Question

The market consensus is that the ABC company has a return on equity equal to 10%, has a CAPM beta of 1.2, and plans to maintain indefinitely its traditional plowback ratio of 0.5. These factors do not change over time. This year’s dividend (i.e., dividend at time 1) is expected to be $2 per share, based on the current information. The annual dividend was just paid. The consensus estimate of the expected market portfolio return is 12%, and T-bills currently offer a 5% return, and these two figures are assumed to be constant over time.

(a) Find the price at which ABC stock should sell.

(b) Calculate the present value of growth opportunities (PVGO) and explain what the value implies.

(c) What is the optimal plowback ratio of ABC company? Calculate the stock value if the company uses this optimal plowback ratio.

(d) Assume the company has a return on equity equal to 15% instead of 10%. Other parameters are the same as before. Calculate the stock price and discuss the optimal plowback ratio.

Answer 1

ROE= 10%

RR(plowback ratio)= 0.5 or 50%

Growth rate= ROE*RR=10%*0.5=5%

As per CAPM,

Reqd. return, ke =RFR+(Beta*Market risk premium)

where Market risk premium= Expected market portfolio return-RFR

ie. Ke=5%+(1.2*(12%-5%))=

13.40%

With the above calculations

we will calculate

(a) the price at which ABC stock should sell

given that the

dividend at time 1, ie D1 is expected to be $2 per share

using the dividend discount model , for constant growth of dividends,

Price,P0=D1/(r-g)

where, P0 is the price, we need to find

D1= the next dividend given as $ 2

r- reqd. return on equity, ke . Found out above as per CAPM, ie.= 13.40%

g= growth rate , found in the beginning as   5%

now, putting all the values in the above formula,

Price,P0=2/(13.40%-5%)

23.81

(b)Present value of growth opportunities (PVGO) and explain what the value implies.

If there is 0% growth , stock price above would have been,

2/(13.4%-0%)= or simply, 2/13.4%----(PD1/r for PV of perpetuity , with 0 growth)

14.93

So, the difference between the above numbers , is the PVGO

ie. PVGO=23.81-14.93=

8.88

It implies the investors' perception about the growth in company's earnings & prospects and consequent expression as means of increased required return.

(c) Optimal plowback ratio of ABC company & stock value if the company uses this optimal plowback ratio.

For any company, optimal plowback ratio , will be 100% , ie. 0% dividends pay-out--

then given this ROE of 10%,

g=10%*100%=

10.00%

Then stock price will be

P0=2/(13.4%-10%)

58.82

(d) Assuming the company has a return on equity equal to 15% instead of 10%,other parameters same as in 1.

now, growth rate= ROE*RR will be

g=15%*0.5

7.50%

Then stock price will be

P0=2/(13.4%-7.5%)=

33.90

Here, if we have 100% plowback,

g will be 15%*100%= 15%

Then stock price =

P0=2/(13.4%-15%)=

-125.00

when plow back increases. Growth rate increases , stock price increases.

when ROE increases above investor's reqd. return, stock price becomes negative.