Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Nortel preferred stock?

Preferred stocks are commonly held in a long-term basis, I mean they are not sold because they pay good interests, so we can assume the investor will hold the preferred stock forever.

In that case, the price would be calculated this way:

If you divide by 1.085 you just discounting 1 dividend at the end of the year.

However, we said the investor will hold the stock forever so he will earn indefinitely $3.75 dividends (infinite number of dividends).

When you calculate the present value of a stream of chash flows, you discount to the present all dividends earned each year. So, the discount factor of that infinite stream of equal cash flows tends to the same discount rate, which in this case is 0.085.

This fact is proved mathematically, and of course assume it is a formula we just apply. If you want, you can search more about the demonstration.

gordon growth model instead of dividend discount modelâ€¦ Gordon growth is a special case of the dividend discount model for a dividend with predictable behavior into the relevant future.

P = D/ r-g but since the dividend is fixed, g=0

this is the simple curriculum based explanation for what Harrogath is saying is a rather sophisticated way.