 5: £2000 interest earned. DCF= £2000 x 0.621 = £1242 in
Total Present value of interest earned £7,580
Present value of the £20,000 invested now (at the end of year 5) £12,420
Total £20,000
Less initial investment £20,000
Net Present Value £0

mge

Sandy, I am very much indebted to you for that answer. You put things very clearly in a way which is easy to understand. I realise it must have taken some time to put together a reply like that, and I'm extremely grateful!