To calculate the cost of retained earnings and the cost of new common stock using the constant-growth valuation model, we use the following formulas:

1. Cost of Retained Earnings ($r_e$):

The cost of retained earnings is the required return on the firm's stock. It can be estimated using the Gordon Growth Model (also called the Dividend Discount Model), given by:

$r_e = \left( \frac{D_1}{P_0} \right) + g$

Where:

• $D_1$ = Projected dividend per share next year = $2.30
• $P_0$ = Current market price per share = $46.00
• $g$ = Dividend growth rate = 8% = 0.08

2. Cost of New Common Stock ($r_n$):

The cost of new common stock takes into account flotation costs and underpricing. The formula is similar to that of retained earnings but adjusted for the underpricing and flotation costs:

$r_n = \left( \frac{D_1}{P_0 - F} \right) + g$

Where:

• $F$ = Underpricing per share + Flotation cost per share = $1.50 + $1.50 = $3.00

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Step-by-step Calculation:

a. Cost of Retained Earnings ($r_e$):

$r_e = \left( \frac{2.30}{46.00} \right) + 0.08$

$r_e = 0.05 + 0.08 = 0.13 \text{ or } 13\%$

b. Cost of New Common Stock ($r_n$):

$r_n = \left( \frac{2.30}{46.00 - 3.00} \right) + 0.08$

$r_n = \left( \frac{2.30}{43.00} \right) + 0.08$

$r_n = 0.0535 + 0.08 = 0.1335 \text{ or } 13.35\%$

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Final Answers:

• a. The cost of retained earnings ($r_e$) is 13%.
• b. The cost of new common stock ($r_n$) is 13.35%.

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Would you like further clarification or details? Here are some additional questions to explore:

1. How does flotation cost impact the cost of issuing new stock?
2. Can the growth rate be negative, and how would it affect the cost of retained earnings?
3. What is the difference between underpricing and flotation cost in stock issuance?
4. How would a higher dividend growth rate affect the cost of equity?
5. What other models can be used to calculate the cost of equity apart from the constant-growth model?

Tip: When calculating the cost of new common stock, always remember to subtract flotation and underpricing costs from the current market price.