Winters Inc., a golf club manufacturer, is currently paying dividends of $5 per share. These dividends are expected to grow at a 15% rate for the next four years and at 6% rate thereafter (forever). What is the value of the stock if the appropriate discount rate is 12%?

To calculate the value of the stock, we use the dividend discount model (DDM):

2. Calculate the dividends for the next four years using the growth rate of 15%.
4. Calculate the terminal value of the stock beyond the fourth year using the perpetuity formula.
6. Discount each of these future cash flows back to the present value using the appropriate discount rate of 12%.
8. Sum up the present values of all the future cash flows to find the total value of the stock.

Step 1: Calculate dividends for the next four years:

Year 1 Dividend = $5 * (1 + 15%) = $5 * 1.15 = $5.75

Year 2 Dividend = $5.75 * (1 + 15%) = $5.75 * 1.15 = $6.6125

Year 3 Dividend = $6.6125 * (1 + 15%) = $6.6125 * 1.15 = $7.60438

Year 4 Dividend = $7.60438 * (1 + 15%) = $7.60438 * 1.15 = $8.74502

Step 2: Calculate the terminal value beyond the fourth year using the perpetuity formula:

Terminal Value = Year 5 Dividend / (Discount Rate - Growth Rate):

$8.74502 / (12% - 6%) = $8.74502 / 0.06 = $145.75033

Step 3: Discount each future cash flow back to the present value:

PV(Year 1) = $5.75 / (1 + 12%)^1 = $5.12

PV(Year 2) = $6.6125 / (1 + 12%)^2 = $5.57

PV(Year 3) = $7.60438 / (1 + 12%)^3 = $5.91

PV(Year 4) = $8.74502 / (1 + 12%)^4 = $6.16

PV(Terminal Value) = $145.75033 / (1 + 12%)^4 = $82.21

Step 4: Sum up the present values of all the future cash flows:

Stock Value = PV(Year 1) + PV(Year 2) + PV(Year 3) + PV(Year 4) + PV(Terminal Value) = $5.12 + $5.57 + $5.91 + $6.16 + $82.21 = $104.97

The value of the stock is approximately $104.97 per share

Calculating the value of a stock using the Dividend Discount Model (DDM) with a financial calculator:

Step 1: Calculate Dividends for the Next Four Years:

We've already calculated the dividends listed above:

• Year 1: $5.75
• Year 2: $6.6125
• Year 3: $7.60438
• Year 4: $8.74502
  • Year 2 Dividend ($6.6125):
    • N = 2 (for 2 years)
    • I/Y = 12 (for the discount rate of 12%)
    • PMT = 0 (since this is not an annuity)
    • FV = 6.6125 (future value, which is the dividend)
    • Compute PV by pressing CPT > PV. This gives you the present value for Year 2's dividend (-5.27)
  • Year 3 Dividend ($7.60438):
    • N = 3 (for 3 years)
    • I/Y = 12 (for the discount rate of 12%)
    • PMT = 0 (since this is not an annuity)
    • FV = 7.60438 (future value, which is the dividend)
    • Compute PV by pressing CPT > PV. This gives you the present value for Year 2's dividend (-5.41)
  • Year 3 Dividend ($8.74502):
    • N = 4 (for 4 years)
    • I/Y = 12 (for the discount rate of 12%)
    • PMT = 0 (since this is not an annuity)
    • FV = 8.74502 (future value, which is the dividend)
    • Compute PV by pressing CPT > PV. This gives you the present value for Year 2's dividend (-5.56)
  • Terminal Value ($145.75033):
    • N = 4 (for 4 years)
    • I/Y = 12 (for the discount rate of 12%)
    • PMT = 0 (since this is not an annuity)
    • FV = 145.75033 (future value, which is the dividend)
    • Compute PV by pressing CPT > PV. This gives you the present value for Year 2's dividend (-92.63)

Step 2: Calculate the Terminal Value:

Again, we've calculated this to be $145.75033.

Step 3: Discount Each Future Cash Flow Back to Present Value:

We use the Time Value of Money (TVM) functionality for each cash flow.

1. For each dividend and the terminal value, we'll calculate the present value (PV) one at a time, as follows:
   • Year 1 Dividend ($5.75):
     • N = 1 (for 1 year)
     • I/Y = 12 (for the discount rate of 12%)
     • PMT = 0 (since this is not an annuity)
     • FV = 5.75 (future value, which is the dividend)
     • Compute PV by pressing CPT > PV. This gives you the present value for Year 1's dividend (-5.13)

Step 4: Sum Up the Present Values of All Future Cash Flows

5.13 + 5.27 + 5.41 + 5.56 + 92.63 = 114.00