<p>It looks like a cash-accounting NPV that includes closing the position (selling the plant, the car, whatever) after the period of consideration. Asset values show up in the final term because cash accounting applies cash outlays to the period in which they actually occur. Typically, that asset value would be net of depreciation and therefore less than <span class="math-container">$I_0$</span>.  Contrast this with accrual accounting, which would spread the depreciation over the period, perhaps by making some reasoned assumption about an annualized depreciation rate.</p>

<p>Note that <em>unlevered</em> free cash flow does <em>not</em> count debt obligations. This means interest payments as well as any principle are not counted by the <span class="math-container">$CF_{year}$</span> terms, and is why liabilities show up in the calculation explicitly, rather than being rolled into the cash flow term.</p>

<p>However, it's not clear to me why discharge of those liabilities is deferred to the third year - or why a "sum of all cash flows" term shows up, which appears to be double-counting. Perhaps if you share the context of where you're seeing this, that will help.</p>

CC BY-SA 4.0
2020-01-07T15:03:17.117Z
2020-01-07T15:12:56.110Z
2020-01-07T15:12:56.110Z
heh
<p>This doesn’t make sense, because Free Cash Flow (in each period) already takes changes in assets and liabilities into consideration.</p>

CC BY-SA 4.0
2020-01-07T14:43:35.390Z
2020-01-07T14:43:35.390Z
ssn
<p>I have found the following NPV (Net Present Value) formula:</p>

<p>CF = <strong>unlevered</strong> cashflow</p>

<p>i = interest rate (WACC)</p>

<p><span class="math-container">$$NPV = -I_0 + \frac {CF_{2019}}{(1+i)} + \frac {CF_{2020}}{(1+i)^{2}} +\frac {CF_{2021}}{(1+i)^{3}} +\frac {(assets_{2021}-liabilities_{2021}) - \sum_{}CF}{(1+i)^{3}}$$</span></p>

<p>I have always seen NPV formula without that last weird addition of assets-liabilities etc.</p>

<p>Can someone explain me its meaning?</p>

<microeconomics><mathematical-economics>
NPV but adding last year net value?
Keka Bron
# NPV but adding last year net value?

(Asked by: username_0 on 2019-12-25)

I have found the following NPV (Net Present Value) formula:

CF = **unlevered** cashflow

i = interest rate (WACC)

$$NPV = -I\_0 + \frac {CF\_{2019}}{(1+i)} + \frac {CF\_{2020}}{(1+i)^{2}} +\frac {CF\_{2021}}{(1+i)^{3}} +\frac {(assets\_{2021}-liabilities\_{2021}) - \sum\_{}CF}{(1+i)^{3}}$$

I have always seen NPV formula without that last weird addition of assets-liabilities etc.

Can someone explain me its meaning?

**Tags:** microeconomics, mathematical-economics

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## 2 answers

### Answer by username_1 on 2020-01-07. Score: 1 | Accepted answer

It looks like a cash-accounting NPV that includes closing the position (selling the plant, the car, whatever) after the period of consideration. Asset values show up in the final term because cash accounting applies cash outlays to the period in which they actually occur. Typically, that asset value would be net of depreciation and therefore less than $I\_0$. Contrast this with accrual accounting, which would spread the depreciation over the period, perhaps by making some reasoned assumption about an annualized depreciation rate.

Note that *unlevered* free cash flow does *not* count debt obligations. This means interest payments as well as any principle are not counted by the $CF\_{year}$ terms, and is why liabilities show up in the calculation explicitly, rather than being rolled into the cash flow term.

However, it's not clear to me why discharge of those liabilities is deferred to the third year - or why a "sum of all cash flows" term shows up, which appears to be double-counting. Perhaps if you share the context of where you're seeing this, that will help.


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### Answer by username_2 on 2020-01-07. Score: 0

This doesn’t make sense, because Free Cash Flow (in each period) already takes changes in assets and liabilities into consideration.


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