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- This topic has 4 replies, 3 voices, and was last updated 9 years ago by John Moffat.
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- August 26, 2012 at 4:04 pm #54252
an illustration eg in kaplan study text.
A firm pays out a constant dividend of 10c in perpetuity. Its cost of equity is 10%.
PV=10+11/1.1^2+10/0.1*1/1.1^2
i didnt understand this step.
pls helpAugust 27, 2012 at 12:19 pm #104694To discount a perpetuity, you multiple by 1/r (where r is the rate of interest).
So, the first part of the third item in your equation is 10 / 0.1 which is discounting the perpetuity.
However, that would assume that the first dividend was in 1 years time and was thereafter every year.
I would guess that the reason they have done more is because the actual pattern of dividends is different, but without seeing the actual question I cannot tell.
August 28, 2012 at 5:37 am #104695it is a case study,
i am typing whatever they gave:A firm pays out a constant dividend of 10c in perpetuity. Its cost of equity is 10%.
The value of the dividend stream to an investor is 10/0.1=100c
(i guess, they are applying perpetuity)They would need to cancel T1 dividend of 10c to pay for it.
The project should earn 10% return i.e, the 10c would be worth 10*1.1=11c the following year.
provided the firm then distributed the additional 11c, the shareholder would have
PV=10+11/1.1^2+10/0.1*1/1.1^2
PV=17.3554+ 82.6446=100c
so in theory, provided the firm invests the withheld dividend in projects that at least earn the shareholders’ required return, the investor’s wealth is unchanged and they will not object.above info along with time diagram,
in that diagram, they show,
at T1=0, T2=10+11, T3=10 perpetuity.i didnt understand the above case study, it flies above my head.
May 25, 2014 at 4:30 pm #170755AnonymousInactive- Topics: 43
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Hi Vipin,
I hope you have understood this theory.
Several days ago, I was stuck at this same question too. You must have read the FTC book, the same as I did. Anyway, as I was saying, I got stuck at this question. And I was hoping that someone else in other part of the world had the same problem, and as always, I turned here, hoping there would be an answer ready for me.
Alas, no such luck.
today, I reread this theory and this question, and I was enlightened. Just as Opentuition Tutor Mr. Moffat said, the theory is about discounting cash flows.
So, here I am, writing my following understandings, hoping it might shed some light on someone who, by chance, do not understand this question and theory, and wind up here by googling. 🙂The Residual Theory is all about the present value of future cash flows. It argues that as long as present value is the same, it doesn’t matter when the cash flows in. And it argues that company shall invest its retentions in projects to generate future cash flows. Only the residua profits that do not meet any projects would be distributed to the shareholders. The cash flow here obviously is dividends.
So here the question is about this situation:
On one scenario, the company do not invest its profits to any projects, and the dividends are distributed annually at 10%. This dividend is a perpetuity, with annual cash flow of 10c at 10% discount rate, thus the PV is calculated at 10c/0.1 = 100c
The other situation is the company rather than distributes its 10c per share dividends to its shareholders at the end of first year, it sees a one-year investment opportunity. And the investment rate of return is 10% annually. So it invests the money to the project at the end of year 1, ie. T1. The return is recorded at the end of year 2, ie T2. So apart from the usual annual dividend of 10c (T2), there is a further cash flow that is generated from the investment opportunity, with return to be 10c * 1.1 = 11c (Note, this cash flow is at the T2). From T3 onwards, the dividends payment is unchanged at 10c each year. So for this part of cash flows, it is perpetuity again and the calculation of “PV” is 10c/0.1 (But we should take note that this perpetuity is not recorded from T1 onward, rather it is from T3 onward, hence the PV is only discounted back at T2.
Now we see all the money is at T2 (normal dividend of T2, investment opportunity cashflow earned at T2, and the perpetuity arrived at T2), and we want to discount them back to T0, to arrive at the true PV.
So the calculation is listed as the following:
PV = (10 + 11)/1.1^2 + 10/0.1 * 1/1.1^2 = 100cThe present value of these two scenarios are the same, at 100c.
One thing should blame the FTC text book, there is an error in the formula. It lacks the parenthesis of the first part of the calculation ( there is no parenthesis between 10 + 11, creating confusion for us students)
Hope you all understand now.
May 25, 2014 at 5:50 pm #170776lukayl: Thank you for answering (but please in future restrict yourself to answering in the general F9 forum – this is Ask the Tutor forum).
Also, if you were stuck on the same thing a few days ago you should have asked here and I would have sorted it out for you 🙂Vipin: What lukayl has written is correct. However don’t worry about the numbers as far as the exam is concerned – if he asks about dividend policy it will be a written part of a question and he will expect one or two lines about the residual theory and the dividend irrelevance theory, the signalling effect of lower dividends, etc..Most of what you would need to be able to say is on page 68 of our Course Notes.
All the residual theory is saying is that companies should invest in projects with positive NPV’s and not worry about paying a lower dividend as a result. The reason being that if the NPV is positive, then the returns from the investments will be higher than the return required by investors and it will lead to higher dividends in the future. In theory shareholders will not mind getting a lower dividend now if it means a higher dividend in the future.
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