Conceptual framework …..present value(under conceptual frame work)

And where’s the problem (other than the fact that you haven’t told me the cumulative discount factor for 8 years at 10%)?

Without you giving me that information, I shall take a wild stab at an answer and suggest that the figure involved is around $26,674,630 ish

Am I anywhere near?

OK – I gather that you were exempt from F2

That’s unfortunate because it’s often the case that the university courses that earn you those exemptions fail to prepare you for your later studies

However, the 5.335 (strictly accurately that should be 5.33493 but you’ll never be expected to work to that level of accuracy) represents the cumulative discount factor for 8 years where the cost of capital is 10%

Imagine this … if you wished to have in your hand in 1 year’s time $100 and you could invest an amount of money TODAY at 10%, how much would you need to invest today in order to have $100 in1 year’s time

That would be $90.91 because $90.91 would earn 10% = $9.09 interest in 1 year and there you now have $100 in one year’s time

What if you wanted $100 in 2 years’ time? How much would you need to invest today to have $100 in 2 years’ time?

Well, we can reduce this to asking “How much would you need to invest today to have $90.91 in 1 year’s time because we know that if we left that $90.91 invested at 10%, that would earn us $9.09 in the next year

So if we invest $82.64 at 10% for 1 year, at the end of that year we would have $8.26 interest as well as the $82.64 invested = $90.91

How did we (simply) arrive at $90.91?

We multiply the final amount of $100 by 1/(1 + the cost of capital expressed as a decimal)

So, $100 * 1/1.10 = $.9091

And to arrive at $90.91 in one year, we multiply that figure by 1/1.10 = $82.64

That 1/1.10 gives us the discount factor for one year at the specified cost of capital (10% in this case) and, for one year at 10%, the discount factor is .9090

For two year, we can arrive at the discount factor for not just one year (.9090) but also for the second year (.9090 * 1/1.10) and that second year’s discount factor is therefore .8264

We can now change the emphasis here and say “What is the TODAY value of $100 in one year’s time?” and the answer is $90.90

And what is the TODAY value of $100 receivable in 2 years’ time. The answer is $82.64

And $100 receivable in 3 year’s time has a today value of $100 * (1/1.10)(1/1.10)(1/1.10)

And in n years’ time it’s $100 * (1/1.10 * n)

So now we know the today value of $100 receivable in one year is $90.91, receivable in 2 years is $82.64, in 3 years it’s $75.13 and so on for 8 years

The appropriate discount factors for those years are therefore .9090 (year 1), .8264 (year 2), .7513 (year 3) and so on

And if we add up those 8 discount factors we shall arrive at a cumulative discount factor of 5.335

So now multiply that end figure receivable each year for the next 8 years by the cumulative discount factor for 8 years at 10% and we arrive at the TODAY value of $100 receivable for each of the next 8 years where the cost of capital is 10% and that comes to $533.50

So you ask where 5.335 comes from. It’s the addition of .9090 + .8264 + .7513 + … + … + … + … + .4665

OK now?

If you’re still in doubt, watch John’s lectures for F2 and / or F3 …

… but be warned! You WILL need to understand this concept of the time value of money for you ACCA studies

OK?

Now, if we are to receive $100 for each of the next two years

So the cumulative discount factor for TWO years is 1.7355

That’s good … but I still recommend that you take the time to watch John’s lectures on F2 and F3.

They really will help you with your efforts at F5 and F7

OK?