Question

Farms Corp. just paid a dividend of $3.20 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year indefinitely. Investors require a 15 percent return on the stock for the first three years, a 13 percent return for the next three years, and an 11 percent return thereafter. What is the current share price?

Please provide some basic explanations for the calculations. There are similar questions already answered but with no explanation at all, which makes them useless. Thank you!

Answer 1

Dividend at Year 0 = $3.20 | Growth rate = 5%

Rate of return: For first 3 years = 15% | For next 3 years = 13% | Thereafter - 11%

To calculate the current share price, we will use Dividend Discount Model. This model is based on cashflows to the investors instead of cashflows to the firm or equity. Since, the firm that we would be valuing is paying dividend and will be growing the dividend, however, if a company doesn't pay dividends or pays irregular dividends, then this model cannot be applied. This is one of the limitations of the model.

In our case, we will use Multi-stage Dividend Discount Model as it has 3 different rates for different periods of the company. This might be a reflection on how risky investors perceive their cashflows. The initial phase of 3 years cashflows are considered to be more risky with higher rate of return than the other years.

We will grow the dividend at 5% for each year until 6 years, post that, we will use perpetuity formula for the calculation of terminal value. There will be 3 stages in the calculation, first is for first 3 years, then for next 3 years and finally the terminal value stage.

First Stage is First 3 years:

Dividend in Year 1 = Div0 * (1 + g) = 3.20 * (1 + 5%) = 3.36

Dividend in Year 2 = Div1 * (1+g) = 3.36 * (1+5%) = 3.53

Dividend in Year 3 = Div2 * (1+g) = 3.53 * (1+5%) = 3.70

Now we will find the PV of First Stage using its required rate of return of 15%

PV of Div1 = Dividend1 / (1 + R) = 3.36 /(1+15%) = 2.92

PV of Div2 = Dividend2 / (1+R)² = 3.53 / (1+15%)² = 2.67

PV of Div3 = Dividend3 / (1 + R)³ = 3.70 / (1+15%)³ = 2.44

PV of First Stage = Sum of all PVs till Year 3 = 2.92 + 2.67 + 2.44 = $8.03

Second Stage is Next 3 years:

Dividend in Year 4 = Div3 * (1+g) = 3.70 * (1+5%) = 3.89

Dividend in Year 5 = Div4 * (1+g) = 3.89 * (1+5%) = 4.08

Dividend in Year 6 = Div5 * (1+g) = 4.08 * (1+5%) = 4.29

Now we will calculate PV of Second Stage using its required rate of return of 13% initially then the 15% rate for first 3 years.

PV of Div4 = Dividend4 / (1+R)⁴ = 3.89 / ((1+15%)³(1+13%)¹) = 2.26

PV of Div5 = Dividend5 / (1+R)⁵ = 4.08 / ((1+15%)³(1+13%)²) = 2.10

PV of Div6 = Dividend6 / (1+R)⁶ = 4.29 / ((1+15%)³(1+13%)³)  = 1.95

PV of Second Stage = Sum of all PVs from Year 3 to 6 = 2.26 + 2.10 + 1.95 = 6.32

Now we will calculate the Final stage which is the Terminal Value which is a growing perpetuity and it continues indefinitely as businesses are assumed to grow and continue forever. Rate for the terminal value is 11%.

Terminal Value or Growing Perpetuity = Dividend6 * (1+g) / (R - g)

Terminal Value at Year 6 = 4.29 * (1+5%) / (11% - 5%)

Terminal Value at Year 6 = 4.50 / 6% = $75.05

Terminal Value calculates Dividend at Year 7 by growing at growth rate for 1 year and then discounting back to 6th year using difference of Rate of return and growth rate. Since Terminal Value becomes a cashflow at Year 6, therefore, its PV will be calculated using rate of 13% for three years and 15% for another three years.

PV of Final stage = Terminal value / (1+R)⁶

PV of Final stage = 75.05 / ((1+13%)³*(1+15%)³)

PV of Final Stage = $ 34.20

Now summing all the PVs of each stage and that sum will be the Current Share Price

Current Share Price = PV of First Stage + PV of Second stage + PV of Final Stage

Current Share Price = 8.03 + 6.32 + 34.20

Current Share Price = $48.54

Hence, the Current Share price is $48.54.