Question

Boom and Fall (B&F) expects to grow its business in the first 3 years and then the business expects the growth to decline after. The company just paid its annual dividend of $1 per share and is planning to increase its annual dividend by 10% for the next 3 years, and then the dividend will decline at an annual rate of 4% forever.

What is the value of B&F stock in one year if the required return is 12%? What would be the impact on B&F stock price if the business growth will not decline after 3 years, therefore management would maintain the same dividend as that of year 3? Explain.

Answer 1

Recent Dividend Paid = $1

Growth in the dividend = 10%

Dividend paid in year 1 = 1*(1 + 10%) = 1*1.1 = $1.1

Dividend paid in year 2 = 1.1*(1 + 10%) = 1.1 * 1.1 = $1.21

Dividend paid in year 3 = 1.21*(1+10%) = 1.21*1.1 = $1.331

Year 4 onwards, the growth rate -4%

Hence, the dividend paid in year 4 = 1.331*(1-4%)

= $1.27776

The dividends are shown as below:

Value of stock = Present values of the dividends

According to the Gordon Growth Model, the present value of perpetuity with growth rate, g, is given as:

PV = D1/(r - g)

where D1 = Expected dividend next year

r = required rate of return = 12%

g = growth rate

Solution 1) Present value of the perpetuity after year 4 will be calculated at year 3 as:

PV (Perpetuity at t=3) : D4/(r - g)

= 1.27776/(12% - (-4%))

= 1.27776/(16%)

= $7.986

The value of the stock at t=1 year is calculated as:

Since the stock price is to be calculated after 1 year, hence, the present values are calculated at the end of year 1

Thus, stock price = Present value of 1.21 at t=1+ Present value of 9.317 at t=1

= 1.21/(1+12%) + 9.317/(1+12%)^2

= 1.080357 + 7.427455

= 8.507813

= $8.51

Solution 2) Current stock price = Present value of expected dividends

= 1.1/(1 + 12%) + 1.21/(1+12%)^2 + 9.317/(1+12%)^3

= $8.578404

If the perpetuity remains constant, then, the present value of perpetuity at t=3 is calculated as:

= 1.27776/(12% - 0%)

= 1.27776/(12%)

= $10.648

The dividends would be:

Thus, current stock price would be given as:

= 1.1/(1 + 12%) + 1.21/(1+12%)^2 + 11.979/(1+12%)^3

= $10.473

Hence, the stock price has increased.

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