Value of Future Cash Flows A firm recently paid a $0.30 annual dividend.The dividend is expected to increase by 8 percent in each of the next four years.In the fourth year,the stock price is expected to be $60.If the required rate for this stock is 10 percent,what is its value?

Question

Quizplus · Accepted Answer

To calculate the value of the stock, we need to find the present value of all the future cash flows.

First, we can use the dividend growth model to find the expected dividends for each year:

- Year 1: $0.30 x 1.08 = $0.324 
- Year 2: $0.324 x 1.08 = $0.3499 
- Year 3: $0.3499 x 1.08 = $0.377 
- Year 4: $0.377 x 1.08 = $0.406

Next, we can use the dividend discount model to find the present value of these dividends:

PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + P4/(1+r)^4

where: 
D1 = dividend for year 1 
r = required rate of return = 10% 
P4 = expected stock price in year 4

Plugging in the values:

PV = $0.324/(1+0.1) + $0.3499/(1+0.1)^2 + $0.377/(1+0.1)^3 + $0.406/(1+0.1)^4 + $60/(1+0.1)^4 
PV = $0.2936 + $0.2967 + $0.2941 + $0.2704 + $38.55 
PV = $42.13

Therefore, the value of the stock is $42.13, which is closest to option C.

Value of Future Cash Flows a Firm Recently Paid a $0.30