Question

Radon Homes' current EPS is $6.45. It was $4.51 5 years ago. The company pays out 50% of its earnings as dividends, and the stock sells for $36.

1. Calculate the historical growth rate in earnings. (Hint: This is a 5-year growth period.) Round your answer to two decimal places.
        %
   
2. Calculate the next expected dividend per share, D₁ (Hint: D₀ = 0.50($6.45) = $3.23). Assume that the past growth rate will continue. Round your answer to the nearest cent.
   $  
   
3. What is Radon's cost of equity, r_s? Round your answer to two decimal places.
        %

Answer 1

Part A:

FV = PV (1+g)^n

Fv = Future Value

PV = Present Value

g = Growth Rate and n is time period

6.45 = 4.51(1+g)^5

(1+g)^5 = 6.45 / 4.51

= 1.43

1+g = 1.43 ^ ( 1/ 5)

= 1.0742

g = 1.0742 - 1

= 0.0742 i.e 7.42%

Growth Rate is 7.42%

Part B:

D1 = D0 (1+g)

D0 = EPS0 * Payout Ratio

= $ 6.45 * 50%

= $ 3.225

D1 = $ 3.225 (1+0.0742)

= $ 3.225 (1.0742)

= $ 3.46

Expected div after a year is $ 3.46

Part C:

Ke = [ D1 / current Price } + growth Rate

= [ $ 3.46 / $ 36 ] + 0.0742

= 0.0962 + 0.0742

= 0.1704 i.e 17.04%

Cost of Equity is 17.04%