The goal of this problem is to find the area inside the lemniscuses r^2 = 16 cos

Question

The goal of this problem is to find the area inside the lemniscuses r^2 = 16 cos 2theta. There are several ways in which symmetry of the region can be used when setting up an integral which represents the area inside this lemniscuses. One possible integral is the following, which integrates the angle from -pi / 4 to pi/4: Fill in the blank with the appropriate integrand, written as a function of f (use f in place of theta). You do not need to simplify your answer. Find the area of the lemniscuses.

Explanation / Answer

We need to find the after tax cost of both the debt issues

The pretax cost of debt of first bond issue = Yield to maturity = 10% . So after tax cost of issue 1 = 10*(1-0.35) = 6.5%

For the second issue, we need to find the YTM using "rate" function in excel as in =rate(nper,pmt,pv,fv) where nper =15, pmt =10% of 1000 =100, pv = 940 and FV =1000

Hence Pretax cost of debt = rate(15,100,-940,1000) = 10.83%

So after tax cost =10.83*1-0.35) = 7.04%

Now we also need to find the price of bond issue 1= pv(rate,nper,pmt,fv) =pv(0.10,10,90,1000) = 938.55. Hence it is trading at 92.855% of the face value

So market value of debt 1 = 20,000,000*0.93855 = 18,771,000

Market Value of debt 2 = 25,000,000 *0.94 = 23,500,000

Total value = 18,771,000 + 23,500,000 = 42,271,000

Weight of issue 1 = 18771000/42271000 = 0.4441

Weight of issue 2 = 1-0.4441 = 0.5559

a. Pre tax cost of debt for Olympic

Pretax cost of issue 1 = Rd1 = 10% and pretax cost of Rd2 = 10.83%

Pre tax cost of debt for Olympic = 10*0.4441 + 10.83*0.5559 = 10.46%

b. After tax cost of debt for Olympic

After tax cost of issue 1 = 6.5% and that of issue 2 = 7.04%

After tax cost of debt for olympic = 6.5*0.4441 + 7.04*0.5559 = 6.80%

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