# Adjusted present value, finance, economics

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1. Oct 10, 2017

Did not find any "place" for this question, but hopefully someone will be able to give me some help with this.

corporate tax: Tc= 25%
return on debt: rD=4%
return on assets = rA= 10%
Debt as amount of total value: D/V = 0.6
Equity as amount of total value = E/V = 0.4
A perptual cashflow before tax: 1 000 0000 (per year)

I'm trying different ways of finding the value of this cash flow.

The first I do is finding the WACC after tax, which I find to be 9,4%

This gives a present8 value of: 1000 0000*(1-0.25)/0.094 = 7 978 723, and this gives a Debt of 0.6*7 978 723 =4 787 234

However, we are supposed to do this with a an APV-approach, where we use the rA which is equal to the return on equity with no leverage (WACC without tax),

the new approach is: 1000 000*(1-0.25)/0.1 + D*Tc where the last part is the present value of the tax shield. the new equation, using the debt (D) I found from the WACC-solution is: 1000 000*(1-0.25)/0.1 +4 787 234*0.25 = 8 696 809

But this is not the same as I found using WACC after tax

What am I doing wrong?

Thanks

2. Oct 10, 2017

### Ray Vickson

Help us put here: what is WACC, what is the APV approach? Just write words instead of using abbreviations which might not be unique or universal. (That is, abbreviations may differ among different books or between different nations.)

3. Oct 10, 2017

### StoneTemplePython

My thinking is that these are fairly standard bits of finance jargon, and OP is actually pretty close to an answer... the formatting is quite bad though.

Weighted Average Cost of Capital : your calculation checks out.
First Valuation: seems fine.

Big idea: in all cases we have after-tax unlevered Free Cash Flow of $0.75MM$. (Note: for convenience I'm going to drop the \$ sign and the MM which indicates millions -- it should be clear that I still mean this though -- if there's ambiguity I can add them back in) .

In your first case, you bake the tax benefit into the discount rate and get a valuation of $7.978723$, which seems fine to me. Then you calculate the portion that goes to debt holders -- also fine.

The second case, seems awkward at best to me though -- I think there's a way to salvage it, but it seems unintuitive to me.

I like the first term in your second case: you're taking your $0.75$ of unlevered FCF and using the raw discount rate of $10\%$ which seems fine. As a gut check compare this value and the first one you computed -- the difference is the value of the tax deductibility of interest and the difference here should just jump out at you.

Another way to think about it is to keep in mind that $\frac{0.75}{0.1}$ represents a summation of discounted cash flows in perpetuity . I.e. it is:

$\frac{0.75}{0.1} = 7.5 = \frac{0.75}{1.1} + \frac{0.75}{1.1^2} + \frac{0.75}{1.1^3} + \frac{0.75}{1.1^4} + ...$

Why not just do the same with the tax benefit that the firm gets each year because it can deduct its interest payments and add it in with the number above?

4. Oct 11, 2017

### Ray Vickson

I was attempting to have the OP supply the information, as I was trying to set up a "teachable moment" with him/her. I wanted the OP to realize that it is fine to use such jargon in a specialized user group, but it is not OK to use it in a general-purpose forum such as this one. So, besides learning something about Finance, he/she might learn something about communication.

5. Oct 11, 2017

Today at 1:52 AM#3
StoneTemplePython Thank you for the answer!
The reason why I am trying to find an answer by this approach is that an assignment I'm working on explicitly tells me to find the value of the project by 4 different approaches. One of these approaches tells us to discount the cash flow as if there was no debt, using the unlevered cost of capital, and then add a part that constitutes the present value of the tax shield - an approach that in the text is referred to as the APV approach, (Adjusted present value). I would not have chosen to find the value this way, but the assignment simply tells me to :P

Mons

6. Oct 11, 2017

### Ray Vickson

There is no reason that different methods should give the same results. The different methods correspond to different "views" of corporate finance and its relation to corporate long-term health. Some companies use one method, while other companies use a different method, and each is convinced of the merit of its approach. In fact, the same company might use different methods in different contexts.

7. Oct 11, 2017

Hm, that feels odd. The text tells me to show all the approaches in order to illustrate that they provide the same result.

Mons

8. Oct 11, 2017

### Ray Vickson

That is true for some special cases---that is, under certain circumstances---but is not true in general.

For your specific problem with all its underlying assumptions, the statement you want is, in fact, true.

Even when the two methods do not deliver identical valuations they often deliver "similar" evaluations, so if you are trying to decide whether to take project A or project B, they might lead to the same project rankings even though the actual evaluations are different for the different methods of valuation.

Anyway, I think the problem you are facing might arise from the way you evaluate debt in the APV method. Google "APV" to see various articles that deal with such matters and work through some numerical examples.

9. Oct 11, 2017

### StoneTemplePython

Fair point. Acronyms and jargon are kind of endemic in finance (and I have a sneaking suspicion that it is to raise entry barriers / sound smart in front of clients, but that's a different discussion).