Question

a cottage is for sale for $580,000. currently it generates annual cash flow, net of all expenses and taxes of $ 35000. if the cottage lasts forever what rate of growth of the annual cash flow will be necessary for you to earn an 8% annual rate of return on your investment

Answer 1

As the initial investment is 580,000, the PV of all the cash flows (with discount rate = 8%) must be equal to 580000.

To find the required growth rate (g), we use the goal seeker function in Excel -

Initially, we assume value of g to be 5% (or any other). Then we find the PV of all the cash flows in year 1 using the terminal vaule formula.

Terminal value = CF * (1+ g) / (r - g)

Here, CF = Cash flow in year 1 = 35000

So, PV at the end of year 1 = PV1 = 35000 * (1+5%) / (8% - 5%)

Now, we find PV of this value at year 0 = PV0 = PV1 / (1+8%)

Now, we use the goal seeker function in Excel to make this value PV0 equal to 580,000 by changing the value of g.

Year
0	-580000
1	35000
g	2.28%
r	8%
PV1	626400
PV0	580000