To find the corporate cost of capital for Midland Energy Resources we will need to find the cost of capital of the three divisions within the company.
The formula for WACC is: WACC=rd * (D/V) * (1-t) + re * (E/V) where, rd= Cost of debt re= Cost of equity D= Market value of debt E= Market value of equity V= D+E= Value of the company (or division) T= Tax rate
To calculate the cost of debt (rd) for each division we will use the data in the case by adding the premium over the US treasury securities of a similar maturity (rd = rf + spread to treasury).

Rd
Rate E&P R&M Petrochemical
Spread To Treasury 1.60% 1.80% 1.35%
Treasury Rate 4.98% 4.66% 4.54%
Rd 6.58% 6.46% 5.89%
We used maturity of 30 years for E&P and R&M as they are usually longer project and 1-year for petrochemicals as they tend to be short term projects.

We then calculate the cost of equity (re) for each division by using the CAPM model mentioned in the case The overall beta for Midland (as mentioned in the case) is 1.25. In order to find the beta for each division we use the public traded companies data mentioned in exhibit 5 and use the formula Asset^β=Equity^β/(1+(1-t)*(D/E) )
The results received are:
Equity β for E&P = 0.93*[1+(1-39.73%)*85.19%]=1.41 (85.19% taken from Exhibit 1)
Equity β for R&M = 1.05*[1+(1-39.73%)*44.93%]=1.33 (44.93% taken from Exhibit 1)
For Petrochemicals there is a need to take the WACC of all 3 divisions:
Midland overall β = weight of E&P * β for E&P + weight of R&M * β for R&M + weight for Petrochemicals * β for Petrochemicals.
The information from Exhibit 3 provide us these details and we can calculate weight of E&P = 114,002.67 / 221,515.33 = 0.51 weight of R&M = 82,048.67 / 221,515.33 = 0.37 weight of E&P = 25,464.33 / 221,515.33 = 0.12
1.25 = (0.51*1.41) + 0.37*1.33) + (0.12* β for Petrochemicals)  β for Petrochemicals = 0.32

The next step is to calculate the EMRP, we can do that using exhibit 6. We will use the last option (1798 – 2006) as it both the longest period as well as the period with the lowest standard error: we will assume the same EMRP for the entire case.
Cost of equity (re) for Midland = 4.98%+5%*1.25=11.23%
Cost of equity (re) for E&P = 4.98%+5%*1.41=12.03%
Cost of equity (re) for R&M = 4.98%+5%*1.33=11.63%
Cost of equity (re) for Petrochemicals = 4.54%+5%*0.32=6.14

We are now able to calculate (using the data from exhibit 1) the WACC for each division of Midland as well as the entire company.
WACC=rd * (D/V) * (1-t) + re * (E/V)
1-t=39.73%=60.27% we will assume the same tax rate for the entire case.
WACC for E&P = 6.58%*0.46*60.27%+12.03%(1-0.46)=8.32%
WACC for R&M = 6.78%*0.31*60.27%+11.63%(1-0.31)=9.29%
WACC for Petrochemicals = 5.89%*0.4*60.27%+6.14%(1-0.4)=5.10%
WACC for Midland = 6.6%*0.422*60.27%+11.23%(1-0.422)=9.17%
The cost of capital for each division is different due to the fact that each division operate in a different industry and as a results the exposure to risk and betas will be different and will affect the cost of capital.

Midland is a big corporation with different divisions. As each division has a different risk level we do not think Midland should use a single corporate hurdle rate but a separate rate for each division to make sure the rate reflect a better calculation and assessment.