You have been hired by the CFO of Lugones Industries to help estimate its cost of common equity. You have obtained the following data: (1) r d = yield on the firm's bonds = 7.00% and the risk premium over its own debt cost = 4.00%. (2) r RF = 5.00%, RP M = 6.00%, and b = 1.25. (3) D 1 = $1.20, P 0 = $35.00, and g = 8.00% (constant). You were asked to estimate the cost of common based on the three most commonly used methods and then to indicate the difference between the highest and lowest of these estimates. What is that difference?

Under CAPM:

Re = Rf + Beta(Rm - Rf)

Rf = 5%

Rm - Rf = 6%

Beta = 1.25

Re = 5% + (1.25 x 6%) = 12.5%

Under dividend discount model:

Re = (Div₁ / P₀) + g

Div₁ = $1.20

P₀ = $35

g = 8%

Re = ($1.20 / $35) + 8% = 11.43%

Under bond yield plus risk premium approach:

Re = Pre-tax cost of debt + risk premium over its own debt

Pre-tax cost of debt = 7%

risk premium over its own debt = 4%

Re = 7% + 4% = 11%

The highest cost of equity results from the CAPM model and it is 12.5% while the lowest results from using the bond yield plus risk approach (11%), the difference is 1.5% between them.

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