Question

GOLDSMITH INC. Balance Sheet at December 31, 2017 2016 2017 $ 11,530 $ 13,680 Cash 11,100 Accounts Receivable 10,680 Inventories 40,140 35,250 64,920 57,460 Total Current Assets Plant Assets, Net 115,890 105,000 $180,810 $162,460 Total Assets $ 9,530 $ 7,990 Accounts Payable 7,760 7,160 Accrued Liabilities Total Current Liabilities 17,290 15,150 Long-term Debt 33,170 41,630 Total Stockholder's Equity 121,890 114,140 $180,810 $162,460 Total Liabilities and Equity GOLDSMITH INC. Income Statement for the year ended December 31, 2017 2016 2017 $95,640 $89,850 Revenues Cost of Goods Sold 42,980 43,960 Gross Profit 51,680 46,870 Selling, General and Admin Expenses 17,310 18,830 Operating Profit 32,850 29,560 2,214 1,988 Interest Expense Pretax Income 27,572 30,636 Income Tax Expense 11,335 10,202 $17,370 $19,301 Net Income The company has 2017 pretax interest expense of $2,214 and a statutory tax rate of 37%. Your online investigation reveals that the company has a beta of 0.9. Assume that the risk free rate in 2017 is 3.5% and the risk premium is 5%. Required a. Calculate net operating profit after tax (NOPAT) for 2017. Assume that the company's statutory tax rate is 37%. b. Calculate net operating assets (NOA) for 2016 and 2017. c. What is the free cash flows to the firm (FCFF) for 2017 for Goldsmith, Inc.? Calculate the company's weighted average cost of capital for 2017 (4 decimals). d. e. What is the residual operating income (ROPI) for 2017 for Goldsmith, Inc.? Use the company's weighted average cost of capital from part d. above.

Answer 1

a) Net operating profit after tax(NOPAT) = Net income + Interest * (1 - Tax rate)

2017 : Tax rate = 37% or 0.37

NOPAT = $19,301 + $2,214 * (1 - 0.37)

NOPAT = $19,301 + $1,394.82

NOPAT = $20,695.82

b) Net operating assets (NOA) = Operating assets - Operating liabilities

Here, Operating assets = Total assets

Operating liabilities = Accounts payable - Accrued liabilities

i) 2016 (NOA) = $1,62,460 - ($7,990 + $7,160)

2016 (NOA) = $1,62,460 - $15,150 = $1,47,310

ii) 2017 (NOA) = $1,80,810 - ($9,530 + $7,760)

2017 (NOA) = $1,80,810 - $17,290 = $1,63,520

c) Free cash flow to the firm = Net profit + Interest * (1 - Tax rate) + Depriciation - Capital expenditure - Changes in working capital

Here, for 2017 : Depriciation = 0

i) Capital expenditure = Plant assets (Year 2017 - year 2017)

Capital expenditure = $1,15,890 - $1,05,000

Capital expenditure = $10,890

ii) Changes in working capital = Working capital for 2017 - Working capital for 2016

Here, Working capital = Accounts recievables + Inventory - Accounts payable - Accrued liabilities

Working capital (2017) = $11,100 + $40,140 - $9,530 - $7,760 = $33,950

Working capital (2016) = $10,680 + 35,250 - $7,990 - $7,160 = $30,780

Changes in working capital = $33,950 - $30,780

Changes in working capital = $3,170

Now,

Free cash flow to the firm = $19,301 + $2,214 * (1 - 0.37) + 0 - $10,890 - $3,170

Free cash flow to the firm = $6,635.82

d) Weighted average cost of capital (WACC) = (Weight of debt * Cost of debt after tax) + Weight of equity * Cost of equity)

Here, for 2017,

Debt = $41,630, Equity = $1,21,890

Total capital (Debt + Equity) = $41,630 + $1,21,890

Total capital = $1,63,520

Weight of debt = Debt / Total capital = $41,630 / $1,63,520 = 0.26

Weight of equity = Equity / Total capital = $1,21,890 / $1,63,520 = 0.74

i) Cost of debt after tax = (Before tax interest / Debt) * (1 - Tax rate)

Cost of debt after tax = ($2,214 / $41,630) * (1 - 0.37)

Cost of debt after tax = 0.0532 * 0.63 = 0.0335

ii) Cost of equity using CAPM

Cost of equity = Rf + Beta * (Rf - Rm)

Rf (Risk free rate) = 3.5% or 0.035

Beta = 0.9

Rf - Rm (Risk premium) = 5% or 0.05

Cost of equity = 0.035 + 0.9 * 0.05

Cost of equity = 0.08

Now,

WACC = (0.26 * 0.0335) + (0.74 * 0.08)

WACC = 0.0087 + 0.0592

WACC = 0.0679 or 6.79%

e) Residual operating income = Operating income - (WACC * Net operating assets)

For 2017 :

Residual operating income = $32,850 - (0.0679 * $1,63,520)

Residual operating income = $32,850 - $11,103

Residual operating income = $21,747