The problem with your analysis is that it doesn't take into account the time value of money. A dollar today is worth more than a dollar in a year, simply because putting a dollar in the bank gives you more than a dollar in year. If the present value of the expected future benefits are greater than the present value of expected costs, as long as your cost of capital is correct the project WILL add value to the firm, regardless of how long it takes. this is called NPV analysis.
The payback period method on the other hand is not based on Economic theory, it doesnt take into account cash flows after the payback period, favors small projects and discriminates against large ones. There's no Economic method to calculate a proper payback period, and so the payback periods are arbitrary.
Many businesses have disregarded great projects that would have added value to the firm but simply had the wrong accept/reject criterion. Accounting methods are not quite appropriate here, since the main point of accounting is to match costs with revenues, and indeed the financial formulas to find a stock's price involve taking the accounting financial statements and working backwards to find the real cash flows again.
About perpetuity, imagine that buying the spectrum was equal to receiving a set number of dollarsfrom the government every year, let's say $1000/year forever. Assume a 6% cost of capital for the company. Now we can easily find out how much this is worth today. 1000/.06 = $16,666.67. (This is a limit simplified down, 1000/(1.06) + 1000/(1.06)^2 + 1000/(1.06)^3 +
That would be the cost you need to pay today to get a perpetual annuity of $1000, kind of like buying rights to the spectrum.
Are you still baffled? It's really just Economics backed with maths.