PROBLEM REVIEW SESSION 2

The equation to calculate cost of equity using the dividend discount model is R e = D 1 /P 0 + g

D1/P0 = 2.00/50.00 =.04 g = (1 – payout ratio) X (ROE) g = (1 -.40) X.16 g =.6 X.16 =.096 Re = =.136 = 13.6%

After-tax cost of debt = Yield to maturity X (1 – Tax Rate)

To solve for Yield to Maturity FV = $1,000 maturity value PMT = $30 semi-annual coupon payment PV = $950 issue amount N = 16 semi-annual periods Solve for i

i =.0341 or 3.41% for each period Multiply by 2 to obtain annual i = 6.82% Tax Rate = 35% After-tax cost is 6.82%(1 – 35%) = 4.43%

R p = D p /(P o – Selling Costs) R p = 3.63/(62.70 – 3.3) R p =.0611 = 6.11%

Capital Asset Pricing Model R e = R f + β(R m – R f ) R e = 4% + 1.2(11% - 4%) R e = 4% +1.2(7%) R e = 4% + 8.4% R e = 12.4%

After-Tax Cost of Debt FV = $1,000 PMT = $36.25 (72.50/2) PV = $875 N = 40 (20 years x 2) Solve for i = = % X 2 = % After-Tax Cost = i X (1 – tax rate) = % X (1 – 40%) = 5.14%

R e = R f + β(R m – R f ) R f = T Bond Rate = 5.5% - bond comparable to stock market β = 1.25 R m = 11.5% - future expected return R e = 5.5% (11.5% - 5.5%) = 13%

Best to use market value of debt and equity Market value of debt = 40,000 bonds X $875 per bond = $35 million Market value of equity = 10 million shares X $7.50 per share = $75 million Total capital = $35 million + $75 million = $110 million W d = $35 million/$110 million = 31.8% W e = $65 million/$110 million = 68.2%

WACC = (W d X K d ) + (W e X K e ) WACC = (31.8% X 5.14%) + (68.2% X 13%) WACC = 1.63% % WACC = 10.5%

Credit Sales = $50,000 Cost of Goods Sold = $40,000 Accounts Receivable = $5,000 Inventory – Ending Balance = $4,600 The operating cycle for this company is closest to: a) 42.0 days b) 47.9 days c) 78.5 days

Operating Cycle = days in inventory + days in receivables Days in inventory = Inventory/Cost of Goods/365 = 4,600/(40,000/365) = days Days in receivables = Receivables/Credit Sales/365 = 5,000/(50,000/365) = days Operating Cycle = = 78.5 days

Three choices to borrow $1 million for 1 month a) Draw down a line of credit at 7.2% with a.5% commitment fee on full amount b) Banker’s acceptance at 7.1%, an all inclusive rate c) Commercial paper at 6.9% with a dealer’s commission of.25%, and a backup line cost of.33% Which option would result in the lowest borrowing cost?

Line of Credit = (Interest + Commitment Fee)/Net Proceeds x 12 (7.2% X $1 million X 1/12) = $6,000 (.5% X $1 million x 1/12) = $ ($6,000 + $416.67)/$1 million x 12 =.077 = 7.7%

Banker’s Acceptance Cost = Interest/Net Proceeds X 12 Interest = (7.1% X $1 million x 1/12) = $5, Net Proceeds = $1 million – Interest = $1 million - $5, = $994, Cost = $5,916.67/$994, X 12 =.0714 = 7.14%

Commercial Paper Cost = (Interest + Dealer Commission + Backup Cost)/Net Proceeds X 12 (6.9% X $1 million) + (.25% X $1 million) + (.33% X $1 million) = $5,750 + $ $ = $6, Net Proceeds = $1 million – Interest - $1 million - $5,750 = $994,250 Cost = $6,236.10/$994,250 X 12 =.0753 = 7.53%

DuPont analysis involves breaking return-on-assets ratios into their: a. Marginal and average components b. Operating and financing components c. Profit margin and turnover components

Return on Assets = Net Income/Assets Profit Margin = Net Income/Sales Asset Turnover = Sales/Assets Therefore Return on Assets = Profit Margin x Asset Turnover

The DuPont system breaks down return on equity into: a. Return on assets and the financial leverage ratio b. Profit margin, the tax retention ratio, and inventory turnover c. Gross profit margin, total asset turnover, and the debt-to-equity ratio

The DuPont system expands upon the calculation of return on equity to consider the financial leverage of a firm Return on equity is a function of a firm’s return on assets, and how much of the assets are financed by the equity of the firm ROE = ROA X (Total assets/Total equity)

A company’s net profit margin is 5%, asset turnover is 1.5 times, and financial leverage is 1.2 times. Its return on equity is closest to: a. 9.0% b. 7.5% c. 3.2%

Return on Equity = Net Income/Equity = Net Income/Revenue X Revenue/Total Assets X Total Assets/Total Equity Net Income/Revenue = Profit Margin = 5% Revenue/Total Assets = Turnover = 1.5 Total Assets/Total Equity = Financial Leverage = 1.2 ROE = 5% X 1.5 X 1.2 = 9.0%