Question

The Apple just paid a $0.8 quarterly dividend. The dividends are expected to grow at 20% per year for the next 3 years. After that, the growth rate is expected to go down to the industry average of 8% per year and stay at this level forever. The required rate of return on Apple is 15% per annum.

1.Draw the time line, showing dividends of Apple.

2.Find the price of Apple stock.

3.Find the value of its growth opportunities (PVGO).

4.What is the effective annual rate (EAR) of return on the Apple stock?

Answer 1

Greetings,

1) At t = 0 , DPS = 0.8

At t = 1, DPS = 0.8*1.2= 0.96

At t = 2, DPS = 0.96*1.2=1.152

AT t=3, DPS =1.152*1.2=1.3824

At t=4, DPS =1.3824*1.08=1.4930

After that dividend will keep on growing at 8% forever ,hence it is not feasible to show all such dividends. For the purpose of calculation of share price, formula of perpetuity will be used.

2) Share price is given by -

PV of first 3 dividends = 0.96/(1+0.15) + 1.152/(1.15)^2+ 1.3824/(1.15)^3 = 2.6148

PV of perpetuity

Horizon Value = 1.4930/(0.15-0.08) = 21.3286

PV of Horizon Value = 21.3286/(1.15)^3 = 14.024

Therefore share price = 2.6148+14.024= 16.6388

3) Present Value of growth opportunities is the difference between the price actually calculated above considering growth and price calculated assuming no growth. The difference is attributable to growth component and is known as PVGO.

Price ignoring growth = 0.96/(0.15)=6.4

PVGO = 16.6388-6.4=10.2388

NOTE - I used expected dividend of next year to calculate no growth price. Some people consider if we are ignoring growth the assume that dividend of 0.8 will remain the constant. So we can compute PVGO by using 0.8 as well instead of 0.96.

4) Effective annual return is an IRR affair i.e. calculated using all future cash flows. Since equity is a perpetual investment hence we assume that investor will sell the share after 3 years for HV =21.3286. This will give us return = 15% only i.e. required rate of return.

OR

EAR = Dividend Yield + Price Yield

DY = Expected dividend next year / Price today = 0.96/16.6388*100 = 5.77%

for calculation of price return, we need expected share price at the end of the Ist year = PV of 2nd and 3rd dividend + PV of HV pulled 2 years back not 3 years back.

PV of two dividends = 2.047

PV of HV = 21.3286/(1.15)^2 = 16.128

Expected Share price at t= 1 = 2.047+16.128 =18.175

Price Yield = (18.175-16.6388)/16.6388*100 = 9.22955%

Therefore EAR = 5.77+9.23 = 15.00% (approx)