Question

A stocks next 2 dividends are as follows: $0.25 and $1.00. After that, the stock is expected to grow at a rate of 4% indefinitely. The required return on this stock is 16%. Compute its fair market value.

Answer 1

After year 2 the dividend will be received in the form of a growing perpetuity.

Year 3 dividend = 1 * (1 + 0.04)

                              = 1* 1.04

                               = $1.04

First we need to find the PV of that perpetuity

In growing perpetuity annual periodic payment increases by fixed percentage each period.

If periodic payment is P, interest rate is r and growth rate is g then PV of growing perpetuity

= P/ (r - g)

Where,

P= 1.04

i= 0.16

g= 0.04

Let's put all the values in the formula,

PV of growing Perpetuity = 1.04/ (0.16 - 0.04)

= 1.04/ 0.12

= 8.67

So PV of perpetuity is 8.67

So now we have all the cash flows from the stock, we need to discount these cash inflows, the PV will be the stock price.

Year	Cash flow	PV factor @ 16%	PV of cash inflow
1	0.25	0.86207	0.216
2	1	0.74316	0.743
2	8.6	0.74316	6.391
		Total	7.350

So the price of the stock is $7.35

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Hope that helps.

Feel free to comment if you need further assistance J