Question

1. A firm is considering selling $30 million worth of 30-year, 9% coupon bonds with a par-value of $1,000. Because bonds with similar risk earn a return greater than 9%, the firm must sell the bonds for $980 to compensate for the lower coupon interest rate. The flotation costs are 3% of par.

The firm is also considering an issuance of 300,000 shares of 10% preferred stock that they expect to sell for $82 per share. The cost of issuing and selling the stock will be $4 per share.

The firm plans to sell shares of common stock that have already been issued. The firm’s common stock has a market price of $98 per share and expects to pay a dividend of $5.61 per share at the end of 2013. The dividends paid on the outstanding stock over the past years ranged from $4.00 in 2008 to $5.24 in 2012.

The firm has determined its optimal structure should be 30% of debt, 20% of preferred stock, and 50% of common stock.  

The firm has earnings before interest and taxes (EBIT) of $17,000,000 and interest expense of $2,700,000. The firm’s applicable tax rate is 40%.

Based on the firm’s financing plans as noted above, what is the value of the firm?

2. What is the profitability index of a project if the initial cost of the project is $40,000 and the cash flow at the end of year 1 is $20,000, year 2 is $30,000, year 3 is $10,000, and year 4 is $30,000 and the applicable interest rate is 9%?

1. 1.81
2. .81
3. .77
4. 1.77

Answer 1

Profitability index :-

Profitability Index Method Formula

Use the following formula where PV = the present value of the future cash flows in question.

Profitability Index = (PV of future cash flows) ÷ Initial investment

Cash flows Discount rate factor( 9%) year

20000 0.9174 1

30000 0.8417 2

10000 0.7722 3

30000 0.7084 4

Present value = 20000 * 0.9174 + 30000 * 0.8417 + 10000 * 0.7722 + 30000 * 0.7084

= 18348 + 25251 + 7722 + 21252 = 72573

Profitability Index = 72573 / 40000

= 1.81 Option A

for caluclation of value of firm -

As a first step, we need to determine the required rate of return rd by solving the following equation:

$980 × (1 - 0.030) =	$90	+	$90	+	$90	+	$90	+	$90
	(1 + rd)1		(1 + rd)2		(1 + rd)3		(1 + rd)4		(1 + rd)5

ans so on till $90 / (1+rd)30

To do it, we can use an online calculator or Microsoft Excel function “IRR.” The required rate of return, including floatation costs, is 8.70%. So, the after-tax cost of debt for Company B will be 5.22%.

k_d = 8.70 × (1 - 0.4) = 5.22%

Kp =

100 * 10% = 10 Annual dividend

P* = 82 -4 = 78

cost of preference shares will be =

10/78 = 12.82%

Ke =

Cost of Equity Dividends per Share (for next year) Current Market Value of Stock Growth Rate rrent Market Value of Stock of Dividenod

Dividend per share = $ 5.61

Market price = 98$

Growth rate =

4 to 5.24 $ 5.24 - 4 = $1.24 in 4 years

Compound annual growth rate = 6.98 % ( Using excel formula )

5.61 / 98 = 5.72 % + 6.98 = 12.70%

WACC = 5.22 * 30% + 12.82 * 20% + 12.70 * 50%

1.566 + 2.564 + 6.35

= 10.48 %

FCFF = EBIT * 1- Tax

= 17 million * 0.6 = 10.2 million

Value of firm = 10.2 / 10.48 % = 97.3282 million