Question

Business has been good for Keystone Control Systems, as indicated by the four-year growth in earnings per share. The earnings have grown from $1.00 to $1.63.

a. Determine the compound annual rate of growth in earnings (n = 4). (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
b. Based on the growth rate determined in part a, project earnings for next year (E₁). (Do not round intermediate calculations. Round your answers to 2 decimal places.)
c. Assume the dividend payout ratio is 40 percent. Compute D₁. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
d. The current price of the stock is $50. Using the growth rate (g) from part a and (D₁) from part c, compute Kₑ. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
e. If the flotation cost is $3.75, compute the cost of new common stock (Kₙ) using growth rate (g) from part a and dividend (D₁) from part c. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

Answer 1

The compound annual rate of growth in earnings is 16.3%

Step-by-step explanation:

To calculate the compound annual growth rate (CAGR) for Keystone Control Systems, with earnings growing from $1.00 to $1.63 over 4 years, you use the formula:

CAGR = [(Ending value/Beginning value) ^ (1/n)] - 1

Substitute the given values:

CAGR = [($1.63/$1.00) ^ (1/4)] - 1 = 0.129 or 12.90%

To determine the compound annual rate of growth in earnings, we can use the formula:

Compound annual growth rate (CAGR) = (Ending value / Beginning value)^(1/n) - 1

where Ending value is $1.63, Beginning value is $1.00, and n is 4. Plugging these values into the formula, we get:

CAGR = ($1.63 / $1.00)^(1/4) - 1 = 0.163 - 1 = 0.163

Therefore, the compound annual rate of growth in earnings is 16.3%.