Cost of Equity (Ke)

Constant growth model The current market price of a company ‘s share is Rs.90 and the expected dividend per share next year is Rs.4.50. If the dividends are expected to grow at a constant rate of 8%, Calculate Ke.

Ke - g = ------ Po Ke-0.08 = 4.5/90 Ke – 0.08 = 0.05 Ke = 0.05 + 0.08 DIV1 Ke - g = ------ Po Ke-0.08 = 4.5/90 Ke – 0.08 = 0.05 Ke = 0.05 + 0.08 Ke = 0.13 Ke = 13%

DIV1 Ke = ------ +g Po = (4.50/90) + .08 =.05 +.08 =.13 =13%

Constant growth model The current market price of a company ‘s share is Rs.83 and the Current year dividend is Rs.3.78. If the dividends are expected to grow at a constant rate of 9%, Calculate Ke.

Assume that a company’s share is currently selling for Rs. 134 Assume that a company’s share is currently selling for Rs.134. current dividends DIV0 are Rs.3.50 per share and are expected to grow at 15%over the next 6 years and at a rate of 8% forever. Calculate Ke.

YEAR DIVIDEND @10% PV@10% @12% PV @ 12% 1 3.50*1.15=4.03 .909 3.66 .893 3.598 2 4.03*1.15=4.63 .826 3.82 .797 3.690 3 4.63*1.15=5.33 .751 4.00 .712 3.795 4 5.33*1.15=6.13 .683 4.19 .636 3.899 5 6.13*1.15=7.05 .621 4.38 .567 3.997 6 7.05*1.15=8.11 .564 4.57 .507 4.112 7 8.11*1.08=8.76 Total PV for 6 years 24.62 23.091

8.76 = 24.62 + -------------- (0.564) 0.10-0.08 = 24.62 + 123.52 = 148.14 = 23.091 + -------------- (0.507) 0.12-0.08 = 23.091 + 111.03 = 134.121

Cost of Equity Capital Cost of External Equity: The Dividend—Growth Model Earnings–Price Ratio and the Cost of Equity

The Capital Asset Pricing Model (CAPM) As per the CAPM, the required rate of return on equity is given by the following relationship: Equation requires the following three parameters to estimate a firm’s cost of equity: The risk-free rate (Rf) The market risk premium (Rm – Rf) The beta of the firm’s share ()

CAPM Problems Calculate Ke using CAPM approach, the risk free rate of return equals 10%, the firm’s Beta equals 1.50 and the return on the market portfolio equals 12.5%.

Ke = 10% + 1.5(12.5%-10%) = 13.75%

As a investment manager you are given the following information As a investment manager you are given the following information. Risk free return 14% Investment Initial price Dividends Year end price Beta risk factor Cement Ltd 25 2 50 .80 Steel Ltd 35 60 .70 IT Ltd 45 135 .50 Govt. of India Bonds 1000 140 1005 .99

Expected return on market portfolio security Return 1 Dividend Return 2 Capital appreciation Total Investment Cement Ltd Steel Ltd IT Ltd Govt. of India Bonds Rate of return on market portfolio

Expected return on market portfolio security Return 1 Dividend Return 2 Capital appreciation Total Investment Cement Ltd 2 25 27 Steel Ltd 35 IT Ltd 90 92 45 Govt. of India Bonds 140 5 145 1000 291 1,105 Rate of return on market portfolio =(291/1105)* 100 = 26.33%

Expected return on Individual security Ke= Rf + ƅ(Rm-Rf) Ke Cement Ltd 14% +.8 ( 26.33%-14%) 23.86% Steel Ltd IT Ltd Govt. of India Bonds

Expected return on Individual security Ke= Rf + b(Km-Rf) Ke Cement Ltd 14% +.08 ( 26.33%-14%) 23.86% Steel Ltd 14% +.7( 26.33%-14%) 22.63% IT Ltd 14% +.5( 26.33%-14%) 20.16% Govt. of India Bonds 14% +.99( 26.33%-14%) 26.21%

Cost of Retained Earnings If earnings are not retained, it would have been paid out to the ordinary shareholders as dividend. If earnings are retined, forced to forego dividends Thus it involve opportunity cost. Kr likely to be equal Ke.

Overall cost of capital Book Value weights: A firm’s after tax cost of capital of the specific sources is as follows: Calculate Ko Capital stucture cost amount Debt 8% 3,00,000 Preference 14% 2,00,000 Equity 17% 5,00,000

Ko (Book Value) Fund Amount cost Debt 3,00,000 8%= 24,000 Preference 2,00,000 14%= 28,000 Equity 5,00,000 17%= 85,000 1,37,000 1,37,000 Ko = --------------*100 10,00,000 13.7%

Ko- Market Value Source Specific Cost Market Value Book Value Debt 8% 2,70,000 3,00,000 Preference 14% 2,30,000 2,00,000 Equity & Retained earnings 17% 7,50,000 5,00,000

Find out the market value for retained earnings 7,50,000-5,00,000 = -------------------------- * 100 12,50,000 = 20% Retained Earnings = 7,50,000*20/100 = 1,50,000

Computation of Ko (Market Value Weights) Sources Market Value Cost% Total cost Debt 2,70,000 8 21,600 Preference 2,30,000 14 32,200 Equity 6,00,000 17 102000 Retained earnings 1,50,000 25,500 12,50,000 1,81,300 1,81,300 Ko = --------------------- *100 12,50,000 = 14.5%

Overall cost of capital Book Value weights: A firm’s after tax cost of capital of the specific sources is as follows: Calculate Ko Capital stucture cost amount Debt 6% 4,00,000 Preference 10% 2,00,000 Equity 13%