Texas Inc. has an EBIT of $450,000 that it expects it will earn forever, and it

Question

Texas Inc. has an EBIT of $450,000 that it expects it will earn forever, and it pays all of its earnings as dividends to shareholders (i.e., no growth). The firm has a corporate tax rate of 40% and has an un-levered beta of .90. The firm has 92,656 common shares issued and outstanding. In the market, you observe that Government T-bills are being sold to yield 4% and the S&P/TSX Composite Index is expected to yield 10%. Assume a world of taxes and a cost for the risk of default.

Calculate the value of the firm. (4 marks)

Calculate the WACC for the firm. (2 marks)

What is the value of a share in the company and what is the EPS? (4 marks)      

What is the value of the firm if the firm issues $600,000 of bonds at par with a coupon rate of 7.5%? The beta for the equity of the leveraged firm is 1.02. (10 marks)      

What is the value of the firm if the firm issues $700,000 of bonds at par with a coupon rate of 8.5%? The beta for the equity of the leveraged firm is 1.40. (10 marks)      

What is the optimal level of debt, $600,000 or $700,000? Explain. (2 marks)

What is the WACC for the firm at the optimal level of debt? (4 marks)                      

Explanation / Answer

Question 1,2,&3

Given, no debt so required return or WACC or cost of equity,r=risk free+beta*(market return-risk free)=4%+0.9*(10%-4%)=9.4%
EBIT=450000
Taxes=450000*40%=180000
Net Income=450000-180000=270000
EPS=270000/92656=2.914004

Dividends or Expected Dividend=270000
g=0 as no growth
Value of the firm=D1/(r-g)=270000/0.094=2872340
Price of 1 share=2872340/92656=31.00004

Question 4

Required return on equity=4%+1.02*6%=10.12%
Cost of debt=7.5% as bonds are issued t par so ytm=coupon rate
Equity=2872340 as calculated above
Debt=600000
Proportion of debt=600000/(600000+2872340)=0.172794
Proportion of equity=1-proportion of debt=0.827206

WACC=0.172794*7.5%*(1-40%)+0.827206*10.12%=9.1489%
Firm value=270000/0.091489=2951174

The most correct way in this question would be to caclulate target D/E which can be found out as

Beta levered=Beta unlevered*(1+(1-tax rate)*Debt/Equity)
Hence, 1.02=0.9*(1+0.6*D/E)
Hence, D/E=0.222

We can find the proportion of Debt and Equity as below:
proportion of debt=0.222/(0.222+1)=0.181669
proportion of equity=1-proportion of debt=0.818331
Now we can use this proportion of debt and equity in the above calculations

WACC=0.181669*7.5%*(1-40%)+0.818331*10.12%=9.099%
Firm value=270000/0.09099=2967359
But we will not use this as the question is such that it assumes the value of debt to be taken in the calculations
Question 5

Required return on equity=4%+1.4*6%=12.4%
Cost of debt=8.5% as bonds are issued t par so ytm=coupon rate
Equity=2872340 as calculated above
Debt=700000
WACC=700000/(700000+2872340)*8.5%*(1-40%)+2872340/(700000+2872340)*12.4%=10.9696%
Firm value=270000/0.109696=2461348

Optimal level fo debt is where WACC is lowest and it is in case of 600000 with WACC=9.1489%

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