Question

At year-end 2525 the company has Total assets of $6,200 financed by Debt of $3,400 and Stockholders’ equity of $2,800 . For 170 common shares outstanding, the equity price-to-book ratio at year-end 2525 is 1.36. During 2526, the company expects an asset turnover ratio (= Salest÷ Total assetst-1 ) of 3.8 and an operating margin (= (Sales – operating expenses) ÷ Sales ) of 7.1%. Interest charges will equal 9% of Debt. Corporate taxes equal 30% of taxable income and the payout ratio always is 60%. Your analyst tells you that at year-end 2526 the company price-to-earnings ratio will equal 4.4.What is the shareholders’ rate of return for year 2526?a. 25.6% b. 21.2% c. 31.0%d. 28.2%e. 23.3%

Answer 1

Answer:

Correct answer is:

a. 25.6%

Explanation:

Year 2525:

Stockholders’ equity of = $2,800

Equity price-to-book ratio at year-end 2525 = 1.36

Number of common shares outstanding = 170

Hence:

Price per share = 2800 * 1.36 / 170 = $22.40

Price per share in 2525 = $22.40

Year 2526:

Given:

Assets = $6,200

Sales = Assets * Asset turnover ratio = 6200 * 3.8 = $23,560

Operating income = Sales * Operating margin % = 23560 * 7.1% = $1672.76

Net Income = (Operating Margin - Interest) * (1 - Tax rate) = (1672.76 - 3400 * 9%) * (1 -30%) = $956.732

Hence:

EPS = Net Income / Number of common shares outstanding = 956.732 / 170

Market price per share = EPS * P/E ratio = 956.732 / 170 * 4.4 = $24.76

Dividend per share = Net Income * payout ratio / Number of common shares outstanding = 956.732 * 60% / 170 = $3.38

Hence:

Shareholders’ rate of return for year 2526 = (Market price in 2526 - Market price in 2525 + Dividend in 2526) / Market price in 2525

= (24.76 - 22.40 + 3.38) / 22.40

= 25.6%

Shareholders’ rate of return for year 2526 = 25.6%

Hence option a is correct and other options b, c, d and e are incorrect.