# Modelling NPV with negative cashflows?

When making capital investment decisions that have cost saving implications instead of cash flow generation, is NPV still valid?

For example: A state wishes to decide whether to replace a section of road (giving it a new lifespan of 30 years) or keep maintaining at. Both scenarios would have no positive cashflows as the stretch of road does not generate revenue, and both NPV's would be negative.

Would NPV still be valid to assist in this decision making?

• Yes, the highest NPV in this case would be the least negative, i.e. the least costly solution to keep the road working. Dec 17, 2019 at 20:33
• Yes, absolutely, as @AlexC says above. The dilemma here is the discount rate you use, which drives the incentives to take the hit early versus drag it out. Two obvious case studies here are the tobacco industry in the last 50 years and managing climate change over the next. Dec 19, 2019 at 1:31

For this type of analysis you'd look at the cash difference - meaning how much cash does it save by rebuilding the road versus maintaining it. The calculate the NPV of that savings, less how much it would cost to borrow the initial outlay.

So if the road cost \$10 Million in year 0 to build but saved \$700,000/year in maintenance over 30 years, you'd have an initial cash flow of -10,000,000 and cash flows of +700,000 over the next 30 years. You'd then subtract the cash flows of the bond used to fund the project. If the NPV of those cash flows is positive, then you'd do the project.

Alternatively you could look at the IRR of the cash flows without the bond. Then you could say you'd have to borrow money for less than that rate to make the project viable.

When making capital investment decisions that have cost saving implications instead of cash flow generation, is NPV still valid?

Yes, although you may need to reevaluate your discount factor.

Both scenarios would have no positive cashflows as the stretch of road does not generate revenue

Presumably, there is some value, otherwise they wouldn't be doing it. Even if they're not directly getting money, they should be able to put a dollar amount on what they think it's worth. If they're uncertain what amount to put, then this uncertainty should be factored into the discounting.

both NPV's would be negative

If the NPV truly is negative, then you would want to take the least negative NPV.

Yes, absolutely. It makes no difference to the NPV framework whether you look at opportunity costs and benefits rather than absolute or net cashflows. The tricky thing here is what you then mean by the IRR/discount rate/time preference.

Let’s say I am involved in international aid. I could spend a lot today in a big project that might make a big difference, reducing my future commitments (which are small but perennial in the alternative scenario).

The trade-off between imminent big cashflows and a stream of smaller future cashflows the other way (or vice versa) is no different than any corporation assessing a potentially profitable investment. No different at all.

What’s often less clear-cut here is the appropriate discount rate. What is the “cost of capital” of international aid?