Gillette Corporation will pay an annual dividend of $0.68 one year from now. Analysts expect this dividend to grow at 11.7% per year thereafter until the 6th year.​ Thereafter, growth will level off at 2.4% per year. According to the​ dividend-discount model, what is the value of a Gillette share if the​ firm's equity cost of capital is 7.5%​?

To calculate the value of a Gillette share, we need to use the Gordon Growth Model (also known as the Dividend Discount Model). This model is used to determine the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate.

Given that the dividend is expected to grow at a different rate for the first 6 years, we need to calculate the present value of these dividends separately. After the 6th year, the dividend growth rate levels off at 2.4% and we can use the Gordon Growth Model.

Here are the steps:

1. Calculate the dividends for the first 6 years:

   • Year 1: $0.68
   • Year 2: $0.68 * (1 + 11.7$0.76
   • Year 3: $0.76 * (1 + 11.7$0.85
   • Year 4: $0.85 * (1 + 11.7$0.95
   • Year 5: $0.95 * (1 + 11.7$1.06
   • Year 6: $1.06 * (1 + 11.7$1.19

2. Calculate the present value of these dividends:

   • PV(Year 1) = $0.68 / (1 + 7.5$0.63
   • PV(Year 2) = $0.76 / (1 + 7.5$0.66
   • PV(Year 3) = $0.85 / (1 + 7.5$0.69
   • PV(Year 4) = $0.95 / (1 + 7.5$0.72
   • PV(Year 5) = $1.06 / (1 + 7.5$0.75
   • PV(Year 6) = $1.19 / (1 + 7.5$0.78

3. Calculate the present value of the dividends from Year 7 onwards using the Gordon Growth Model:

   • D7 = D6 * (1 + 2.4%) = $1.19 * 1.024 =$1.22
   • P7 = D7 / (r - g) = $1.22 / (7.5$22.22
   • PV(P7) = P7 / (1 + r)^6 = $22.22 / (1 + 7.5$14.57

4. Add up all the present values to get the intrinsic value of the stock:

   • P0 = PV(Year 1) + PV(Year 2) + PV(Year 3) + PV(Year 4) + PV(Year 5) + PV(Year 6) + PV(P7)
   • P0 = $0.63 +$0.66 + $0.69 +$0.72 + $0.75 +$0.78 + $14.57 =$18.80

So, according to the dividend-discount model, the value of a Gillette share is approximately $18.80.