# 2 stage DDM

Why do you discount the terminal value stock value with n number of years of high growth years?

For example, if dividend is \$1 and will increase 10% each year for the next 10 years and then 5% in perpetuity, the dividend on the 11th year is 1*(1.1)^10*(1.05) = 2.72

Assume required equity return is 7%. CFAI says present value is 2.72/(1.07)^10.

Shouldn’t that be (1.07)^11 because the dividend payment happens in year 11?

At the end of year 10 (after just receiving the last dividend from the high-growth phase) the present value of the constant growth phase (= terminal value) is

terminal value = PVt=10 = D11/(r-g) = 2.72 / 0.02 = 136

In order to get the present value at t=0 you then have to discount this with n=10 (as the above was the present value at the end of year ten) so

PVt=0, terminal value = D11/(r-g) * 1,07^(-10) = terminal value / 1,07^10 = 69.14

If on the other hand you are looking at the present value of just the single dividend payment made at the end of year 11, then you have discount it with n=11 (as the dividend is paid at the end of year eleven):

PVt=0, dividend = D11 / 1,07^11 = 1.29