K Group just paid a $1.25 dividend per share. The dividend is

expected to grow at 28% per annum for the next eight years. After
that, this growth rate is expected to be 6% indefinitely.
Presume that the beta of K Group is 1.2, and the risk premium 7.5%
and the risk-free rate is 4%.
The current share price of K Group and is $80,
Is the current share price of K Group underpriced?

To determine whether the current share price of K Group is underpriced, we can use the Dividend Discount Model (DDM) to calculate the intrinsic value of the stock.

The DDM calculates the present value of all expected future dividends. In this case, we have a dividend that is expected to grow at a rate of 28% per annum for the next eight years and then continue to grow at 6% indefinitely.

Here's how you can calculate the intrinsic value of the stock:

Step 1: Calculate the expected dividends for the next eight years.
- The current dividend is $1.25 per share.
- To calculate the expected dividends for each of the next eight years, we need to multiply the current dividend by (1 + growth rate).
- The growth rate is given as 28%, so the expected dividends for each year can be calculated as follows:

Year 1: $1.25 * (1 + 0.28) = $1.60
Year 2: $1.60 * (1 + 0.28) = $2.05
Year 3: $2.05 * (1 + 0.28) = $2.62
Year 4: $2.62 * (1 + 0.28) = $3.35
Year 5: $3.35 * (1 + 0.28) = $4.29
Year 6: $4.29 * (1 + 0.28) = $5.49
Year 7: $5.49 * (1 + 0.28) = $7.02
Year 8: $7.02 * (1 + 0.28) = $8.98

Step 2: Determine the present value of the dividends for each year.
- To calculate the present value of the dividends, we need to discount each year's dividend by the appropriate discount rate.
- The discount rate is the risk-free rate (4%) plus the risk premium (7.5%).
- The present value of each year's dividend can be calculated using the formula: Present Value = Dividend / (1 + Discount Rate)^Time

Present Value Year 1 = $1.60 / (1 + 0.115)^1 = $1.43
Present Value Year 2 = $2.05 / (1 + 0.115)^2 = $1.64
Present Value Year 3 = $2.62 / (1 + 0.115)^3 = $1.89
Present Value Year 4 = $3.35 / (1 + 0.115)^4 = $2.12
Present Value Year 5 = $4.29 / (1 + 0.115)^5 = $2.37
Present Value Year 6 = $5.49 / (1 + 0.115)^6 = $2.52
Present Value Year 7 = $7.02 / (1 + 0.115)^7 = $2.61
Present Value Year 8 = $8.98 / (1 + 0.115)^8 = $2.62

Step 3: Calculate the present value of the perpetuity.
- After the eighth year, the dividend growth rate is expected to be 6% indefinitely.
- The present value of the perpetuity can be calculated using the formula: Perpetuity Value = Dividend / (Discount Rate - Growth Rate)

Perpetuity Value = $8.98 / (0.115 - 0.06) = $149.67

Step 4: Calculate the total intrinsic value of the stock.
- The total intrinsic value is the sum of the present value of the dividends for the next eight years and the present value of the perpetuity.

Total Intrinsic Value = $1.43 + $1.64 + $1.89 + $2.12 + $2.37 + $2.52 + $2.61 + $2.62 + $149.67 = $167.27

Step 5: Compare the intrinsic value to the current share price.
- The current share price of K Group is given as $80.
- If the intrinsic value is higher than the current share price, the stock would be considered underpriced.

Intrinsic Value = $167.27
Current Share Price = $80

Based on the calculations, we can see that the intrinsic value ($167.27) is higher than the current share price ($80). Therefore, we can conclude that the current share price of K Group is underpriced.