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SPM is derived from the compound interest formula via the present value of a perpetuity equation. The derivation requires the additional variables X {\displaystyle X} and R {\displaystyle R} , where X {\displaystyle X} is a company's retained earnings, and R {\displaystyle R} is a company's rate of return on equity.
is the constant growth rate in perpetuity expected for the dividends. r {\displaystyle r} is the constant cost of equity capital for that company. D 1 {\displaystyle D_{1}} is the value of dividends at the end of the first period.
The present value of $1,000, 100 years into the future. Curves represent constant discount rates of 2%, 3%, 5%, and 7%. The time value of money refers to the fact that there is normally a greater benefit to receiving a sum of money now rather than an identical sum later.
for each future cash flow (FV) at any time period (t) in years from the present time, summed over all time periods. The sum can then be used as a net present value figure. If the amount to be paid at time 0 (now) for all the future cash flows is known, then that amount can be substituted for DPV and the equation can be solved for r , that is ...
MedICT has chosen the perpetuity growth model to calculate the value of cash flows beyond the forecast period. They estimate that they will grow at about 6% for the rest of these years (this is extremely prudent given that they grew by 78% in year 5), and they assume a forward discount rate of 15% for beyond year 5. The terminal value is hence:
Imagine investing $1,000 on Oct. 1 instead of Oct. 31 — it gains an extra month of interest growth. To account for this time advantage, the formula for the future value of an annuity due is:
If the discount rate for stocks (shares) with this level of systematic risk is 12.50%, then a constant perpetuity of dividend income per dollar is eight dollars. However, if the future dividends represent a perpetuity increasing at 5.00% per year, then the dividend discount model, in effect, subtracts 5.00% off the discount rate of 12.50% for 7 ...
The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.