In this class, let's learn how to get the present value of perpetual cash flows. Suppose, you have a building and receive a rent every month. As long as you own the building, you will get the rent forever. Then the value of the building is the present value of the future rent cash flows without maturity. That is called perpetuity. Let's say the rent is $1,000 per month. And the rent is due at the end of each month. Rent payment at the end of the month is unusual. But let's assume that for a moment. Later, we will see what happens to the value of a building if rent payment is made at the beginning of the month. Next let's assume that the return on investment required by real estate investors is 6% per year. That is the discount rate for the rent cash flow is 6% divided by 12 = 0.5% per month. Then the value of the building is $100,000 divided by 0.5% = $200,000. You may wonder why I divide the rent by discount rate to get the value of a building. In order to understand this formula, let's consider a bank savings account that pays you 0.5% per month on the balance forever. If you want to receive $1,000 of interest every month from the savings account, how much do you have to put up in the savings account? The equation to solve for the amount to put up in the account is Amount X 0.55% = $1,000. If you divide $1,000 by 0.5%, you get $200,000. Therefore, the amount you have to put up in the savings account is $200,000, right? In this equation, $1,000 is the perpetual cash flow. 0.5% is interest rate. And $200,000 is the present value of perpetual cash flow of $1,000. Using this example, we can make a formula for present value for perpetual cash flows that is cash flow divided by rate is equal to present value. If the rent is paid at the beginning of each month, the value of a building is present value of perpetual rent plus the first month rent. That is present value equal to cash flow divided by rate plus cash flow. You can apply this formula to find the value of real estate as well as the company. If a company is mature, you assume that the company's cash flow is the same forever or grows at a constant rate. Then you can use the same formula to find this terminal value of a company in a mature stage. We are going to learn that later. You can also find the present value of a perpetuity using present value function of Excel by putting large number of periods for NPER. Let's confirm this with Excel. Why don't you start Excel. In Excel, type in PV. And then type in 0.5% for rate. And then type in 10,000 for NPER. That's an arbitrary number. And then type in 1,000 for PMT. And then type in 0 for FV. The result is -200,000. That is, in order to get $1000 every year forever. You have to invest $200,000 today and you also interpret this as the present value. As you can find in this result when the number of payments are large enough, the payment is similar to perpetuity and the present value of these payments is almost the same as present value of perpetuity. Next, let's consider a case where annual rent from a building is increasing every year by inflation rate of 3%. It is more realistic since there is an inflation in the real world. This kind of cash flow is called growing perpetuity. Suppose the annual rent is $12,000 and required return on investment is 6% per year. Then the Present Value of a building is $12,000 / (6%- 3%) = $400,000. You can make a formula for growing perpetuity as Cash Flow divided by (Rate- Growth Rate) is equal to Present Value. This formula is derived using the infinite geometry series formula. You may wonder how this formula is made. But we are not going to discuss it since it is beyond the scope of this course. So we are going to use this formula for present value of growing perpetuity as it is given.