Question

Lexton limited has anequity beta of 1.10. the market risk premium in zambia is expected to be 5% and the yield on government bonds is currently trading at K94.50 . The coupon rate is 8%. The maturity date is five years time and the corporation tax is rate is 28% . interest is payable annually in arrears , the company has just paid the coupon interest for the current year

a) what is lextons cost of equity based on the capital asset pricing model(CAPM)

b) what is the after cost of debt

c) lexton paid a dividend of K0.12 per share and the dividend per share is expected to grow at 7% indefinitely. The companys share price is K2.30 .What is the companys cost of equity.

d) what is the weighted average cost of capital (WACC) if the target debt -equity ratio is 50% ( use the cost of equity as per CAMP)

Answer 1

a) CAPM = R_f + Market risk premium X Beta of the security

R_f = Risk free rate of return , it is the rate of return on a risk free security.

Cost of equity on the basis of CAPM = R_f + Market risk premium X Beta of equity

Here risk free rate of return = 8% as it is the rate of return on government bond which is considered a risk free security because government securities are considered to be default free.

Market risk premium = 5% = 0.05

Beta of equity = 1.10

Cost of equity using CAPM = R_f + Market risk premium X Beta of equity

= 0.08 + 0.05 X 1.10

= 0.08 + 0.055

= 0.135

= 13.5%

B) After tax cost of debt = Coupon rate of debt ( 1 - corporate tax rate)

coupon rate = 8% = 0.08

Corporate tax rate = 28% = 0.28

After tax cost of debt = Coupon rate of debt( 1 - corporate tax rate)

= 0.08( 1- 0.28)

= 0.08( 0.72)

= 0.0576

= 5.76%

C) Price of share at time n = D_n( 1 + growth rate in dividends) \ ( cost of equity - growth rate of dividends)

P_n = D_n( 1+ g) \ (k_e - g)

D_n = 0.12

k_e = ?

g = growth rate = 7% = 0.07

P_n = 2.30

P_{n =} D_n( 1+ g) \ ( k_e - g)

2.30 = 0.12( 1+ 0.07) \ ( k_e - 0.07)

2.30 = 0.12(1.07)\ ( k_e - 0.07)

2.30 = 0.1284\ ( k_e - 0.07)

( k_e - 0.07) = 0.1284\ 2.30

k_e - 0.07 = 0.05582609

k_e = 0.05582609 + 0.07

k_{e =} 0.12582609

Cost of equity = 12.58% ( approx)

D) WACC = w_d X cost of debt + w_e X cost of equity

w_{d =} Weight of debt in firm's capital

w_e = Weight of equity in firm's capital

As target debt- equity ratio is 50% means capital of firm will be made up of 50% equity and 50% debt.

So

w_d = 50% = 0.50

w_e = 50% = 0.50

After tax cost of debt = 5.76%

Cost of equity on the basis of CAPM = 13.5%

WACC = w_d X after tax cost of debt + w_e X cost of equity

= 0.50 X 5.76% + 0.50 X 13.5%

= 2.88 + 6.75

= 9.63%