I’ve encounter this basic problem today and it kind of puzzeld me. Let’s say I consider entering in a project with revenues of 500$ and cost of 300$ both at t=1. Let’s assume that they are both risk free so we can discount them at a risk-free rate of 3%, then my NPV for the project would be 500/1.03-300/1.03 = 200/1.03 = 194,2
Now let’s assume a similar project with still risk free revenues of 500$, but risky costs with expected value of 300$ both at t=1. So if we add say, a 2% risk premium to the costs ,we would have a NPV of 500/1.03-300/1.05 = 199,7.
In the other words, Ceteris paribus, a project with riskier cost should be more attractive? what’s wrong here? If we added a risk premium to the net cash flow, we would obviously have a smaller NPV!
yeah, that would be my first thought too, usually when we use a valuation method, like FCFF valuation, it’s like if we are using net cash flows. To put some context to my question, I was reading a paper where the author was citing five misusage of the npv analysis. One of his critique was that if costs and revenues have different risk profiles, we should discount them separately with different discount rate.
Now if revenues are risky and cost riskless, you don’t get any weird result, but if you have risky cost and riskless revenues you get the weird result I was trying to show. Do you think there is argument against decomposing cash flows?
“Do you think there is argument against decomposing cash flows?”
Money is fungible - your utility relates only to the total amount of money you own at the end of the period. Gain $100 + Lose $10 = $90. It is exactly the same as Gain $110 + Lose $20 = $90. So, why would you want to discount the components differently under these two scenarios?
well, if your evaluating a real project, you me be able to measure the risk of different components of the project more reliably individually ( like costs and revenues, or maybe even different types of revenues). But i agree with you, if you have a good way to estimate the risk of the net cash cash flow, it may be optimal to discount this amount.
Again, under the assumption that we can measure the risks of the individual components, i still find it weird that an increase in the risk of the cost the project would increase it’s NPV, don’t you think?
If you can measure the risk of individual components, you can measure the overall cashflow risk…
“i still find it weird that an increase in the risk of the cost the project would increase it’s NPV, don’t you think?”
As I have been trying to communicate (with apparent failure), adding positive risk premium to cost makes no sense and the result is counter to logic or practical use.