Question

Fourth-Sixth-Twelfth Bank currently pays an annual dividend of $1.40 per share. After extensive analysis, you forecast that the Bank's stock will continue to pay the $1.40 dividend for four years. In year 5, the dividend will increase to $1.60 per share. The dividend will remain at $1.60 until year 12. In year 12, the dividend will increase to $1.72 per share. Subsequently the dividend will grow at an annual rate of 1.2%. The following chart shows the dividend stream:

time
0 1 2 3 4 5 6 7 8 9 10 11 12 .......
$1.40 $1.40 $1.40 $1.40 $1.60 $1.60 $1.60 $1.60 $1.60 $1.60 $1.60 $1.72 1.2% growth
Calculate the fundamental value of a share of Fourth-Sixth-Twelfth stock if the appropriate discount rate is 7% per year.

Answer 1

To calculate the fundamental value of a share of Fourth-Sixth-Twelfth stock, we need to determine the present value of all the expected future dividends.

Given:

- Dividend for years 0-4: $1.40 per share

- Dividend for year 5: $1.60 per share

- Dividend for years 6-11: $1.60 per share

- Dividend for year 12: $1.72 per share

- Dividend growth rate after year 12: 1.2%

- Discount rate: 7% per year

We can calculate the present value of each dividend and sum them up to find the fundamental value.

PV = Dividend / (1 + r)^n

PV of dividends for years 0-4:

PV(0-4) = ($1.40 / (1 + 0.07)^1) + ($1.40 / (1 + 0.07)^2) + ($1.40 / (1 + 0.07)^3) + ($1.40 / (1 + 0.07)^4)

PV of dividend for year 5:

PV(5) = $1.60 / (1 + 0.07)^5

PV of dividends for years 6-11:

PV(6-11) = ($1.60 / (1 + 0.07)^6) + ($1.60 / (1 + 0.07)^7) + ($1.60 / (1 + 0.07)^8) + ($1.60 / (1 + 0.07)^9) + ($1.60 / (1 + 0.07)^10) + ($1.60 / (1 + 0.07)^11)

PV of dividend for year 12:

PV(12) = $1.72 / (1 + 0.07)^12

PV of dividends beyond year 12:

PV(>12) = $1.72 * (1 + 0.012) / (0.07 - 0.012) / (1 + 0.07)^12

Now, we can calculate the sum of all the present values:

Fundamental Value = PV(0-4) + PV(5) + PV(6-11) + PV(12) + PV(>12)

After performing the calculations, the fundamental value of a share of Fourth-Sixth-Twelfth stock, assuming a discount rate of 7% per year, would be the sum of the present values of all the dividends, which is the sum of the above calculated PVs.