The cash flow X follows an Ornstein–Uhlenbeck process: it wobbles, and it is pulled back towards its normal level θ at rate κ, so its expected value is θ + (x − θ)e^(−κt). Discounted at a constant r, a claim on it forever is worth θ/r + (x − θ)/(r + κ), and a lease of T years is worth θ/r·(1 − e^(−rT)) + (x − θ)/(r + κ)·(1 − e^(−(r+κ)T)). The wobble moves the paths but not the values: a linear cash flow only cares about its average.
With a random end made of N exponential stages of mean T/N, every e^(−cT) becomes (1 + cT/N)^(−N), compound interest with N periods, and the value converges to the exact one as N grows. The numbers on this page are computed here from these formulas; the post checks them against Python and against 200,000 simulated cash flows.