Titan Mining Corporation has 9.7 million shares of common stock outstanding and 410,000 4.3 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $45 per share and has a beta of 1.25; the bonds have 10 years to maturity and sell for 116 percent of par. The market risk premium is 8.5 percent, T-bills are yielding 5 percent, and the company’s tax rate is 22 percenta. What is the firm's market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.)b. If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Hi, first we have to determine what percentage of the company´s capital is debt (bonds) and what portion is equity (shares). To do that, we need to find out the amounts of each of the sources mentioned above.

[tex]Debt(Bonds)=410,000*1,000=410,000,000[/tex]

[tex]Equity(shares)=9,700,000*45=436,500,000[/tex]

Therefore, the percentage of debt and equity is as follows.

[tex]Debt(percentage)=\frac{ 410,000,000 }{410,000,000+436,500,000} =0.484347[/tex]

[tex]Equity(percentage)=\frac{ 436,500,000 }{410,000,000+436,500,000} =0.515653[/tex]

Now, for the second question, we need to find out the yield of the bond and the cost of the shares (K(e)). First, let´s do the bond.

We need to solve for yield the following equation

[tex]Price=\frac{Coupon((1+Yield)^{n}-1) }{Yield(1+Yield)^{n} } +\frac{FaceValue}{(1+Yield)^{n} }[/tex]

That is

[tex]1,160=\frac{43((1+Yield)^{20}-1) }{Yield(1+Yield)^{20} } +\frac{1,043}{(1+Yield)^{20} }[/tex]

Since this is a very hard to solve, we need to use the MS Excel fuction called IRR, for that, please relate to the excel sheet attached to this answer and notice that in period 0, you have a positive cash flow and is equals to $1,160 and the coupons are $1,000*0.043=$43 (that is because the question says "4.3 percent semiannual bonds outstanding"). In period 20 (which is 10 years or 20 semesters) the last cash flow is -$1043, which is the face value plus the coupon. The function is located in cell C9.

Now, since the output of this formula is effective semi-annually, we have to find the effective annual rate, that is using the following formula.

[tex]r(annual)=(1+0.032)^{2} -1=0.0651[/tex]

The yield of the bond is 6.51% effective annual.

On the other hand, the cost of equity is found by using the following equation.

[tex]K(e)=rf+beta*MRP[/tex]

Where:

rf = risk free rate (that is the T-bills yield)

MRP= Market risk premium (in our case, 8.5%)

K(e)=cost of equity

So, everything should look like this.

[tex]r(e)=0.05+1.25*0.085=0.1563[/tex]

So the K(e)= 15.63%

Now, the discount rate to be used for the evaluation of a project by this company is called WACC (weighted average cost of capital), which is found using the following formula.

[tex]WACC=Kd*DebtPercent*(1-Taxes)+Ke*EquityPecent[/tex]

Kd= Cost of debt (6.51%)

Debt Percent=48.4347%

Equity Percent=51.5653%

Taxes =22%

Ke= Cost of equity (15.63%)

So, this is how we find it.

[tex]WACC=0.0651*0.484347*(1-0.22)+0.1563*0.515653=0.1052[/tex]

So, the WACC (discount rate) is 10.52%

Best of luck.