[cpa1988]

Fernwell wants to buy shares of Gurst Company in two years. Fernwell uses a constant growth dividend discount model with a presumed dividend growth rate of 5%. If Fernwell’s discount rate is 10% and Gurst’s current year dividend is $20, what is the approximate price Fernwell will pay?

a. $400

b. $463

c. $420

d. $441

Explanation:

Choice “b” is correct. Fernwell will pay approximately $463, computed as follows:

Step #1, Compute dividend in subsequent year:

Equation

P= D / (R-G)

D = $20 x (1.05)^2

D= $22.05

***How are they getting 1.05 for R-G?

Step #2, Apply growth rate to computed dividend:

P= D / (R-G)

P= (22.05×1.05) / (.10-.05)

P= $463

I guess I am just confused by the first step of the problem. It seems like R= .10 and G= .05, so how does that turn into 1.05?

[cpa1988]

Or just know that the price of a dividend in one year is equal to the price of the dividend today multiplied by 1+growth rate? Again I tried to do this chapter in 4 hours so I am doing all of this for the first time in … 3 years. Should probably be common knowledge but oh well

[cpa1988]

and is the (1.05) in step squared because it is the second year since they have had the dividend or because they are buying shares in two years?

[h0wdyus]

what is the formula to be used here. Can you describe.

FAR - 81 29th Aug 2013
AUD - 84
REG - 82
BEC - 89 29th Aug 2014
Using Yager

FROM NJ

[theCPA15]

You have to find the dividend that will be paid in year three because the cost in year two will be dependent on the future cash flows of the stock. It's easier for me to think of it like this:

this year's dividend: 20

next year's dividend: (20)(1.05)=21

dividend two years from now: (21)(1.05)=22.05

dividend three years from now: (22.05)(1.05)=23.1525

Then use the equation: D/(R-G), which means dividend for year three divided by the discount rate minus the growth rate.

so…23.1525/(.1-.05) gets you the answer.

[M.O.D.]

1.05 is the dividend growth, it is given.

formula is 10% = next year's dividend/share price + 5%

10% = 20×1.05/X + 5%

X = 420

420×1.05×1.05 = 463

or

10% = 20×1.05×1.05×1.05 (for two years ahead forward dividend)/X + 5%

X = 463

BA Mathematics, UC Berkeley
Certificates in CPA and EA preparation, College of San Mateo
CMA I 420, II 470
FAR 91, AUD Feb 2015 (Gleim self-study)

[Author]

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