Question

Marcel Co. is growing quickly. Dividends are expected to grow at a rate of 0.20 for the next 4 years, with the growth rate falling off to a constant 0.01 thereafter. If the required return is 0.14 and the company just paid a $1.95 dividend, what is the current share price? Answer with 2 decimals (e.g. 45.45).

Answer 1

In this question we need to find the cash flow of each year from this stock, then discount those cash inflows using the discount rate, PV of the cash inflow will be price of the stock

Let's first calculate Dividend of each year

Year	Last year dividend	Growth rate	calculation	Dividend
0				1.95
1	1.95	20%	1.95* (1+ 0.2)	2.3400
2	2.34	20%	2.34* (1+ 0.2)	2.8080
3	2.81	20%	2.808* (1+ 0.2)	3.3696
4	3.37	20%	3.3696* (1+ 0.2)	4.0435
5	4.04	1%	4.0435* (1+ 0.01)	4.0839

After year 4 dividend will be received in the form of an growing perpetuity

we need to find the PV of perpetuity

PV of growing perpetuity = Next year dividend/ (Discount rate - constant dividend growth rate)

where,

Next year dividend = $4.0839

Discount rate or required rate of return = 0.14

Constant dividend growth rate = 0.01

Lets put all the values in the formula to find the PV of perpetuity

PV of perpetuity = 4.0839/ (0.14 - 0.01)

                                   = 4.0839/ 0.13

                                   = 31.41

Now we have all the dividend amount which will yield from the stocks, next step is to discount the dividend amount using the required rate of return

Year	Dividend	PV factor	PV factor	PV of dividend
1	2.34	1/(1+ 0.14)	0.89286	2.089286
2	2.81	1/(1+ 0.14)^2	0.79719	2.23852
3	3.37	1/(1+ 0.14)^3	0.71178	2.398415
4	4.04	1/(1+ 0.14)^4	0.63552	2.569717
5	31.41	1/(1+ 0.14)^4	0.63552	19.96162
			Total	29.25756

Stock price = $29.26

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