PROBLEM REVIEW SESSION 2

Using the dividend discount model, what is the cost of equity capitalfor Togo Manufacturing Company if the company will pay a dividendof $2.00 next year, has a payout ratio of 40%, a return on equity of16%, and a stock price of $50?

a) 9.50%b) 11.50%c) 13.60%

The equation to calculate cost of equity using the dividend discount model is

Re = D1/P0 + g

D1/P0 = 2.00/50.00 = .04

g = (1 – payout ratio) X (ROE)g = (1 - .40) X .16g = .6 X .16 = .096

Re = .04 + .096 = .136 = 13.6%

Smith Company has been informed by its investment bankersthat it could issue $1,000 face value bonds with a 6% couponpaid semi-annually and an 8 year maturity at $950 per bond.If Smith Company's marginal tax rate is 35%, its after-taxcost of debt is closest to:

a) 6.82%b) 4.43%c) 3.41%

After-tax cost of debt =

Yield to maturity X (1 – Tax Rate)

To solve for Yield to Maturity

FV = $1,000 maturity valuePMT = $30 semi-annual coupon paymentPV = $950 issue amountN = 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%

A firm is paying an annual dividend of $3.63 for its preferred stock which is selling for $62.70. There is a selling cost of $3.30. What is the after-tax cost of preferred stock if the firm's tax rate is 33%? A. 2.02%B. 4.09%C. 5.79%D. 6.11%

Rp = Dp/(Po – Selling Costs)

Rp = 3.63/(62.70 – 3.3)

Rp = .0611 = 6.11%

Oak Enterprises has a beta of 1.2, the market return is 11%, and the T-bill rate is 4%. What is their expected required return of common equity? A. 11%B. 12.4%C. 8.4%D. 4.8%

Capital Asset Pricing ModelRe = Rf + β(Rm – Rf)

Re = 4% + 1.2(11% - 4%)

Re = 4% +1.2(7%)

Re = 4% + 8.4%

Re = 12.4%

AssetsCurrent assets 38,000,000Net plant, property, and equipment 101,000,000Total assets $139,000,000

Liabilities and equityAccounts payable $10,000,000Accruals 9,000,000Current liabilities $19,000,000Long term debt (40,000 bonds, $1,000 par value) 40,000,000Total liabilities 59,000,000Common stock (10,000,000 shares) 30,000,000Retained earnings 50,000,000Total shareholders equity 80,000,000Total liabilities and shareholders equity $139,000,000

Current Stock Price = $7.50Bond Price = $875 per bondBond Information = $1,000 par value, 7.25% coupon Semi-Annual payments, 20 year maturityBeta = 1.25T-Bill Rate = 3.50%T-Bond Rate = 5.50%Expected Market Return = 11.50%Market Return past 5 years = 14.50%Tax Rate = 40%

What is the best estimate of the after-tax cost of debt?

a)      4.64%b)      4.88%c)      5.14%d)      5.40%e)      5.67%

Using the CAPM approach, what is the best estimate of the cost of equity?

a)      13.00%b)      13.52%c)      14.06%d)      14.62%e)      15.21%

Which of the following is the best estimate for the weights to be used when calculating the WACC?

a)      wc = 68.2%

b)      wc = 69.9%

c)      wc = 71.6%

d)      wc = 73.4%

e)      wc = 75.3%

What is the best estimate of the WACC?

a)      9.88%b)      10.18%c)      10.50%d)      10.81%e)      11.14%

After-Tax Cost of Debt

FV = $1,000PMT = $36.25 (72.50/2)PV = $875N = 40 (20 years x 2)Solve for i = .042834 = 4.2834% X 2 = 8.5669%After-Tax Cost = i X (1 – tax rate) = 8.5669% X (1 – 40%) = 5.14%

Re = Rf + β(Rm – Rf)

Rf = T Bond Rate = 5.5% - bond comparable to stock market

β = 1.25Rm = 11.5% - future expected return

Re = 5.5% + 1.25(11.5% - 5.5%) = 13%

Best to use market value of debt and equityMarket value of debt = 40,000 bonds X $875 per bond

= $35 millionMarket value of equity = 10 million shares X $7.50

per share = $75 millionTotal capital = $35 million + $75 million = $110

millionWd = $35 million/$110 million = 31.8%

We = $65 million/$110 million = 68.2%

WACC = (Wd X Kd) + (We X Ke)

WACC = (31.8% X 5.14%) + (68.2% X 13%)WACC = 1.63% + 8.87%WACC = 10.5%

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

Operating Cycle = days in inventory + days in receivables

Days in inventory = Inventory/Cost of Goods/365 = 4,600/(40,000/365) = 41.98 days

Days in receivables = Receivables/Credit Sales/365 = 5,000/(50,000/365) = 36.50 days

Operating Cycle = 41.98 + 36.50 = 78.5 days

Three choices to borrow $1 million for 1 montha) Draw down a line of credit at 7.2% with a .5%

commitment fee on full amountb) Banker’s acceptance at 7.1%, an all inclusive ratec) 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) = $416.67($6,000 + $416.67)/$1 million x 12 = .077 = 7.7%

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

$5,916.67 = $994,083.33Cost = $5,916.67/$994,083.33 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 + $208.33 + $277.78 = $6,236.10

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 componentsb. Operating and financing componentsc. Profit margin and turnover components

Return on Assets = Net Income/AssetsProfit Margin = Net Income/SalesAsset 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 ratiob. Profit margin, the tax retention ratio, and inventory

turnoverc. 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 = 1.5Total Assets/Total Equity = Financial Leverage = 1.2

ROE = 5% X 1.5 X 1.2 = 9.0%