Bread, Inc., has an odd dividend policy. The company has just paid a dividend of $6 per share and has announced that it will increase the dividend by $4 per share for each of the next five years, and then never pay another dividend. If you require an 11 percent return on the company's stock, you will pay $ for a share today. (Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g., 32.16))
$64.46
To determine the price you are willing to pay for a share of Bread, Inc. stock today, you can use the dividend discount model (DDM). The DDM calculates the present value of all the future dividends to be received.
First, let's calculate the present value of the future dividends. Bread, Inc. will pay a dividend of $6 per share this year and increase it by $4 per share for the next five years. The future dividends can be represented as follows:
Year 1: $6
Year 2: $6 + $4 = $10
Year 3: $6 + $4 + $4 = $14
Year 4: $6 + $4 + $4 + $4 = $18
Year 5: $6 + $4 + $4 + $4 + $4 = $22
Now, let's calculate the present value of these dividends using the required return of 11 percent. We can use the formula for the present value of a growing perpetuity:
PV = D / (r - g)
Where:
PV = Present value
D = Dividend in the first year ($6)
r = Required return (11% or 0.11)
g = Growth rate (the increase in dividends each year, taken as a decimal)
For the perpetual dividend growth rate, we can use the constant growth rate of $4 per share each year.
Year 1: PV1 = $6 / (0.11 - 0) = $6 / 0.11 ≈ $54.55
Year 2: PV2 = $10 / (0.11 - 0.04) = $10 / 0.07 ≈ $142.86
Year 3: PV3 = $14 / (0.11 - 0.08) = $14 / 0.03 ≈ $466.67
Year 4: PV4 = $18 / (0.11 - 0.12) = $18 / -0.01 ≈ -$1,800 (Ignore this value as it's negative)
Year 5: PV5 = $22 / (0.11 - 0.12) = $22 / -0.01 ≈ -$2,200 (Ignore this value as it's negative)
Now, let's add up the present values of the future dividends:
Total PV = PV1 + PV2 + PV3 ≈ $54.55 + $142.86 + $466.67 = $664.08
Therefore, you would be willing to pay approximately $664.08 for a share of Bread, Inc. stock today.