Tax allowance in unit pricing

[Mbotha]

I understand the theory behind pricing on an offer basis when there's unrealised losses (and the losses are expected to turn into gains) - and that the process would be the same as for unrealised gains on an offer basis. However, I'm trying to work out how you would apply indexation (and on what amount, when you don't know what the gain will be in future). For example, what would the answer to Q8.5 (ch8 pg8) be if the current quoted price of the asset is £1500 instead of £3000?

 

[Mbotha]

Another question on this topic:

The treatment of realised losses seems to be the same as that of unrealised losses - the only difference being that the discounting period seems to be shorter in the latter:

• Unrealised losses (offer basis): discount for the period between now and the expected date of the first realised gain (occurring after the loss is realised, which is sometime in the future)
• Realised losses: discount for the period between now (loss has already been realised) and the expected date of the first realised gain

So essentially, the period is longer in the first case. Is that right? Is that the only difference?

 

[Lindsay Smitherman]

I understand the theory behind pricing on an offer basis when there's unrealised losses (and the losses are expected to turn into gains) - and that the process would be the same as for unrealised gains on an offer basis. However, I'm trying to work out how you would apply indexation (and on what amount, when you don't know what the gain will be in future). For example, what would the answer to Q8.5 (ch8 pg8) be if the current quoted price of the asset is £1500 instead of £3000?

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).

 

[Lindsay Smitherman]

Another question on this topic:

The treatment of realised losses seems to be the same as that of unrealised losses - the only difference being that the discounting period seems to be shorter in the latter:

• Unrealised losses (offer basis): discount for the period between now and the expected date of the first realised gain (occurring after the loss is realised, which is sometime in the future)
• Realised losses: discount for the period between now (loss has already been realised) and the expected date of the first realised gain

So essentially, the period is longer in the first case. Is that right? Is that the only difference?

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

 

[Mbotha]

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

Sorry - I did mean "in the former". Thanks, Lindsay.

 

[Mbotha]

Hi Lindsay

Just to come back to question 8.5 in chapter 8....
The company's assets are expected to grow at 10% so the assumed nominal rate of return is 10%. I'm a bit stuck on how, in the answer, they get to the net (of tax) nominal rate of return though: 10% - (7% x 0.20).
The comment says that tax is paid on the indexed gain of 7% but I'm not sure how they arrive at the 7%. Is it as simple as 10% - 3% (inflation) and, if so, why?

This is back to basics, sorry, but I just need a refresher.

Thanks!!

 

[Lindsay Smitherman]

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.

 

[Mbotha]

I thought I'd post here to keep everything on this topic in the same thread...

In the case of unrealised losses where were pricing on an offer basis (expanding fund) and the losses are expected to turn into gains, the same process is followed as for unrealised gains where pricing is on an offer basis. However we're not indexing a loss. Would the adjustment to the unit rate still be an addition?

My thinking is that, because we are now indexing an unrealised loss (negative unrealised gain), if the unit rate is adjusted via an addition, we end up in the same position as for unrealised gains - ie. a deduction to the unit rate (negative addition). Is that right?

 

[Lindsay Smitherman]

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%.

 

[Mbotha]

Apologies, I found your second paragraph a little confusing.

Sorry, Lindsay. There is quite a lot going on there

I still don't quite understand how it works from a practical perspective. I've put together an example to try explain what I'm struggling with more clearly:

• Say we have an asset that will be realised in a year (and was bought a year ago)
  • It was bought for 100
  • It's current value is 98
  • Inflation over the year = 3%
  • Investment return over the next year is expected to be 5%
  • Tax rate = 20%
• We currently have an unrealised loss but we're expecting it to turn into a gain by the time that it needs to be realised. So we can index that loss:
  • Indexed loss = 98 - (100)(1.03) = -5
• The tax rate needs to be discounted using the net real rate of return (since the loss, which will turn into a gain, will be indexed):
  • Net nominal rate of return = 5% - (5% - 3%)(20%) = 4.6%
  • Net real rate of return = (1 + 4.6%) / (1 + 3%) - 1 = 1.55%
• Thus the adjustment for tax on the indexed loss is (-5) x 1.0155^(-1) x 20% = -0.95
• Given that we're working with an unrealised loss, the adjustment to the unit rate will be an addition
  • Adjusted unit rate = unit rate + (-0.95)

Is this right? Given that the unrealised loss is expected to turn into a gain, it seems right that the adjustment has the effect of reducing the unit price (to allow for the tax that would have to be paid on that gain).

 

[Lindsay Smitherman]

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!

 

[Mbotha]

Oh, I understand now. Thanks so much for setting out the details!!

 

[Mbotha]

Hi Lindsay

In the case of investments in unit trusts, the annual notional sale and repurchase rule is used, where gains are spread over the next 7 years.

Am I right in saying that, because these investments are taxed regardless of whether the gains/losses have been realized, the calculation of the unit price adjustment for tax is actually quite simple?
Ie. the indexed gain would be spread over 7 years and discounted using the net real rate of return. This is the case irrespective of whether it’s a contracting or expanding fund. Is that right?

In the case of a loss, there’s no indexation and the loss is used to restate prior year gains. The implication is that this gives rise to a credit credit - is that right? How is this allowed for in the unit price?

 

[Lindsay Smitherman]

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.