Valuation Assuming 2-Stages of Dividends
We can also use the dividend discount model even when the firm's dividends are not the same every year. For example, a firm can have an initial period with higher dividends while the firm is growing (1st stage), but, when the firm matures, it would lower its dividends (2nd stage). To value this type of asset, the idea is to think about how the cash flows are laid out each year and discount those cash flows back to the present. However, after you layout the cash flows, you may be able to see that you can perform some of the calculations using simplifying formulas. Specifically, in the above case, the 2nd stage where there is a lower dividend amount paid forever, you can use the Perpetuity with Growth formula you learned earlier.
In the 1st stage, the high dividend payments occur for a finite period of time. We can layout the cash flows for the first few years and then discount each of those annual cash flows to the present. In the 2nd stage, we use the Perpetuity with Growth formula to value the lower dividend payments into perpetuity.
In this exercise, assume that the preferred stock pays a higher dividend rate of 10% from Year 1 to 5 or $2.50 per year (high_div). The relevant discount rate (kp) for Years 1 to 5 is 10%. The present value of the dividends from Year 6 onwards, which we calculated in the prior exercise, is stored in memory as pref_value_low. What is the value of this preferred stock?
Note: Since we add the value of an extra five years of cash flows, the value of the preferred stock in this example will be higher than the value of the preferred stock of $7.76 in the prior exercise.
This exercise is part of the course
Equity Valuation in R
Exercise instructions
- Calculate preferred dividend during 1st stage.
- Add variable for the number of discount periods.
- Calculate discount factors.
- Calculate present value of the dividends for Years 1 to 5.
- Calculate present value of all cash flows from the 1st stage.
- Add the value during 1st stage to the value of the 2nd stage (low dividend period).
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Preferred dividend in Years 1 to 5
high_div <- ___
# Create vector of Year 1-5 dividends
pref_cf <- rep(high_div, 5)
# Convert to data frame
pref_df <- data.frame(pref_cf)
# Add discount periods
pref_df$periods <- ___
# Calculate discount factors
pref_df$pv_factor <- ___
# Calculate PV of dividends
pref_df$pv_cf <- ___
# Calculate value during high stage
pref_value_high <- ___
# Calculate value of the preferred stock
___