Concept of Pre Tax discount Rate and Post tax discount Rate

rent = 10000(1-.3)= 7000 after tax

cost of capital = 7 % after tax

suppose this is a future outflow after 1 year..its present value will be= 7000/1.07=6542

 COST OF Capital is always post tax..NOT PRE TAX

as per ur example-if u are discounting the outflow of 10000 with 10% rate...u get 9090

pay the tax and ur outflow will be = 9090(1-.3)= 6363

See the difference is arising coz of  the present and future value concepts..u 1st pay the tax and then discount the cash flow...in case u are discounting the cash flow inclusive of tax amount, in a way u are discounting the tax amount along with it..this is why the difference is arising...

Regards!!

Originally posted by : Sunshine...
	as per ur example-if u are discounting the outflow of 10000 with 10% rate...u get 9090 pay the tax and ur outflow will be = 9090(1-.3)= 6363

Hi Sunshine, why have u deducted tax after discounting at pre tax discount rate? Pre tax discount rate is determined after considering the tax effect,  so that when u discount by pre tax discount rate u get discounted cash flows after tax(not before tax). Therefore u should not deduct tax again. The correct amount is Rs. 9090(not 6363) 

Pls check this link..It may be useful.  /forum/pre-and-post-tax-dis-rate-155549.asp

i was just looking at the outflows as per NRV methhod..

Originally posted by : Jithin
	Originally posted by : Sunshine...   as per ur example-if u are discounting the outflow of 10000 with 10% rate...u get 9090 pay the tax and ur outflow will be = 9090(1-.3)= 6363     Hi Sunshine, why have u deducted tax after discounting at pre tax discount rate? Pre tax discount rate is determined after considering the tax effect,  so that when u discount by pre tax discount rate u get discounted cash flows after tax(not before tax). Therefore u should not deduct tax again. The correct amount is9090(not 6363)  Pls check this link..It may be useful.  /forum/pre-and-post-tax-dis-rate-155549.asp

Wonderful link shared by Jithin.But Jithin i disagree with ur interpretation tat correct amt is 9090.

sunshine is right.

This is wat understood.

Pre tax cash Flows discounted by Pre tax Discount rate is not equal Post tax cash Flow discounted by post tax discount rate except in case of cash flows discouned to pepetuity without growth.

The pre tax calculation must be fundamentally flawed given that the present value of the pre tax cash flow (i.e. 9090) exceeds the after tax value of the cash flow even if it was paid after one 1year (i.e. 7000).

So its logically incorrect to ascertain  Present value of outflow in fututre without considering tax saving.

Pls correct me if i am wrong.

I didnt say that 9090 is the right amount. Logically it is not & it should not be. But when u discount using the pre tax discount rate, 9090 is the one & only correct amount(whether the amount is appropriate or not is another matter) . 

The treatment suggested by Sunshine is fundamentally wrong. When u discount cash flows before tax using a pre tax discount rate, u already get the discounted cash flows after tax. On what basis should we deduct tax again? It is totally inappropriate. Sunshine effectively treated both the rates as post tax discount rates(even though she didnt intend to do so with the 10% rate).

Also The difference in Sunshine's solutions was not due to the present value future value concepts as she was saying. Both the situations explained by her are actually the same. The variations in the amounts  was only due to the difference in the discount rates adopted by her. For example, in the first situation when the tax is initially deducted by her, she got Rs.6542. In the 2nd situation where she discounted the whole cash outflow(inclusive of tax), she got Rs.6363. Now recompute the discounted cash flows after tax in the 2nd situation using 7% instead of 10% & see what u get. 10000/1.07=9345.79. Now let us deduct the tax amount..9345.79 x (1-.3)=Rs.6542. U get the same amount as in situation 1. So the difference is only due to the difference in the discount rates. 

Jithin Bhai ,

Firstly i would really like to appreciate u for consistently involving in discussion & making each of  us THINK.!

Now i would like put forward points of my research.

1)Cash flows involving fixed interest(say cash flows under loan option i e Principal + interest)wil be discounted  by market intst rate(discount rate) which is equal to fixed interest rate itself which will revert u ur present value of loan ie loan amt itself .No matter u discount cash flow before tax by before tax discount rate or u discount after tax cash flow by after tax discount rate,ur result will be the same.

Tenchnically u were right -When we discount pre tax cash flows by pre tax discount rate it should give back Cash flow after tax only.But there is an exception which ill discuss eventually.

Example: 1)say u take a loan of 9090 for 10% interest rate.At the end of year one ur cash flow will be 10000 i e 9090(principal) and 909 interest

case1: Discount rate 10%-10000/1.1=9090 .this is CFAT pre tax basis.

             Discount rate 7%- 9090+909(.7)/1.07=9090.this CFAT post tax basis.

Principle proved :if u discount CFBT by pre tax discount rate u get back CFAT only

case 2:Discount rate 15%-10000/1.15 =8695 .this is CFAT pre tax basis

             Discount rate 10.5-   9090+909(.7)/1.105=8802.This is CFAT post tax basis.

As u mentioned this contradictiction is due the wrong concept tat post tax rate =pre tax rate (1-t).

if u carefully observe tax saving is considered only for interest paid /recieved not for principal amt.so impact is not much of difference in pre & post tax rate discount rate.The impact is 8802-8695=107

case 3: u pay lease rental of 10000

           Discount rate 10%=10000/1.1 = 9090 .this is CFBT only pre tax basis.

         Discount rate 7%  =10000(.7)/1.07=6542.this is CFAT post tax basis.

the difference here is massive i e 9090-6542=2548.i wanted to prove this point.

Why?

Because tax Saving is considered on entire outflow i e 10000 unlike previous cases.

I am sure ull agree to me here tat in case of any expense or lease rentals paid .where entire outflow is eligible to tax saving i e 10000(.3) in this case.U cannot call it as Cash flow after tax i e 9090 cannot be called as Cash flow after tax.

It has to be Cash flow before tax only after considering time value of money of 10% .

So wat conclusion do we draw:Every time consider post tax discount rate & not Pre tax.The pre tax discount rate has fundamental error.

Ur perceptions are welcome for more analysis.

Jithin Bhai ,

Firstly i would really like to appreciate u for consistently involving in discussion & making each of  us THINK.!

Now i would like put forward points of my research.

1)Cash flows involving fixed interest(say cash flows under loan option i e Principal + interest)wil be discounted  by market intst rate(discount rate) which is equal to fixed interest rate itself which will revert u ur present value of loan ie loan amt itself .No matter u discount cash flow before tax by before tax discount rate or u discount after tax cash flow by after tax discount rate,ur result will be the same.

Tenchnically u were right -When we discount pre tax cash flows by pre tax discount rate it should give back Cash flow after tax only.But there is an exception which ill discuss eventually.

Example: 1)say u take a loan of 9090 for 10% interest rate.At the end of year one ur cash flow will be 10000 i e 9090(principal) and 909 interest

case1: Discount rate 10%-10000/1.1=9090 .this is CFAT pre tax basis.

             Discount rate 7%- 9090+909(.7)/1.07=9090.this CFAT post tax basis.

Principle proved :if u discount CFBT by pre tax discount rate u get back CFAT only

case 2:Discount rate 15%-10000/1.15 =8695 .this is CFAT pre tax basis

             Discount rate 10.5-   9090+909(.7)/1.105=8802.This is CFAT post tax basis.

As u mentioned this contradictiction is due the wrong concept tat post tax rate =pre tax rate (1-t).

if u carefully observe tax saving is considered only for interest paid /recieved not for principal amt.so impact is not much of difference in pre & post tax rate discount rate.

case 3: u pay lease rental of 10000

           Discount rate 10%=10000/1.1 = 9090 .this is CFBT only pre tax basis.

         Discount rate 7%  =10000(.7)/1.07=6542.this is CFAT post tax basis.

the difference here is massive i e 9090-6542=2548.i wanted to prove this point.

Why?

Because tax Saving is considered on entire outflow i e 10000 unlike previous cases.

I am sure ull agree to me here tat in case of any expense or lease rentals paid .where entire outflow is eligible to tax saving i e 10000(.3) in this case.U cannot call it as Cash flow after tax i e 9090 cannot be called as Cash flow after tax.

It has to be Cash flow before tax only after considering time value of money of 10% .

So wat conclusion do we draw:Every time consider post tax discount rate & not Pre tax.The pre tax discount rate has fundamental error.

Ur perceptions are welcome for more analysis.

Hi CA Finalist bhai..Glad to know that I am making people think. Actually I myself started thinking only after reading ur query. Now I think ur post will make me study the leasing chapter.

As mentioned earlier, I made all the above analysis based on general capital budgeting topic where the entire cash flow is impacted by tax. I havent yet started studying leasing. So now let me spend a few days with the leasing chapter..afterwards I will come back & give my reply..so wait 4 a few days..will be back soon..

Regards,

Jithin. 

Does pre tax rate have fundamental error:

U wud agree that discounting CFBT at a certain rate would give u an amount equal to CFAT discounted at post tax rate. For example, in case c above, we get 6542 when we discount 10,000 at 52.56%. According to me, that certain rate is pre tax rate. So u cant say that a pre tax rate doesnt exist. There is no fundamental error associated with the pre tax rate. Actually the fundamental error is with regard to the methods available for determining the pre tax rate. We already know that the formula'pre tax rate=post tax rate/(1-t)' is flawed. Actually we dont have a proper formula using which we can derive pre tax rate from the post tax rate,e.g. in case c, we cant explain how 52.56% can be obtained as the pre tax rate just by knowing that the cost of capital is 7%. The reason for this is the practical difficulties we face in expressing the post tax rate-pre tax rate relationship which is not fixed but varying according to situations. For example, in some situations, the entire cash flows are taxed(as in case c). In some situations, only a part of the cash flows are taxed(as in case a & b). In some other cases, a part of the cash flows is taxed at some rate whereas the other part is taxed at another rate,e.g.cash flows from sale of assets are taxed at a rate different from  cash flows attributble to profits from business. Now how do we define the relationship between pre tax rate & post tax rate such that it represents all the above cases...It is quite difficult rite..

Conclusion:The pre tax rate is not preferred bcoz & only bcoz there is no proper method to ascertain this rate.

In case c, 9090 is CFBT discounted at pre tax rate 10%?

Yes of course. But case c isnt an exception here. When u discount CFBT at a particular rate, u get the CFBT discounted at that particular rate. It is a very obvious thing.

Could an amount be CFBT discounted at pre tax rate & at the same time be CFAT discounted at post tax rate?

Yes, it can be so. When u discount CFBT at the real pre tax rate(not the formula based pre tax rate), u get CFAT discounted at post tax rate. For example, in case c, we get 6542 by discounting CFBT 10,000 at the real pre tax rate 52.56%. So 6542 can be expressed as CFBT discounted at pre tax rate. 6542 also refers to CFAT(Rs.7000) discounted at post tax rate( 7%).

Conclusion:At the real pre tax rate, discounted CFBT(discounted at pre tax rate)=discounted CFAT(discounted at post tax rate). Just because a sum is CFBT discounted at pre tax rate does not mean that it cant be CFAT discounted at post tax basis. So when u say that 9090 is CFBT discounted at pre tax rate, it does not mean that 9090 cant be CFAT discounted at post discount rate. Of course, 9090 isnt CFAT discounted at post tax rate. But that is bcoz 9090 is obtained by  discounting  CFBT at the formula based pre tax rate(which is not the correct rate). It has nothing to do with the fact that 9090 is CFBT discounted at pre tax rate.  

Can we discount CFAT at pre tax rate as an alternative to discounting CFBT at pre tax rate?:

In case c, CFBT discounted at pre tax rate 10%=Rs.9090. When u deduct present value of  tax from 9090, u get 9090 - 9090 x 0.3=6363, which is CFAT discounted at pre tax rate 10%. Now the difference between CFAT discounted at pre tax rate & CFAT discounted at post tax rate is not very big,e.g.Rs.179(6542-6363) whereas the difference between CFBT discounted at pre tax rate & CFAT discounted at post tax rate is huge,e.g2548(9090-6542). So is it better that we discount CFAT at pre tax rate instead of discounting CFBT at pre tax rate for capital budgeting purpose?

We know that when cost of capital is used as discounting factor in NPV method, our decision to accept or reject a project will be solely based on whether the CFAT discounted at post tax rate is positive or negative. So the whole capital budgeting decision depends upon the DCFAT(discounted at post tax rate). Whatever rate u use or whatever method u adopt, u need to arrive at CFAT discounted at post tax rate in order to make  a decision. We already know that we will not get CFAT discounted at post tax rate by discounting  any of CFBT & CFAT at pre tax rate. Now let us see why we dont get CFAT discounted at post tax rate. When u discount CFBT Rs10000 at 10% formula based pre tax rate, u r actually looking to get the DCFAT (discounted at post tax rate). The reason for not getting DCFAT(discounted at post tax rate) is attributed to the wrong pre tax rate adopted. If u had adopted the real pre tax rate,e.g.52.56%, u would have definitely got CFAT discounted at post tax rate. But we cant say the same about CFAT discounted at pre tax rate. When u deduct present value of  the tax,e.g.9090 x 0.3=2727, from 9090, u know that u will  be getting only  DCFAT (discounted at pre tax rate). Here u cant in any way get DCFAT(post tax rate).  In the first case where the answer is 9090, it is wrong just bcoz of the wrong pre tax rate adopted. But where u get 6363, it is wrong bcoz of the wrong method adopted(by deducting tax discounted at pre tax rate,e.g.2727  from CFBT discounted at pre tax rate, u cant expect to get CFAT discounted at post tax rate). Here u r not going to get the right amount 6542 in any circumstance.

 Therefore CFAT discounted at pre tax rate should not be used for decision making purpose under the NPV method.  As I mentioned in an earlier post, it is fundamentally wrong.  The fact that the difference is very small  does not make DCFAT (discounted at pre tax rate) equivalent to DCFAT(discounted at post tax rate). Also the difference isnt small always.Where the cash flows are perpetual, the difference will be huge.  

Conclusion:CFAT discounted at pre tax rate have no relevance in decision making in the NPV method where discounting rate used is the cost of capital.

Why is the difference so massive(Rs.2548) in case c:

 U have rightly pointed out that the huge difference in case c is on account of the entire expenditure being eligible for tax savings(even though this is not the primary reason). Greater the tax impact, greater will be the difference between CFBT & CFAT. Even after  both the CFBT & CFAT are discounted at pre tax rate(formula based) & post tax rate respectively, the difference will still remain big(as in case c). But what will happen when the CFBT is discounted at the real pre tax rate? In that case, however big is the difference between CFBT & CFAT , it will be wiped off since the CFBT discounted at real pre tax rate equals CFAT discounted at post tax rate. So this means that  ultimately the cause 4 d difference is the wrong determination of the pre tax rate. To bring more clarity to the whole matter, let us use a simple formula as given below.

The difference

OR

DCFBT(discounted at adopted pre tax rate) - DCFAT(discounted at post tax rate)

=CFBT/(1+adopted pre tax rate) - CFBT(1+real pre tax rate).

Now let us analyse case c using the above formula. In case c, CFBT=10000, adopted pre tax rate=10% & the real pre tax rate=CFBT/CFAT discounted at post tax rate  -  1=10000/6542 – 1=52.8584%. So as per the formula, the difference=10000/(1+0.10)-10000/(1+0.528584)=9090-6542=2548(the same as u specified). Now let us adopt a higher pre tax rate, say 30% instead of 10%. The revised difference=10000/(1+0.30)-10000/(1+0.528584)=1150. Now if u further raise the adopted pre tax rate to 40%, u will get difference=10000/(1+0.40)-10000/(1+0.528584)=602. What do u observe here? As the pre tax rate which we use comes closer to the real pre tax rate, the difference becomes lesser & lesser. Now letz take case b. Here CFBT=10000, adopted pre tax rate=15% & real pre tax rate=10000/8802 – 1=13.6105%. The difference=10000/1.136105-10000/1.15=107(same as u got). If u  increase the adopted pre tax rate to 30%, the difference will be=10000/1.136105-10000/1.30=1110. Letz see what happens if we raise the adopted pre tax rate to 50%. The difference=10000/1.136105 – 10000/1.5=2135(now hasnt it become massive like in case c). Here we can observe that the difference gets bigger as we use a pre tax rate which is far away from  the real pre tax rate(in reality, nobody would adopt 30% or 50% as pre tax rate in case b since the amount we get by discounting at any of these rates is lower than the CFAT discounted at post tax rate..I just gave these rates in case b as further explanation regd the fact that the difference is caused by wrong determination of pre tax rate).

Conclusion: Now u cant anymore argue that the difference in case c is so big due to the fact that tax savings are available on the whole expenditure(thats the reason why I gave the above formula which is based only on the pre tax rates & isnt affected by the proportion of expenditure which is eligible 4 tax savings).The massive difference in case c is primarily caused by an error in determination of the pre tax rate.

Originally posted by : Jithin
	3)What if only pre tax rate is given in the question  U have 2 options. 1st one-use pre tax rate. 2nd one-compute post tax rate from the formula Post tax rate=Pre tax rate(1-t) & discount using this rate. I say its better to go with the 1st option. When we compute the post tax rate from the above formula, we r not going to get the correct post tax rate as the formula itself is flawed. Also when pre tax rate is given in the question, I think we should regard it as properly determined. I dont think that the pre tax rate given will be so low that the amount u get by discounting at pre tax rate will be higher than the actual post cash flows(that u receive after 1 year). For instance, in ur example, assume that the pre tax rate is 50%(I know its too high but just assume). Now letz discount 10,000 using 50%. U get 10000/1.50=6667 which is lower than 7000, the post tax cash flows. So it all depends upon the pre tax rate u use. If u discount using the right pre tax discount rate, the answer will not be illogical at all-u will get the same amount as u get by discounting at the cost of capital. Actually the crux of the whole issue lies in the practical difficulties one face in determining the appropriate pre tax rate. But from examination point of view, why do we have to bother about all this when the pre tax rate is readily given in the question & post tax rate is not mentioned. In such a situation, just use the pre tax rate & do the problem. Thats how I feel..

Above I had argued to use pre tax rate when post tax rate is not given. I had also given some reasons 4 that. But we can also argue the other way around. It is said to be practically very very difficult to determine pre tax rate. So u can argue that the question would not be referring to the real pre tax rate which is very unlikely to be determined in real life situations..Rather the rate would be based on pre tax post tax formula. If that is the case, then u can use the formula to find the post tax rate & discount at that rate.

In short, if u think pre tax rate in the question is the real one, then u can discount at pre tax rate. If u think that pre tax rate is formula based, then u have to derive post tax rate from the formula. So it all depends on how u view it. But ur or mine view is not what that matters in exams. What that counts is the institute's view. So it is better that we go thru the practice manuals,suggested answers,etc. & see what treatment is adopted by the institute in situations where only pre tax rate is mentioned.