Bloomberg Co. announced today

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

In this method we discount the cash flow of future expecteddividend using required return of which is given as 10% or 0.1 tocalculate 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 arediscounting it.

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

Let’s apply this formula in our question.

You see first dividend which we are going to get is in nextperiod, 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 thedividend is going to be zero. And then after we are going to get aconstant dividend of $1.3. And here r which is required rate ofreturn 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 presentvalue of first dividend that we get of $2.6 and for next five yearswe get nothing as you can see. And after that we receive a constantdividend 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 aninfinite geometric progression. We can use the formula to solve thesum 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 termof 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 GPformula 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 getreduced to $7.34. Substituting this value in equation (1) weget,

Po = 2.36 + 7.34

Po = $9.70

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

So the correct option must be option E.

Note : this question is predominantly formula based. Asyou can see there is lot of maths, just follow each step carefullyand you’ll be able to do it. If you still have any doubts Iencourage you to ask through comment section.