Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The company will pay a $14 per share dividend in 10 years and will increase the dividend by 8 percent per year thereafter. If the required return on this stock is 14 percent, what is the current share price?

To calculate the current share price of Metallica Bearings, Inc., we need to determine the present value (PV) of all future dividends and the future sale price at the end of year ten.

Since the company is not paying any dividends for the next nine years, the dividends we need to consider are only from year ten onwards.

First, let's calculate the present value of the future dividends:

Dividend in year 10 = $14

The dividend will increase by 8% per year after year 10, and the required rate of return is 14%. We can use the dividend discount model formula to calculate the present value of the dividends:
PV = D1 / (1 + r)^1 + D2 / (1 + r)^2 + ... + Dn / (1 + r)^n

Where:
PV = Present Value of Dividends
D1 = Dividend in year 10
r = Required rate of return

Using this formula, let's calculate the present value of dividends for years 10 to infinity:

PV = [14 / (1 + 0.14)^1] + [14 * 1.08 / (1 + 0.14)^2] + [14 * 1.08^2 / (1 + 0.14)^3] + ...

Next, we need to calculate the future sale price of the stock at the end of year ten. To find this, we can use the formula for the future value of a single cash flow:

Future Value (FV) = Dividend in year 10 * (1 + g) / (r - g)

Where:
FV = Future Value of the stock at year ten
g = Dividend growth rate after year 10

Using this formula, let's calculate the future sale price at year ten:

FV = 14 * (1 + 0.08) / (0.14 - 0.08)

Now, we can calculate the current share price by summing up the present value of dividends and the future sale price and discounting them to the present:

Current share price = PV + FV / (1 + r)^10

Plug in the values and calculate to find the current share price.

To determine the current share price of Metallica Bearings, Inc., we need to calculate the present value of all the future dividends. Since the company is not paying dividends for the first nine years and will start paying dividends in the 10th year, we need to calculate the present value of dividend payments from year 10 onwards.

First, let's calculate the dividend payment in the 10th year. We are given that the dividend in the 10th year will be $14 per share.

Next, we need to calculate the dividends in the subsequent years. We know that the dividend will increase by 8% per year. So, the dividend in the 11th year will be $14 * (1 + 8%) = $14 * (1 + 0.08) = $14 * 1.08 = $15.12 per share. Similarly, the dividend in the 12th year will be $15.12 * (1 + 8%) = $15.12 * (1 + 0.08) = $15.12 * 1.08 = $16.33 per share, and so on.

Now, we need to calculate the present value of these future dividend payments. To do this, we will use the formula for the present value of a growing perpetuity:

Present Value = (Dividend / (Discount Rate - Growth Rate))

Using the given information, the discount rate is 14% and the growth rate is 8%.

Present Value = ($14 / (0.14 - 0.08))

Present Value = ($14 / 0.06)

Present Value = $233.33

Therefore, the current share price of Metallica Bearings, Inc. is $233.33.

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