"Zoom Tech, Inc. has been growing fast and just announced today that it will begin paying annual dividends next year. Dividends for the first three years will be $0.25, $0.50, and $0.75 a share, respectively. After that, dividends are projected to increase by 6 percent per year. What is one share of this stock worth today at a required return of 12.5 percent

$6.55 per share

Explanation:

Worth of the stock is the present value of all the cash flows associated with the stock. Dividend is the only cash flow that a stock holder receives against its investment in the stocks. We need to calculate the present values of all the dividend payments.

Formula for PV of dividend

PV of Dividend = Dividend x ( 1 + r )^-n

1st year

PV of Dividend = $0.25 x ( 1 + 12.5% )^-1 = $0.22

2nd year

PV of Dividend = $0.50 x ( 1 + 12.5% )^-2 = $0.40

3rd year

PV of Dividend = $0.75 x ( 1 + 12.5% )^-3 = $0.53

After three years the dividend will grow at a constant rate of 6%, so we will use the following formula to calculate the present value

PV of Dividend = [ $0.53 x ( 1 + 6% ) / ( 12.5% - 6% ) ] x [ ( 1 + 12.5% )^-4 ]

PV of Dividend = $5.40

Value of Stock = $0.22 + $0.40 + $0.53 + $5.40 = $6.55

Price = $9.73

Explanation:

According to the dividend valuation model , the current price of a stock is the present value of the expected future dividends discounted at the required rate of return.

So we will discount the steams of dividend using the required rate of 12.5% as follows:

PV = Div × (1+r)^(-n)

r- required rate of return, n-year

Year                                          Present Value ( PV)

1            0.25 ×  1.125^(-1)   = 0.2222

2           0.5 ×      1.125^(-2) = 0.3950

3           0.75 ×   1.125^(-3)   = 0.5267

Year 4 and beyond

This will be done in two(2 ) steps as follows:

PV in year  3 = 0.75 × 1.06/(0.125-0.06) = 12.230

PV in year 0  =   12.230 × 1.125^(-3) = 8.5900

Price of stock

0.2222 + 0.3950 + 0.5267 + 8.5900

= 9.734093

Price = $9.73

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