# How to Calculate NPV with Taxes

In this article, I will show you how to calculate the net present value of a project when taxes are taken into consideration. So the first thing we’re going to do is we’re going to take all the cash flows of the project and we’re going to convert them to an after-tax basis using the company’s tax rate then we’re gonna discount all the cash flows to their present value just like you would with a normal NPV problem.

So let’s take this problem right here as an example

So we’ve got a pizzeria that pays \$60,000 cash today to buy a pizza oven and then they’re gonna use that oven to generate \$20,000 of cash flow each of the next 4 years they’re gonna depreciate the oven taking \$15000 of depreciation every year and at the end of year 4 they’re gonna sell the oven for \$6000 and they’ve got an income tax rate of 21% and then a discount rate of 8% that we’ll use to find the present values.

So let’s work on this problem. So in period zero which is today, we’re gonna have a negative  -\$60,000 we’re not gonna have to discount that or worry about after-tax or anything like that. So let’s move now to period one we’re gonna receive \$20,000 but remember we’re gonna have to pay tax on this \$20,000 we’re receiving. So you take  \$20,000 and multiply it by (1 – the tax rate). One minus 21% so it is 79% and that’s gonna give you \$15,800.

So we’re gonna put \$15,800 in period 1 and here’s what this means we receive \$20,000 of cash however we had to pay tax on that money at 21% and if you calculate the tax and subtracted it from the \$20,000 you would give \$15,800. Now we’re also going to get a tax deduction for the depreciation. Now normally in real life depreciation would not be the same amount every single year because for tax purposes usually you have accelerated depreciation where you take more depreciation in the early years of the asset but to make this problem simple we’re just gonna say \$15,000 every year for 4 years.
So we’re gonna take that \$15,000 and we need to know what is the value of that tax deduction because that deduction is going to reduce the amount of tax we have to pay and how do we figure that out? Well we multiply it by our tax rate 21%. So \$15,000 times 21% is \$3,150. So our cash flows on an after-tax basis for the very first period we’d have \$18,950.

Another way of getting that well I’m just going to take \$20,000 of income that we had, subtract the \$15,000 of deduction the tax deduction of depreciation, then \$20,000 minus \$15,000 would mean you’d have \$5000 of taxable income you multiply that by 21% which is (\$5000 x 21% = \$1,050) that means you’ll have to pay in the first year \$1,050 in taxes. So this would be a cash outflow for taxes but you receive \$20,000 so \$20,000 minus the tax you pay of \$1,050 that would also give you \$18,950.

So I’m just saying there’s just there’s a couple different ways to do it. Now but I’m just going to continue with the first way where we’re converted the after-tax cash flows first. So for the second year we’re also gonna receive \$20,000 but after we multiply by (1 – the tax rate) that’s \$15,800 and again we’re gonna have this depreciation to reap. By the way if you don’t understand why I’m doing this (\$15,000 X 21%) remember that although depreciation is a non-cash, like it doesn’t it’s not like we’re getting cash but by depreciating an asset we’re getting a tax deduction of \$15,000 and that’s saving us or we don’t have to pay \$3,150 of taxes. Okay so if you’re thinking about well depreciation is not a cash flow why are you doing this it’s because it’s giving us a tax break and we’re saving \$3,150 of taxes. So again we’re gonna have \$18,950. So the these here are after-tax cash flows remember I said that’s the first step we’re going to do convert to after-tax basis and I’m for the third period they’re the same thing \$18,950.
The fourth year we’ve got one little different so we got \$15,800 we’ve got  \$3,150 but then we also sell a machine we have a gain of \$6000 that’s going to be taxed, we take \$6000 times (1 – the tax rate) which will be 79% so that means that we’re gonna get \$4,740 after we pay tax on that gain. we’re gonna receive four thousand seven hundred and forty dollars. So I’ll add it too then we’ll get \$23,690.

We’re gonna discount each of these to the present value. So these after tax cash flows now we need to discount them remember our discount rate is 8% So divided by (1.08) to the first power. Why am I doing that? Well you take your cash flow divided by (1+ the discount rate) to the n’th power, where n is the period.
So we’re gonna divide the year two cash flows divided by (1.08) to the second power, here you’ve 3rd year cash flows divided by (1.08) to the third power and then here 4th year cash flows divided by (1.08) to the fourth power.
So now here our after tax cash flows and we discount this \$18,950 divided by (1.08) to the first power so that comes out to \$17546 then the 2nd one this one is \$16,247 and then 3rd one is \$15,043, okay? and then last number 4th one here is \$17,413. Now if we add them across we get to \$6249 that is the net present value of this project now because the project has a positive net present value the NPV is greater than zero assuming the company has the capital to do this project, they should accept the project.

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