Question

QUESTION: Mr. Goemin has just been hired to compute the cost of capital of debt, bonds, preference shares and ordinary shares for LCDLtd.

• Because LCD’s short term and long term debts do not trade very frequently, Mr. G has decided to use 11% as cost of debt, which is the yield to maturity on a portfolio of bonds with a similar credit rating and maturity as LCD’s outstanding debt. In addition, LCD faces a corporate tax rate of 30%.

• LCD’s bonds are frequently traded. A LCD bond has a $1500 face value and a coupon interest rate of 15% that is paid semi-annually. The bonds are currently selling for $1525 and will mature in 7 years.

• LCD’s preference shares pay a 8% dividend on a $150 face value. The market price at which the preference shares could be sold is only $85. LCD’s corporation tax rate is 30%.

• LCD’s ordinary shares paid a $1.55 dividend last year. Firm’s dividends are growing at a rate of 7% per year and this growth rate is expected to continue into the foreseeable future. The price of these shares is currently $30.

• The risk-free rate is 8.5% per annum and the average expected rate of return in the market is 18.5% per annum, also LCD’s ordinary shares have a beta of 0.55.

Under the assumption that the firm’s present capital structure reflects the appropriate mix of capital sources for the firm, it is determined the market value of the firm’s capital structure as follows:

Source of Capital	Market Values
Debt	$1850000
Bonds	$3500000
Preference Shares	$3000000
Ordinary Shares	$5500000
Retained Earnings	$1500000

Required:

(a) What is LCD’ after-tax cost of debt? (3marks)

(b) What is the cost of LCD’s Bonds? (3 marks)

(c) What is LCD’s cost of preference shares? (3marks)

(d) What is the cost of LCD’ ordinary shares? (3marks)

(e) What is LCD’s cost of retained earningsbased on the CAPM? (3 marks)

(f) What is LCD’s WACC? (5 marks)

Answer: Use the formula sheet

Answer 1

Amounts are in $

(a)

LCD after tax cost of debt

= 11% x (1 - tax rate)

= 11% x (1-30%)

= 7.7%

(b)

LCD after tax cost of bonds

Let the interest rate be "r"

Coupon x PVIFA(14,r%) + Repayment x PVIF(14,r%) = 1,525

1,500 x (15%/2) x PVIFA(14,r%) + 1,500 x PVIF(14,r%) = 1,525

By using trial and error metjod, we found that at r = 7.305% per half year (14.61% per annum) , the equation is satisfied.

Pre tax cost = 14.61%

Post tax cost = 14.61%(1-30%) = 10.227%

(c)

Cost of preference share = Dividend/Price

= ($150 x 8%)/$85

= 0.14118 or 14.118% or 14.12%

(d)

Cost of common shares (using Gordon Growth model)

Price = Past Dividend(1+g)/(r-g)

30 = 1.55(1+0.07)/(r-0.07)

r-0.07 = 1.6585/30

r - 0.07 = 0.0552833

r = 0.0552833 + 0.07

r = 0.125283 or 12.53%

(e)

Cost of retained earnings based on CAPM

Rate = Risk free rate + Beta (Market return - risk free return)

Rate = 8.5% + 0.55 (18.5%-8.5%)

Required rate = 8.5% + 5.5%

Cost of retained earnings = 14%

(f)

WACC Computation

Source	Amount	Weight	Cost	Weighted Cost
Loan	1,850,000	0.1205	7.7	0.92785
Bond	3,500,000	0.228	10.227	2.331756
Preference share	3,000,000	0.1955	14.118	2.760069
Equity Share	5,500,000	0.3583	12.53	4.489499
Retained earnings	1,500,000	0.0977	14	1.3678
	15,350,000	1		11.8725%

Weighted average cost of capital = 11.8725%