Question

Question 1 Part I

The capital structure of a company with relevant market information are shown as below:

Common stock: There are 55 million shares outstanding of $10 par. The stock has a beta coefficient of 1.8. The management of the company just paid an annual dividend of $1.5 per share and the market expects that the dividend growth rate to be 20 percent for coming three years and grow by 5 percent per year thereafter in the foreseeable future. The required rate of return on your company’s stock is 15 percent.

Preferred stock: 12 million shares currently selling at $96 per share, with dividend rate of 6 percent and face value of $100.

Debt: Three years ago, the company issued 9 million 15-years 8% semi-annual coupon bonds with par value of $1,000 that are still outstanding. The yield-to-maturity (in terms of an effective rate of return) on the bond is 16% per annum.

Market: The current Treasury bill yields 3 percent and the expected return on the market is 12 percent. The company is in the 40% corporate tax bracket. Required:

(a) Estimate the current common stock value using the Dividend Growth Model. (b) Calculate the bond price today. [answers in a whole dollar amount]

(c) Based on answers in above (a) and (b), determine the company’s capital structure weights (WE, WP, WD) for equities and debt. [answers in %]

(d) Compute the cost of equity (RE) using CAPM, cost of preferred stock (RP), and pre-tax cost of debt (RD). [answers in %]

(e) Assuming that the company is going to maintain the current capital structure, calculate the weighted average cost of capital (WACC) of the company. [answer in %]

Answer 1

1. Value of stock using dividend growth:

Value of stock = D₁ / (k - g)

where:
D₁ = next year's expected annual dividend per share
k = the investor's discount rate or required rate of return,

g = the expected dividend growth rate (note that this is assumed to be constant)

Last year Dividend	D0	1.50
growth rate	year 1	20%
	year 2	20%
	year 3	20%
3+ growth indefinitely		5%
dis rate		15.00%

	working	Dividend
year 1	D1 = 1.60*1.03	1.80
year 2	D2 1.65*1.03	2.16
year 3	D3= 1.70*1.03	2.59

value of stock at the end of year 3

= 2.56*(1+0.05)/(0.15-0.05)

27.22

So now we have the value of shares at the end of 3^rd year and the dividend to be received in 3 yrs

So we need to find the value of share today,

Year	Dividend/ stock value	working	Discount factor = 1/(1+r)^n	Discounted cash Flow= Cash flow * discount value
year 1	1.80	1/ (1+0.15)^1	0.87	1.57
year 2	2.16	1/ (1+0.15)^2	0.76	1.63
year 3	2.59	1/ (1+0.15)^3	0.66	1.70
year 3	27.22	1/ (1+0.15)^3	0.66	17.89
			Total	22.80

So the current price of share= $22.80

2. price of bond today

Value of bond of coupon bond = C*(1-(1+r)^-n)/r +F/(1+r)^n

• C = Periodic coupon payment = 1000*8%*1/2= 40
• F = Face / Par value of bond= 1000
• r = Yield to maturity (YTM) and= 16% per year or 8% semi annual
• n = No. of periods till maturity= 15-3= 12

here the payments are semi annual , so no of period= 12*2= 24

value of bond = 40*(1- (1+0.08)^-24)/0.08 + 1000/(1.08)²⁴

=421.15+157.70

= $578.85

3. weights are as follow

Particular	Quantity	price per shr	Total value	Weights= value/ total
shares	55,000,000	22.80	1,254,000,000	16.47%
preferred stock	12,000,000	96.00	1,152,000,000	15.13%
Bonds	9,000,000	578.85	5,209,647,018	68.41%
	Total		7,615,647,018	100.00%

4. cost of equity

Cost of new equity= R(f)+ β{E(m)-R(f)}

R(f) = Risk-Free Rate of Return= 3%

E(m)= 12%

Beta =1.8

Cost of equity = 0.03+ 1.8(0.12-0.03)

0.03+0.162

0.192

or 19.20%

cost of preferred stock= preferred dividend/ current price

= 100*.06 / 96

= 0.0625 or 6.25%

Pre tax Cost of debt = 16%

5. WACC

WACC= {kd (1-t)*debt/ (debt+ equity preferred stock )}+ {ke*equity/(debt+ equity preferred stock )}+ {Kp*Preference stock/(debt+ equity preferred stock )}

Particulars	Cost	tax	After tax cost	weights= market value / total	after tax cost * weights
Bonds	16.00%	40%	=0.16*(1-0.40 )= 0.096 or 9.6%	68.41%	.096*68.41%	0.0657
preferred stock	6.25%	0%	6.25%	15.13%	0.0625*15.13%	0.0095
Equity	19.20%	0%	19.20%	16.47%	0.1920*16.47%	0.0316
			total			0.1067

So WAC= 0.1067 or 10.67%