Question

You are analyzing Jillian’s Jewelry (JJ) stock for a possible purchase. JJ just paid a dividend of $1.50 yesterday. You expect the dividend to grow at a rate of 6% per year for the next 3 years; if you buy the stock, you plan to hold it for 3 years and then sell it.

A.What dividends do you expect for JJ stock over the next 3 years?

The correct answer is $1.79

B.JJ’s stock has a required return of 13% and so this is the rate you’ll use to discount dividends. Find the present value of the dividends stream; that is. Calculate the PV of D1, D2, and D3, and then sum these PVs.

The correct answer is $3.97

C.JJ stock should trade for $27.05 3 years from now (i.e you expect p3=$27.05) discounted at 13% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $27.05

The correct answer is $18.74

D.If you plan to buy the stock, hold it for 3 years, and then sell it for $27.05, what is the most you should pay for it?

The correct answer is $22.71

E.Use the constant growth model to calculate the present value of this stock. Assume that g= 6% and is constant.

F. Is the value of this stock dependent on how long you plan to hold it? In other words, if you planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, p0? Explain your answer

Answer 1

Answer:

A. D1 = 1.50*1.06 = 1.59

D2 = 1.59*1.06 = 1.69

D3 = 1.69*1.06 = 1.79

B. PV of D1=(1.50*1.06)/1.13^1=1.41

PV of D2=(1.50*1.06^2)/1.13^2=1.32

PV of D3=(1.50*1.06^3)/1.13^3=1.24

PV of all dividend = (1.50*1.06)/1.13^1 + (1.5*1.06^2)/1.13^2 + (1.5*1.06^3)/1.13^3

PV of all dividend = 1.59/1.13 + 1.6854/1.2769 + 1.786524/1.442897

PV of all dividend = 1.407079646 + 1.319915 + 1.238150748

PV of all dividend = 3.965145814288893

PV of all dividend = 3.97

C. PV = 27.05/(1+13%)^3

PV = 27.05/(1.13)^3

PV = 27.05/1.442897

PV = 18.74701

PV = 18.75

D. The most you should pay for it :

= (1.50*1.06)/1.13^1+(1.5*1.06^2)/1.13^2+(1.5*1.06^3)/1.13^3+27.05/1.13^3

=22.71

E. Value = (1.50*1.06)/(13%-6%)

Value = 1.59 / 7%

Value = 1.59 / 0.07

Value = 22.714286

Value =22.71

F. No, the value is not dependent on the holding period, you can see from above that the value of infinite time period estimated in E equals to the value calculated when there was 3 years holding period.