Capital budgeting

If you invest 600 today 2014 , buying land, you have positive CF inflows(rents) for 15 years of 70 each year, and some positive NPV. It is now second year ,2016,you have bought the land ,but you have not started the project yet and you want to make new calculation of NPV as of today,2016 – what outflow as price you put of the already bought land ?

CF0 (2014) = -$600

CF1 = $0

CF2 = $0 (I’m assuming the project starts in 2017)

CF3 = $70

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CF17=$70

NPV = -600 + (t=1 to 17) Σ CFt / (1+r)^t

If you’ve already bought it, it’s a sunk cost; you don’t include the cost.

Use zero.

you are calcularing the NPV from 2014 perspective , the idea is to calculate it from 2016 perspective… what is the value of this -600 two yeras later…do you have to increase this value with the interest you have paid those two years for the loan you have taken for this 600 ,tjis 600 are not interest free …

the idea is not if you have to proceed the project or not…the idea is that you proceed with the project but you pospone it with 2 yeras and what is the value of this 600 two yeras later…600 + interest on it or…

The opportunity cost here in case the project does continue is accounted for in the discount rate, then you assess the initial investment that was required for the following cash flows to take place, regardless of when they begin. Then you net out the PV of cashflows with the IO.

If you put down 600 cash and after two years the project was abandoned, then yes you lose money (assuming you can’t get the 600 back) and opportunity interest equal to either the risk free interest rate on investment, or the interest rate of another project with a similar risk profile (the r you would have used to discount the CFs had it completed).

But in terms of ‘NPV’, you don’t lose more money than you spend, so it stays -$600. You have an economic loss greater than that, but not an expicit one.

It’s my understanding that this is not a sunk cost, but rather an opportunity cost that should be considered a cash flow as opposed to being included in the discount rate. The land could be sold or used to generate rent if not used to the purpose specified in the capital budget.

Then you calculate the NPV of the project if you rent the land, and compare that to the NPV of the project.

Pick the higher one. Simple.

Good point.

In that case, the proper initial cost is the current value of the land: the price for which you could sell it in 2016, or the PV of the rent it could generate, whichever is higher.

It cannot stay -600, at least you should add the interesrt that you paying for the money you borrowed to buy this land…the interest for those 2 yeras…yes you have economic loss but the real outflow is :

2014 (-600)

2015 (-60) - interest 10%x600

2016 (-60) interest 10%x600,

so total outflow -600+(-60)+(-60)=(-720) so in 2016 you should put as outflow (-720), so because of delay the initial outflow has risen

You’re close, you use the PV of debt as an initial outflow, and net that out with the PV of the CFs. NPV is the netting out of the PVs of inflows and outflows.

So if you borrow that $600 at 10% interest for let’s say, 5 years of the project until you can pay it back from proceeds, the discount rate for the project would be matching the risk free rate of return on the project’s period (assume 15% on a 15 yr T-Bond), then NPV can also be re-written as:

PV of debt = -$500 (n=5, FV=600, PMT=60, r = 15%)

NPV = -$500 + PV of CFs at r = 15%

If NPV>0 then it’s a profitable investment.