# Melissa Popp is thinking about buying some shares of R.H. Lawncare Equipment, at \$48 per share. She expects the price of the stock to rise to \$60 over the next 3 years. During that time she also expects to receive annual dividends of \$4 per share.

A. What is the intrinsic worth of this stock, given a 12% required rate of return?
B. What is its expected return?

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## To calculate the intrinsic worth of the stock, we will use the dividend discount model (DDM). The formula for DDM is:

Intrinsic Worth = (Dividends per Share / Required Rate of Return) + (Expected Stock Price / (1 + Required Rate of Return)^t)

Where:
- Dividends per Share = \$4
- Required Rate of Return = 12% or 0.12
- Expected Stock Price (Future Price) = \$60
- t = time in years, which in this case is 3 years

Let's calculate the intrinsic worth:

A. Intrinsic Worth:
Dividends per Share / Required Rate of Return = \$4 / 0.12 = \$33.33 (rounded to two decimal places)

Expected Stock Price / (1 + Required Rate of Return)^t = \$60 / (1 + 0.12)^3 = \$60 / (1 + 0.12)^3 = \$60 / 1.404928 = \$42.69 (rounded to two decimal places)

Intrinsic Worth = \$33.33 + \$42.69 = \$75.02

Therefore, the intrinsic worth of this stock is \$75.02.

B. Expected Return:
To calculate the expected return, we will use the formula:

Expected Return = (Expected Dividend / Initial Stock Price) + ((Expected Stock Price - Initial Stock Price) / Initial Stock Price)

Where:
- Expected Dividend = \$4 (annual dividend)
- Initial Stock Price = \$48

Expected Return = (\$4 / \$48) + ((\$60 - \$48) / \$48) = 0.083333 + 0.25 = 0.333333 (rounded to six decimal places) or 33.33% (rounded to two decimal places)

Therefore, the expected return of this stock is 33.33%.

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## To calculate the intrinsic worth of the stock given a 12% required rate of return, we need to use the discounted cash flow (DCF) method.

A. The intrinsic worth of a stock is the present value of its future cash flows, which includes both the dividends received and the price appreciation over the given time period. To calculate this, we will use the formula for the present value of a growing perpetuity:

Intrinsic worth = (Dividends / (Required rate of return - Dividend growth rate)) + (Price appreciation / (1 + Required rate of return) ^ number of years)

Given:
- Dividends = \$4 per share annually
- Required rate of return = 12%
- Dividend growth rate = 0% (as mentioned, dividends are expected to remain constant at \$4 per share)
- Price appreciation = \$60 - \$48 = \$12
- Number of years = 3

Substituting these values into the formula:

Intrinsic worth = (4 / (0.12 - 0)) + (12 / (1 + 0.12) ^ 3)
= 33.33 + 8.11
= \$41.44

Therefore, the intrinsic worth of this stock, given a 12% required rate of return, is approximately \$41.44 per share.

B. The expected return of the stock is calculated by dividing the intrinsic worth by the current market price of the stock and then subtracting 1.

Expected return = (Intrinsic worth / Market price) - 1
= (41.44 / 48) - 1
= (0.8627) - 1
= -0.1373

By converting the expected return to a percentage, we find that the expected return of this stock is approximately -13.73%.

Please note that a negative expected return suggests that the stock may be overvalued or not favorable compared to the required rate of return.

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