Explain How You Got Your Answers Recapitalization Tapley Inc

Explain How You Got Your Answersrecapitalization Tapley Inc

Please explain how you got your answer(s): RECAPITALIZATION Tapley Inc. currently has total capital equal to $5 million, has zero debt, is in the 40% federal-plus-state tax bracket, has a net income of $1 million, and pays out 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 5% per year, 200,000 shares of stock are outstanding, and the current WACC is 13.40%. The company is considering a recapitalization where it will issue $1 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 11% and its cost of equity will rise to 14.5%.

a. What is the stock’s price per share as of right now (assuming no recapitalization yet)?

b. Assuming that the company maintains the same payout ratio, what will be its stock price following the recapitalization? Assume that shares are repurchases at the price calculated in Part a.

Please explain how you got your answer(s): EVALUATING RISK AND RETURN Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

a. Calculate each stock’s coefficient of variation.

b. Which stock is riskier for a diversified investor?

c. Calculate each stock’s required rate of return.

d. On the basis of the two stocks’ expected and required returns, which stock would be more attractive to a diversified investor?

e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y.

f. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Paper For Above instruction

The evaluation of corporate financial strategies such as recapitalization and the assessment of risk and return for investment portfolios are fundamental in financial management. This paper synthesizes the analytical processes used to address complex financial questions derived from real-world scenarios, demonstrating step-by-step calculations grounded in scholarly finance theories and models.

Part 1: Stock Price Estimation Without Recapitalization

Initially, we assess the intrinsic value of Tapley Inc. share before any recapitalization. The firm’s market value of equity can be derived from the Gordon Growth Model (Dividend Discount Model for a perpetually growing dividend), given the company's earnings, payout ratio, and growth rate (Brealey, Myers, & Allen, 2017).

The net income of $1 million, with a payout ratio of 40%, implies dividends of $0.4 million annually. Assuming constant growth at 5%, the dividend per share (DPS) is calculated as:

Dividends Per Share (DPS) = Total Dividends / Number of Shares = $400,000 / 200,000 shares = $2 per share.

The expected dividend in the next year (D1) is thus:

D1 = DPS (1 + g) = $2 1.05 = $2.10.

The stock’s intrinsic value per share (P) is calculated as:

P = D1 / (r - g), where r is the required rate of return, which can be approximated here through the current WACC of 13.40%. Therefore, P = $2.10 / (0.134 - 0.05) ≈ $2.10 / 0.084 ≈ $25 per share.

This valuation yields a share price of approximately $25 before recapitalization.

Part 2: Stock Price Post-Recapitalization with Maintained Payout Ratio

Following the proposed recapitalization, the company plans to issue $1 million debt and repurchase stock, which affects the firm’s capital structure and potentially alters its cost of equity and overall valuation (Modigliani & Miller, 1958). The recapitalization impacts the valuation through leverage effects, which can influence the cost of equity (Sharpe, 2010).

Assuming the payout ratio remains at 40%, the dividend payout ratio remains unchanged, and the firm maintains growth at 5%, the new valuation must incorporate the increased leverage. The new equity value can be estimated under the Modigliani-Miller framework with corporate taxes, considering the tax shield value of debt (Graham & Harvey, 2001). The tax shield benefit is:

Tax Shield = Debt Tax Rate = $1,000,000 40% = $400,000.

Adding this benefit to the unleveraged firm value provides a leveraged firm value:

V_L = V_U + Tax Shield = $25 million + $0.4 million = approximately $25.4 million.

The partial payout adjustment includes repurchasing shares at current stock prices, reducing the number of shares outstanding to:

New Number of Shares = (Total equity value) / (Stock price) = ($25.4 million) / ($25) ≈ 1,016,000 shares.

Thus, the stock price after recapitalization is:

Price per Share = (Equity Value - Debt) / Number of Shares = ($25.4 million - $1 million) / 1,016,000 ≈ $24.86 per share.

This indicates a slight decrease in stock price due to leverage effects, assuming no market imperfections.

Part 3: Risk and Return Analysis of Stocks X and Y

Stock X and Y are analyzed utilizing model frameworks like the coefficient of variation (CV), CAPM required returns, and risk assessment for diversified portfolios. The coefficient of variation, a measure of risk per unit of return, is calculated as:

CV = Standard Deviation / Expected Return.

For Stock X: CV = 35% / 10% = 3.5.

For Stock Y: CV = 25% / 12.5% = 2.0.

Thus, Stock X exhibits higher relative risk per unit of return (Elton, Gruber, Brown, & Goetzmann, 2014). From a diversified investor perspective, lower CV suggests Stock Y is less risky.

The required rate of return based on the CAPM is:

Required Return = Risk-Free Rate + Beta * Market Risk Premium.

For Stock X: 6% + 0.9 * 5% = 6% + 4.5% = 10.5%.

For Stock Y: 6% + 1.2 * 5% = 6% + 6% = 12%.

Comparing these, Stock Y’s expected return (12.5%) exceeds its required return (12%), indicating it is undervalued; Stock X’s expected return (10%) is slightly below its required return (10.5%), indicating overvaluation or market risk considerations.

Calculating the portfolio’s return with investments of $7,500 in Stock X and $2,500 in Stock Y:

Portfolio Return = ($7,500 / $10,000) 10% + ($2,500 / $10,000) 12.5% = 0.75 10% + 0.25 12.5% = 7.5% + 3.125% = 10.625%.

If the market risk premium increases to 6%, the new required returns are:

Stock X: 6% + 0.9 * 6% = 6% + 5.4% = 11.4%.

Stock Y: 6% + 1.2 * 6% = 6% + 7.2% = 13.2%.

Stock Y’s required return increases more significantly, indicating higher sensitivity to market risk premium changes, consistent with its higher beta coefficient.

Conclusion

The analysis illustrates the valuation adjustments resulting from recapitalization strategies and the importance of risk assessment for diversified portfolios. Leveraging and leverage-induced tax benefits can alter firm valuation, while combining assets with different risk profiles necessitates understanding their ratios of risk to return. Moreover, changes in macroeconomic risk premiums significantly influence stock attractiveness, guiding investors in portfolio allocation decisions (Brealey, Myers, & Allen, 2017; Modigliani & Miller, 1958).

References

• Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance (12th ed.). McGraw-Hill Education.
• Graham, J. R., & Harvey, C. R. (2001). The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics, 60(2-3), 187-243.
• Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2014). Modern Portfolio Theory and Investment Analysis (9th ed.). Wiley.
• Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. The American Economic Review, 48(3), 261-297.
• Sharpe, W. F. (2010). Portfolio Theory and Capital Markets. Routledge.