Cost of Capital in management of diff firms.pptx

gives clear understanding

1. Cost of Capital

2. Cost of Debt P = ∑ C*(1-T) + F ( 1+ K d ) t (1+K d ) n Where P = Net amount realized on debt issue C= Annual Interest payable T = Tax Rate F = Redemption Price n- = Maturity period of Debt t =1 t=n

3. An Approximation Kd = [C*(1-t) + (( F – P) / n) ] / [( F + P)/ 2]

4. Question Ramson Ltd., issues 10% debentures of face value Rs.100 each and realizes Rs.90 per debenture . The dentures are redeemable after 12 years at a premium of 8%. Company is paying income tax @45%. The cost of debt is

5. Answer Kd = [C*(1-t) + (F – P) /n] / (F + P)/2 I = Annual Interest to be paid = Rs.10 t = 0.45 F = Rs.108; P = 90 n = 12 years Kd = [10*(1- 0.45) + ((108 – 90) / 12) ] / [ (108 + 90)/2 ] = 0.0707 = 7.07%

6. Cost of Term Loan Cost of Term Loan = I*(1-t)

7. Cost of Preference Capital P = ∑ D + F ( 1+ K p ) t ( 1+K p ) n Where P = Net amount realized per preference share D= Preference dividend per share payable annually F = Redemption Price n- = Maturity period of Preference Capital t =1 t=n

8. An Approximation K p = [D + (F – P) /n] / (F + P)/2

9. QUESTION A preference share issues at 12% worth Rs 60,000 at 5% discount and after 6 years it redeem at 10% premium. The flotation cost is 5% and tax rate is 20%. Find out the cost of preference share capital .

10. SOLUTION Dividend on preference share ( D p ) = 60,000*12/100 = Rs.7200 Discount = 60,000*5/100 = Rs.3000 Flotation Cost = 60,000*5/100 = Rs.3000 Net Proceeds (NP) = Rs . (60,000-3000-3000) = Rs . 54,000 Premium amount = 60,000*10/100 = Rs . 6000 Redemption Value = Rs . (60,000+6000) = Rs . 66,000 K p  = D p + ((RV-NP)/n)/ (RV+NP)/2 = 7200+ ((66,000-54,000)/6) / (66,000+54,000)/2 = 9200/60,000 = 15.33%

11. QUESTION Company ABC a small company issued 50, 000 shares of 10 each and pays Rs.8 per shares as dividend. Further issue 10, 000 debentures of Rs . 100 each and the interest pays by the company is 8%. Company wants to expand its business by opening a new branch in different cities. It wants to finance its expansion project through 6% preference shares. Find out: Cost of preference share if issues 100 of Rs . 80 each at 3% discount and redeem at 5% premium after 8 years. Which one is good for the company redeemable preference share or irredeemable preference share? Flotation cost Rs . 10 each.

12. SOLUTION Discount= 80*0.03 = 2.4 Issue price= 80-2.4 = 77.6 Net proceeds = 77.6 – 10 = 67.6 Dividend = 0.06*80 = 4.8 Premium amount = 80*0.05 = 4 Redemption value = 80 + 4 = 84 Irredeemable Preference share: K p  = Dp /NP = 4.8 / 67.6 = 7.10%

13. Redeemable Preference share: Net proceeds = 80 – 2.4 - 10 = 67.6 K p  = D p + ((RV-NP)/n)/ (RV+NP)/2 = 4.8 + ((84-67.6)/8)/ (84+67.6)/2 = 4.8 + (2.05 / 75.8) = 4.8 + 0.027 = 4.827% The cost of redeemable preference shares is less than irredeemable preference share by 2.27%. So, the redeemable preference share is beneficial for the Company ABC.

14. Perpetual Preference Capital P = ∑ D (1+ K p ) t Which is simply K p = D/ P t =1 t= ∞

15. Cost of Equity – Dividend Capitalisation Approach P = D 1 / (1+K s ) 1 + D 2 / (1+K s ) 2 + D 3 /(1+K s ) 3 + …. D ∞ /(1+K s ) ∞ P = ∑ D t / (1 + K s ) t If we assume that the dividend per share remains constant every year , lets say i.e. D then P = D/(1+k s ) + D/( 1+k s ) 2 + D/(1+k s ) 3 + ….. D/(1+k s ) n On Simplification P = D/K s Or K s = D /P t = 1 t = ∞

16. Cost of Equity – Dividend Capitalisation Approach When the dividend increases at a constant rate , the share valuation equation becomes: P = D 1 /(1+Ks) + D 1 (1+g)/(1+Ks) 2 + D 1 (1+g) 2 /(1+Ks) 3 + … On simplification it becomes: P = D 1 / Ks –g Or K s = D 1 / P + g

17. QUESTTION Raj Textiles Ltd. wishes to determine its cost of equity capital, Ke . The prevailing market price of the share is Rs . 50 per share. The firm expects to pay a dividend of Rs . 4 at the end of the coming year 2003. The dividends paid on the equity shares over the past six years are as follows : Year Dividend ( Rs .) 2002 3.80 2001 3.62 2000 3.47 1999 3.33 1998 3.12 2.97 The firm maintained a fixed dividend payout from 1996 onwards. The annual growth rate of dividends, g , is approximately 5 percent.

18. SOLUTION P = D 1 / Ke – g 50 = 4 / ( Ke – 0.05) Ke = (4 / 50 ) + 0.05 Ke = 0.08 + 0.05 = 13% The 13% cost of the equity share represents the return expected by existing shareholders on their investment so that they should not disinvest in the share of Raj Textiles Ltd. and invest elsewhere.

19. Cost of Equity – CAPM As per CAPM K j = R f + Β j *(R m – R f ) Where R f = Risk free rate of return K j = Required or Expected rate of return on security j Β j = Beta Coefficient of security j R m = Expected return on the market portfolio

20. WACC WACC = Wd * Kd + We* Ke + Wp * Kp + I*(1-t)

21. QUESTION A firm has the following capital structure and after tax costs for the different sources of funds used : Source of Funds Amount ( Rs ) Proportion (%) After tax cost (%) Debt 40,00,000 20 4.50 Preference Shares 20,00,000 10 9.00 Equity Shares 60,00,000 30 11.00 Retained Earnings 80,00,000 40 10.00 200,00,000 100 Calculate cost of weighted capital by using book value method.

22. SOLUTION METHOD OF FINANCING PROPORTION (%) COST (%) WEIGHTED COST (%) Debt 20 4.50 0.90 Preference Shares 10 9.00 0.90 Equity Shares 30 11.00 3.30 Retained Earnings 40 10.00 4.00 9.10

23. QUESTION BHARAT AGRO Ltd. has assets of Rs.2,80,000 which have been financed with Rs.64,000 of debt and Rs.1,10,000 of equity and a general reserve of Rs.18,000. The firm’s total profits after interest and taxes for the year ended 31st March 2004 were Rs.25,700. It pays 13% interest on borrowed funds and is in the 60% tax bracket. It has 1,000 equity shares of Rs.100 each selling at a market price of Rs.125 per share. The firm pays 60% of its earnings as dividends . Calculate The EPS The Cost of Debt The Cost of Equity The Weighted average cost of Capital

24. SOLUTION a) Earning Per Share = Earnings after Interest and Taxes / No. of Shares = 25700 / 1000 = 25.7 b) Cost of debt ( Kd ) = I (1–t) = 13 (1–0.60) = 5.2%.

25. SOLUTION CONTD.. b) Cost of debt ( Kd ) = I (1–t) = 13 (1–0.60) = 5.2%.

26. SOLUTION CONTD.. c) Cost of equity = Ke = (DPS / MP ) * 100 Where Ke = Cost of equity capital DPS = Dividend Per Shares; (DPS = 60% of EPS = 0.6 x 25.7 = 15.42) MP = Market Price of Share Ke = (15.42 / 125 ) * 100 = 12.34%

27. SOLUTION CONTD.. d) Weighted Average Cost of Capital Source of Capital Amount Specific Cost Total Cost Debt 64,000 5.2% 3,328 Equity 1,10,000 12.34% 13,574 Reserves 18,000 12.34% 2,221.20 1,92,000 19,123.20 WACC = ( 19,123.20 / 1,92,000 ) * 100 = 9.96%

28. WACC Stock Information Industry : Pharmaceuticals Common stock quote (March 28, 2003 ) : $56.96 Price/earnings ratio : 24.21 Earnings per share : $2.18 Indicated annual dividend : 0.82 Yield (percent ) : 1.55 Beta coefficient : 0.47 Shares outstanding : 2,969,972,000 The Company's marginal tax rate is estimated to be 28 percent . The Company's cost of debt can be estimated by the average effective interest paid on its debentures and notes payable , which is calculated to be 5.85 percent before taxes.

29. R isk-free rate R f = 3.907 F irm’s beta = 0.47 M arket risk premium = 5.9 percent The Company's market value of debt as per its December 29, 2002 balance sheet includes (in millions) loans and notes payable of US$ 2,117 and long-term debt of US$ 2,022, for a total of US$ 4,139 million . Q. Calculate the WACC ?

30. Ke = 3.907 + 0.47(5.9 ) = 6.68 percent The market value of equity can be calculated by multiplying the current share price times the number of current shares outstanding , US$ 56.96 × 2,969,972,000 = US$ 169,169.6 million Thus , Wd = 2.38 percent and We = 97.62 percent . WACC = (1 – .28)(2.38 percent × 5.85 percent) + (97.62 percent × 6.68 percent ) = 6.62 percent

31. (Beta for an Individual Security) = Bj = Cov ( Kj , Km) / σ 2 m (Beta for a Portfolio) = Bp = Cov ( Kp , Km) / σ 2 m

32. Beta – Levered & Unlevered

33. Risk components in levered Beta Levered beta which reflects the capital structure of the company. The levered beta has two components of risk, business risk and financial risk . Business risk represents the uncertainty in the projection of the company’s cash flows which leads to uncertainty in its operating profit and subsequently uncertainty in its capital investment requirements. Financial risk represents the additional risk placed on the common shareholders as a result of the company’s decision to use debt, i.e. financial leverage. If capital structure comprised of 100% equity then beta would only reflect business risk. This beta would be unlevered as there is no debt in the capital structure. It is also known as asset beta .

34. Relationship between Levered and Unlevered Beta β L = β U [1 + (1 – T ) D / E ] β L = levered beta (beta at the current level of debt), and β U = unlevered beta (beta when there is no debt in the capital structure ). V = D + E That is, the value of the firm equals the sum of values of debt and equity. Multiplying both sides by their respective beta, β A V = β D D + β E E

35. Dividing both sides by V β A = β D * D / V + β E * E / V That is, asset beta is the weighted average of debt and equity beta . β L = β U [1 + (1 – T ) D / E ] β U = β L / [1 + (1 – T ) D / E ]

36. How do we relever Beta in WACC? To obtain the equity beta of a particular company, we start with a portfolio of assets of that company or alternatively a sample of publicly traded firms with similar systematic risk. We will first derive the betas of these individual assets or firms from market prices. The derived betas are levered betas as they would reflect the capital structure of the respective firms. They have to be unlevered so as to only reflect their business risk components. From the unlevered betas, obtain a weighted average unlevered beta using as weights the proportions of the assets in the company’s asset portfolio or derive an average across all comparable firms. The weighted unlevered beta thus obtained would now be relevered based on the capital structure of the company in order to determine the equity or levered beta for the company. This beta would reflect not only the business risk but also the financial risk of the company.

37. Example BetaCorp is a corporation that has two primary business lines  – personal hygiene and consumer off the shelf pharmaceuticals. We are estimating its levered beta for the purpose of determining its cost of equity. The personal hygiene subsidiary is worth USD 20 million while the consumer pharma subsidiary is worth USD 30 million. The firm has a debt-to-equity ratio of 1. Assume that the tax rate for all firms is 30%. The risk free rate is 7% and the market risk premium is 6%. The following information is for firms with comparable systematic risk: Note that the average betas above denote the average of the levered or equity betas of these firms. Comparable Firms Average Beta Average D/E Ratio Personal Hygiene 0.9 20% Medical 1.2 60%

38. Unlevered Beta for the personal hygiene business = 0.9 / (1+ 0.2*(1-0.3)) = 0.79 Unlevered Beta for the consumer pharma business = 1.2 / (1+ 0.6*(1-0.3)) = 0.85 The Beta for BetaCorp will be the weighted average of unlevered betas where the weights are in proportion to the subsidiaries value in the firm, i.e. Unlevered Beta for BetaCorp = 0.79*20m/50m + 0.85*30m/50m = 0.82 Levered Beta for BetaCorp = 0.82*(1+1*(1-0.3)) = 1.40 Cost of Equity = 7%+1.40*6% = 15.39%.

39. Question Company X is a non-listed private company. Here are some details available with you: Total Debt $ 2 million Total Equity $ 5 Million Debt to Equity ratio 40% Tax rate 30%

40. a comparable company which is similar in nature to the Company X is operating in the same industry and it has the same product line and risk profile as Company X. So, you have collected the following data about the comparable company: find out the beta for the Company X. Calculated Beta 1.2 Total Debt $ 4 million Total Equity $ 8 Million Debt to Equity ratio 50% Tax rate 35%

41. Answer Unlevered Beta ( β Company A) = 1.2 / 1 + [ (1- 0.35) (0.5) ] = 0.91 Levered beta (β Company X) = Unlevered Beta * 1 + [ (1- Tax) (Debt/Equity) ] = 0.91 * 1 + [ (1- 0.3) (0.4) ] = 1.17