Eakins Inc.’s common stock currently sells for $37.50 per share, the company expects to earn $2.75 per share during the current year, its expected payout ratio is 70%, and its expected constant growth rate is 6.00%. New stock can be sold to the public at the current price, but a flotation cost of 8% would be incurred. By how much would the cost of new stock exceed the cost of retained earnings? Do not round your intermediate calculations.

Question

Eakins Inc.’s common stock currently sells for $37.50 per share, the company expects to earn $2.75 per share during the current year, its expected payout ratio is 70%, and its expected constant growth rate is 6.00%. New stock can be sold to the public at the current price, but a flotation cost of 8% would be incurred. By how much would the cost of new stock exceed the cost of retained earnings? Do not round your intermediate calculations.

BlackTom AI · Accepted Answer

We start by restating the key data and then compute the two costs of financing.
Given: P0 = $37.50, EPS = $2.75, payout ratio = 0.70, growth g = 6.0%, flotation cost f = 0.08 for new stock.
First, compute the dividend next year under the assumption of constant growth.
D0 (the current dividend) = payout ratio × EPS = 0.70 × 2.75 = $1.925.
D1 (dividend next year) = D0 × (1 + g) = 1.925 × 1.06 = $2.0405.

1) Cost of retained earnings (the cost of equity from retained earnings):
For a constant growth dividend model, rs = D1/P0 + g.
rs = 2.0405 / 37.50 + 0.06 = 0.05448 + 0.06 = 0.11448, i.e., 11.448%.

2) Cost of new stock (the cost of equity when issuing new shares with flotation):
Net proceeds per new share = P0 × (1 − f) = 37.50 × 0.92 = $34.50.
Ke (cost of new stock) = D1 / Net proceeds + g = 2.0405 / 34.50 + 0.06 = 0.05918 + 0.06 = 0.11918, i.e., 11.918%.

3) Difference: Ke − rs = 11.918% − 11.448% = 0.470 percentage points, which is approximately 0.47%.

Notes and potential pitfalls to avoid:
- It is essential to use D1 (not D0) when applying the Gordon growth formula D1/P0 + g.
- For new stock, always adjust the price received by netting out flotation costs, hence net proceeds = P0 × (1 − f).
- If you round intermediate steps, you can drift from the precise difference; the instruction is to avoid rounding intermediate values.

Summary: The cost of new stock exceeds the cost of retained earnings by about 0.47 percentage points (roughly 0.470%). If an exam option shows 0.45%, it would be a rounded figure close to the calculated 0.47%.

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