Tax allowance in unit pricing

Indexation from the asset purchase date to the current date would be known: it is historic inflation. The allowance for indexation going forwards is in the use of a real (rather than nominal) discount rate, i.e. the nominal interest rate is reduced by the rate of expected future inflation - so this is an assumption that the company has to make.

It is difficult to apply the scenario (unrealised losses that are expected to turn into gains) to your adapted version of Question 8.5, because if the current quoted price is £1500 then the loss is not expected to become a gain at the intended point of sale under the stated investment return and time to sale assumptions!

But basically, if you wanted to calculate the current indexed value of the unrealised loss (although realised losses are not indexed, if you expect it to become a gain in future then that gain will be indexed - so you could allow for indexation now) then simply replace £3,000 with £1,500 in the calculation to give you the negative indexed unrealised gain, i.e. the indexed unrealised loss. And if you wanted to calculate the non-indexed value of the unrealised loss (e.g. if you did not expect it to become a gain in future, so would not receive any indexation relief once realised) then that loss would simply be £500 (difference between initial cost and current lower value).

 

Yes, that's right - assuming that you meant "in the former" in your first sentence?

 

Yes, that's right. Tax is only paid on the gain in excess of inflation, ie it is paid on the indexed gain. So if the nominal per annum gain is 10%, tax is only payable on the excess of this gain over inflation (which is 3%) - so only 7% suffers tax.

 

Apologies, I found your second paragraph a little confusing.

If there is an unrealised loss, then the deferred tax adjustment would be an addition to the unit price.

This is the same as saying that the unit price does not have to be reduced by the full fall in equity/property value, because we can gain tax relief on that fall (it is negative I).

For example, if we simplistically say that the discounted tax rate that we want to apply is 10%, then if equity values fall by 20% (an unrealised loss) we would only reduce unit prices by 18% (=20% x {1 - 10%}) rather than by the full 20%.

So the tax adjustment is an addition to the unit price that would otherwise be calculated; in this case it is an addition of 2%.

 

Thanks for setting this out. Your calculations look OK (other than the 0.95 should be 0.985?) but the 0.985 would increase the unit price, not reduce it.

I think it might be helpful if we considered the situation where we ignore indexation.

Let's say for simplicity that we have 100 units and one asset backing those units. The asset was bought for 100 a year ago and today is worth 98. So the unit price was 1.00 a year ago and today is 0.98 if we ignore taxation over the period (also ignoring bid/offer spreads etc for simplicity).

Let's say that we expect an investment return over the next year of 12% and the tax rate is 20%. Let's assume that the loss will turn into a gain which we will realise in one year's time. So the tax adjustment = Loss x tax rate x v, where i = 80% x 12% = 9.6%.

Hence tax adjustment = 2 x 20% / 1.096 = 0.365
And this is an addition to the asset value used for the unit price calculation (since we started with a loss not a gain)
Therefore unit price = 98.365/100 = 0.98365

In other words, the unit price has not been reduced by as much as the full equity loss of 2%. This is because we can effectively gain some tax relief on a subsequent gain as a result of having made this loss.

Let's think about the following year to see how that works. Let's say that the 12% (pre-tax) investment return actually happened so that the value of the underlying assets is now 98 x 1.12 = 109.76. That means that we have made an investment return (I) of 11.76 over the year (= 109.76 - 98), which would normally be assumed to be taxable at 20%. But actually we are only taxed on a realised gain of 9.76 (= 109.76 - 100). So the actual amount of tax payable is lower as a result of the prior year unrealised loss.

To be equitable to all unitholders, the unit price at the end of the first year is increased to allow for the tax benefit being carried forward, so that those unitholders who exit after one year are being given credit for that tax benefit. After all, these are the unitholders that have suffered the equity market fall that gave rise to the tax benefit. And otherwise, the benefit of the lower ultimate tax amount would be given solely to those who exit from year two onwards.

Your argument above seems to be anticipating tax payable for a gain which has not yet happened, and reducing the unit price for that future tax - so that unitholders who exit in the first year (and who have not had any benefit from that equity market gain) will be penalised for tax on future gains that have not yet happened. The opposite is the case: they should be given credit for the tax benefit that will be carried forward from the unrealised losses accrued during that first year.

You can then layer indexation into the calculation: it makes the numbers messier but it boils down to the same overall principle.

Is that clearer? I hope so!

 

Yes, that sounds about right.
Capital losses will either reduce the deferred tax liability or generate a deferred tax asset - provided the company has sufficient gains against which to offset the loss.
A deferred tax liability reduces the unit price; a deferred tax asset increases the unit price.