So there's an allowance for the cost if the lease going up with inflation but not for the payments being made to go up year on year? That's the reason that just divided one by the other, as otherwise yes payments in year 1 will be high but by year 27 will be low. In this case £300 million and £176 million (assuming 2% inflation for 27 years devaluating the value of the payments for the final year).
I'm not sure that I quite understand your point, so I'll describe what is understood by NPV and explain a bit more the model I used. Health warning - I am not an accountant but I have done such calculations in the past in trying to work out the best course of action! This is also a very brief outline - NPV calculations can be a lot more complicated!
Money has a time value which basically says that incomes and expenditures today or next week have a more direct effect on you that the same amount in 10 or 20 years time - even if the transactions now and those in the future were equally certain, that is, there is no risk involved. In other words, future payments are of less value to you now than the payments being made to you now. For example, a payment being made
now can be invested immediately and earn interest or can be used to pay a bill and avoid you being dragged through the County Courts! Payments to be made in the future are a bit more, well, theoretical!
This reduction in the current value of future cash flows depends largely on the inflation rate and what the market's expected rate of return is for the particular class of transaction or business. There are sets of formulae for calculating NPV, but basically one takes the transaction (positive for income or negative for expenditure) at some point in the future - normally at fixed time intervals, weeks, months or years - add the two together and discounts the result by the nominal inflation rate (or rate of return) expected between now and then. The result is the Present Value at that point in time. Each of these Present Values over the life of the programme or investment is then added together and the sum is the Net Present Value.
In order to be able to compare the profitability or otherwise between different investment opportunities a standard discount rate is used - here that tends to be the Treasury's Test Discount Rate which is set at 3.5%. Note that this is not necessarily the expected inflation rate - it is simply a standard number which gives consistency between different sets of calculations.
So I assumed the annual payment for the diagrams contracted for in the IEP agreements would increase by 1% - costs do increase but these can be countered by more efficient working methods or the discovery that some part doesn't need so much maintenance as expected. So 1% seems about right.
Not all the trains will be in service in Year 1 so I assumed only part of the £300 million will fall due in that year, Year 2 more trains would be in service and the full Train Service Provision Payments would first fall due in Year 3. After this I increased the £300 million by 1% compound for the next eighteen years. All the annual payments from Year 2 onwards were then reduced by 3.5% compound and these answers, including Year 1, were summed to get the NPV. It's quite easy on a spreadsheet!
And my calculation - for such a crude model - is not a million miles from the figure published by the DfT. So I reckon that the annual Train Service Provision payment for the contracted diagrams on the Western is probably somewhere between £275 million and £325 million per year.
