# Math Help - NPV

1. ## NPV

Hello and thank you for reviewing this post: Any insight would be grateflu on this end.

Can an NPV of investment be negative?
Is there a calculator on line that can check my work for a investment building with cost 35mil, straight line depr basis to zero over ten year, own for 12 years sell it 6 million. Generate revenue of 8 mil per year with expenses of 3 mil. Taxable bond paying at 8% and marginal tax rate of 25% What is your NPV of this investment?

I started with NATCF to figure out Net after tax cash flow.
I followed on with NPV:

Years 8% discount NPV
0- -35M = -35M
1-5 4.625M with using table NPV 3.993 = 18.567M
6-10 4.625M 6.710-3.993 = 12.56
11-12 3.75M 7.536-6.710 = 3.0975
total = -.87
you have a 12 year salvage value
6 M - 6M(.25) = 4.5Million
Do you add the 4.5 M to -.87? for 3.63NPV

Any insight...

Thanks

Scarter

2. I saw your other post about not receiving an answer to these problems, so here I am. I think it's too late to help with your hw, but maybe this answer will benefit you in the future.

A negative NPV means you would lose money on the project, investment, underlying asset, etc. This just means that your initial payment is greater than the cash flows yielded from the project down the road. However, this only refers to the measurable, monetary benefits. A project may end up being positive when other things are taken into account (goodwill, free advertising, etc.).

The best way to do this particular problem is in Excel or a like program. For each year, calculate the After Tax CF in that year, then discount at your WACC to present value. So, it sounds like you were on the right track.

Each Year Consists of:
+Revenue
-Expenses
-Interest
-Depreciation
=EBT (Earnings Before Taxes)
-Taxes (assumed 0 for taxes if EBT is negative)
+Depreciation
=EAT(Earnings After Taxes)

While year 12 or t12 also contains the profit from the sale of the asset at the end of the year.

The initial cost is $35,000,000 and interest payments are 8% for a payment of$2,800,000 each year. In all reality, if you borrowed the money in bonds at t0, you would pay the interest through t12 and then pay back the principle at t12. This means the amount you repay (in terms of today) is $35,000,000/(1+.06)^12 =$17,393,928 (this is your CF0).

Discount Rate(r)= WACC= (Cost of Debt)*(1- Tax Rate)= .08*(1-.25)=.06

See the attached image for the spreadsheet I made and numbers that I got. In the end, I had a positive NPV: \$3,106,710. I hope I'm not missing information or assuming something I'm not supposed to assume.

Cheers,

~TC