Question

Bloomberg Co. announced today that its next annual dividend will be $2.60 per share. After that dividend is
paid, the company expects to encounter some financial difficulties and is going to suspend dividends for 5
years. Following the suspension period, the company expects to pay a constant annual dividend of $1.30 per
share. What is the current value of this stock if the required return is 10 percent?
A. $2.36
B. $3.55
C. $7.34
D. $8.07
E. $9.7

Answer 1

To solve this question, we need to use a method called, Dividend discount method or DDM in short.

In this method we discount the cash flow of future expected dividend using required return of which is given as 10% or 0.1 to calculate the present value of the stock.

In general present value is calculated as,

Po = A + A1/(1+r) + A2/(1+r)^2+ A3/(1+r)^3+..........+ An/(1+r)^n

Here, Po = Present value of future cash flow.

r= Discount rate.

A = amount received today.

A1= amount received after 1 period, that's why we are discounting it.

Similarly A2, A3, and so on are the amounts the we receive in respective period.

Let's apply this formula in our question.

You see first dividend which we are going to get is in next period, that is 1 year later. So there is no dividend paid today. The first dividend is $2.6

And also after the first dividend, for the next five years the dividend is going to be zero. And then after we are going to get a constant dividend of $1.3. And here r which is required rate of return is discount rate. Let's put this in our formula.

Po = 2.6/(1+0.1) + 0/(1+0.1)^2 + 0/(1+0.1)^3 + 0/(1+0.1)^4 + 0/(1+0.1)^5 + 0/(1+0.1)^6 + 1.3/(1+0.1)^7 + 1.3/(1+0.1)^8+..............+ 1.3/(1+0.1)^n

Here n can be infinite.

The first term on right hand side of the equation is the present value of first dividend that we get of $2.6 and for next five years we get nothing as you can see. And after that we receive a constant dividend of $1.3 for the rest of the life.

Po = 2.6/(1.1) + 1.3/(1.1)^7 + 1.3/(1.1)^8+.........+1.3/(1.1)^n

Po = 2.36 + 1.3/(1.1)^7 + 1.3/(1.1)^8 +......... + 1.3/(1.1)^n - - - - - - (1)

As you can see the second term on the right hand side is an infinite geometric progression. We can use the formula to solve the sum of infinite GP.

Sum of infinite Sn = A/(1 - d)

Here A = first term which is here is 1.3/(1.1)^7

And d = common ratio, which is calculated by dividing any term of GP preceding term.

d = 1.3/(1.1)^8 ÷ 1.3/(1.1)^7

d = 1.3/(1.1)^8 × (1.1)^7/1.3

d = 1/(1.1).

Now putting the values of A and d in the sum of infinite GP formula we get,

Sn = 1.3/(1.1)^7 ÷(1- 1/1.1)

Sn = 1.3/(1.1)^7 ÷ (1.1 - 1)/1.1

Sn = 1.3/(1.1)^7 ÷ (0.1)/1.1

Sn = 1.3/(1.1)^7 × 1.1/0.1

Sn = 13/(1.1)^6

Sn = 13/1.77

Sn = 7.34

So the second term on the right hand side of equation 1 get reduced to $7.34. Substituting this value in equation (1) we get,

Po = 2.36 + 7.34

Po = $9.70

So the present value of the stock is $9.7, which we calculated using the dividend discount method.

So the correct option must be option E.

Note : this question is predominantly formula based. As you can see there is lot of maths, just follow each step carefully and you'll be able to do it. If you still have any doubts I encourage you to ask through comment section.