Body Guards Ltd.'s (BG) balance sheets showed total assets of $100 million and total liabilites of $42 million. Fair values of assets and liabilities were equal to their book values except for a ten year old building whose appraised value was $5 million higher than book. BG has 10 million shares outstanding. BG earned $2.00 per share and paid a dividend of $0.50. Dividends grow at 6% per year. BG enjoys a P/E multiple of 5. BG's cost of capital is 12%. What is the value of a share using the balance sheet method, the liquidation method, the P/E ratio method, and the dividend growth method respectively?

Question

Quizplus · Accepted Answer

Balance Sheet Method: 
-Value of assets = $100 million - $5 million (for building) = $95 million
-Value of equity = $95 million - $42 million = $53 million
-Value per share = $53 million / 10 million shares = $5.30 per share

Liquidation Method: 
-Value of assets = $100 million - $42 million = $58 million
-Value per share = $58 million / 10 million shares = $5.80 per share

P/E Ratio Method: 
-Earnings per share = $2.00
-P/E multiple = 5
-Value per share = $2.00 x 5 = $10.00 per share

Dividend Growth Method: 
-Dividend in year 1 = $0.50
-Dividend growth rate = 6%
-Cost of capital = 12%
-Value per share = $0.50/(12%-6%) = $8.33 per share
-Expected dividend in year 2 = $0.50 x 1.06 = $0.53
-Expected value in year 2 = $0.53/(12%-6%) = $8.83 per share
-Total value per share = $8.33 + $8.83 = $17.66 per share (dividend discount model)
-Value per share = $17.66 / 2 = $8.83 per share (using average of first two years of dividends)
 
Based on the calculations above, the best choice(s) is E as it shows the closest value of share price that can be obtained from the four methods used.