October 10, 2012 i. Risk-Free Rate
Risk-free rates will depend on when the cash flow is expected to occur and depend upon the period over which investors want the return to be guaranteed. Consequently, we need to take the time horizon into consideration to find out the most suitable risk-free rate. Midland Energy Resources is a well-established company with 120-year history. It is not a company which relies on seeking special opportunity to earn instant profit so that 1-Year T-bond rate is obviously not a proper option. Instead, a long-term development is expected through capital allocation. Here, we choose 30-Year over 10-Year T-bond rate.
Someone may argue that 10-Year is suitable since long-term expected cash flow will be affected by political risk in the Exploration and Production division. This may be true but the company also plans to invest in sophisticated extraction method to extend the lives of older fields as well as developing undeveloped reserves. With such heavy investment the company could not expect a shorter return period and all of these methods may shield the company from those negative affects to some extent. The 30-Year T-bond rate is also preferred by examining the other two divisions. The Refining and Marketing, which is the company’s largest division in aspect of revenue, has long-lived productive assets resulting in a relatively long return period. Moreover, although the profit margin of R&M division is decreasing steadily with a long-term trend in this industry, a longer-term global shortage of refining capacity is predicted, which would eventually spur the industry. All of the above indicate a long period of return, which is 30-Year. The Petrochemicals division is a substantial business in the company and it also has a long-term outlook. Recently the company spent more capital in the near-term on more efficient equipment to maintain steady development for this division. 30-Year rate is suitable not only because we have to wait enough long time the all new facilities are in effect, but also the company expects a long term growth in this division.
To consider the company as a whole, the 30-Year T-bond rate, which is 4.98%, is preferred.

ii. Cost of Debt
The cost of debt can be calculated by adding a premium (spread to Treasury) over the U.S T-bond rate of a similar maturity. This can be expressed as the following equation: rd=rf+∆r, where ∆r is the spread to Treasury rate ①
The values of cost of debt for the consolidated company, as well as the three operation divisions in Midland, can be calculated using equation ① and the results are listed in column 4 of Table 1. Business Segment | Credit Rating | Spread to Treasury | Cost of Debt | Consolidated | A+ | 1.62% | 6.60% | E&P | A+ | 1.60% | 6.58% | R&M | BBB | 1.80% | 6.78% | Petrochemicals | AA- | 1.35% | 6.33% |
Table 1 Costs of Debt of Midland Inc.
Among the three business divisions, the Petrochemicals has the best credit rating (AA-), which leads to a lowest spread to Treasury as well as the lowest cost of debt value (6.33%). The Petrochemicals division has the lowest possibility of defaulting not only because it is a substantial business but also because it may not have so much debt due to its size of business. Although its capital spending is expected to grow, this should be a sign of steady growth instead of increasing risk of the business because it mainly focuses on replacement of older and less efficient equipment.
On the other hands, the R&M division has the lowest credit rating (BBB), resulting in a relatively high cost of debt. The credit rating reflects company’s ability to pay back and a lower rating means higher risk of defaulting, which requires a higher interest rate in return. The R&M division is the largest division in Midland but its profit margin is relatively low comparing to its business size. In addition, its profit margin declined steadily over the previous 20 years and it is facing stiff competition in the market. Unless it can prove itself still to be profitable to spur new investment, or it will impair its ability to pay back and increase the risk of defaulting.
The E&P division has a credit rating of A+ and then gets a modest cost of debt among three divisions. E&P is the most profitable business with no doubt, which demonstrates its ability of paying back. However, it is a risky business as well. A significant portion of E&P’s productive assets and proven reserves are in politically volatile countries and long-term expected cash flow and collateral value will be jeopardized by political risk, which indicates its riskiness and supports less borrowing than expected. Since Midland has the relatively higher cost of debt division R&M, a lower division Petrochemicals and a modest division E&P, then the consolidated company has a credit rating A+ and a 6.6% cost of debt when considered as a whole.
Furthermore, the rating and cost of debt of the consolidated company is very close to the E&P, which is reasonable that E&P is of modest business size and continued heavy investment is expected.

iii. Tax Rate
It is straight forward that from the data given in Exhibit 1, different tax rates applied to Midland’s from 2004 to 2006 can be obtained as stated in Table 2 below. | 2004 | 2005 | 2006 | Income before Taxes | $17,910 | $32,723 | $30,447 | Taxes | $7,414 | $12,830 | $11,747 | Tax Rate | 41.40% | 39.21% | 38.58% |
Table 2 Tax Rates of Midland’s Consolidated Company
In order to finding the appropriate tax rate for Midland to use when calculating WACC, there are three unique approaches have been identified. 1. Simply taking the average on the three different tax rates from 2004 to 2006. 2. Build a linear relationship between the time (year) and the tax rate and estimate the corresponding tax rate at year = 2007. 3. Find the values of differences (∆tax rates) between two consecutive years. Take an average on them and use the result as the difference (∆tax rate) between 2006 and 2007. And subtract this ∆tax rate from the value of the tax rate of 2006 for the estimated tax rate of 2007 (this is a log approach).
Approach 3 was finally been adopted in this case because it is the most reasonable one among these alternatives. Since the tax rates from 2004 to 2006 suggested a strong inclining that the tax rate is decline year after year, the estimated tax rate should not rules out this trend so approach 1 is not viable. Approach 2 was eliminated from the selection because when comparing with approach 3, it may introduce more errors into the estimated result since it was not that precise.
A plot of estimated interest rates versus time using all above three approaches is provided as Graph 1 in the Appendix.
From the Table 3 below, for the final estimated tax rate we recommend for Midland for calculating the WACC is t = 37.17%.

| 2004 | 2005 | 2006 | 2007 (Prediction) | Income before Taxes | $17,910 | $32,723 | $30,447 | N/A | Taxes | $7,414 | $12,830 | $11,747 | N/A | Tax Rate | 41.40% | 39.21% | 38.58% | 37.17% | ∆ Tax Rate | N/A | 2.19% | 0.63% | | | | | Average ∆ Tax Rate | 1.41% |
Table 3 Estimated Tax Rate for Midland’s WACC Analysis iv. Equity Market Risk Premium
It is reasonable to use market risk premium (EMRP) of 5%. First, because based on the selected historical data, during year 1798-2006, average EMRP is 5.1% with lowest standard error of 1.2%, 5.1% is a more stable and reliable value than the rest of data. Although taking a slightly higher estimate would not be counterproductive in view of the recent statistics for 1987-2006 and 1967-2006. But still we have to be careful about the higher standard error (deviation). And according to the selected market risk premium survey results, respondents' risk premiums are all below 5%.
Moreover, there are many unpredictable and unsure factors that might affect the future performance of Midland such as overseas political volatility. As a company, it is better to be more prudent to make future estimates. Taking everything into account, an EPRM of 5% is safe and reasonable. v. Cost of Equity of Midland Consolidated
The cost of equity rE can be found by: rE=rF+βEquity(EMRP) ②
Thus, by adopting data from Exhibit 5, the estimated Midland’s consolidated cost of equity at this time is 11.23%. rE=4.98%+1.25*5%=11.23% vi. Consolidated WACC of Midland
The consolidated WACC of Midland can be found by:
WACC=rDDD+E1-t+rEED+E ③
Thus, by adopting data from Exhibit 5, the consolidated WACC of Midland at this time is 8.60%.
WACC=59.3%1+59.3%1-37.17%4.98%+1.62%+1-59.3%1+59.3%4.98%+1.25*5%=8.60%

vii. Un-levered Asset Beta of Midland Consolidated
Unlevered asset beta for the consolidated company of Midland can be found by equity beta and D/E ratio given in Exhibit 5 in the case. This can be expressed as the following equation: βAssetU=(1-λ)βEquity, where λ=DD+E ④
Thus, the un-levered asset beta of the consolidated company of Midland is 0.785, which is obtained as (a summery is provided in Table 4): βAssetU=1-DEDE+1βEquity=1-0.5931.593*1.25=0.785 | Equity Market Value | Net Debt | D/E | Equity Beta | D/D+E | Un-levered Asset Beta | Midland Energy Resources (Consolidated) | $134,114 | $79,508 | 59.30% | 1.25 | 37.22% | 0.785 |
Table 4 The Un-levered Asset Beta of Midland Consolidated

viii. WACC and Cost of Equity of Mortensen’s Estimation
In order to find the cost of equity of the consolidated company under its future target capital structure, the un-levered asset beta should be calculated first based on data given in Exhibit 5 and equation ④, then find the re-levered equity beta.
To re-lever an un-levered equity beta value, the following equation may apply: βEquity,2=1(1-λ2)βAssetU ⑤
Since the rF (the risk-free rate, which is 4.98% in this case) and the EMRP (5%) is given, the only remaining thing is to find the un-levered equity beta and re-lever it again using the new D/D+E value and put all these results into equation ② and ③ to obtain the estimated cost of equity and WACC of consolidated company of Midland. Detailed calculation steps are listed below and a summary table (Table 5) is also provided. λ2=DD+E=42.20% βEquity,2=11-λ2βAssetU=11-0.422*0.785=1.358 rE=rF+βEquityEMRP=4.98%+1.358*5%=11.77% rD=rF+ΔrSpread to Treasury=4.98%+1.62%=6.60%
WACC=rDDD+E1-t+rEED+E=6.60%*42.2%*1-37.17%+11.77%*1-42.2%=8.55%
| D/D+E | Spread to Treasury | Un-levered Asset Beta | Re-levered Equity Beta | Midland Energy Resources (Consolidated) | 42.2% | 1.62% | 0.785 | 1.358 | | Cost of Debt | Cost of Equity | WACC | | | 6.6% | 11.77% | 8.55% | |
Table 5 WACC and Cost of Equity of Mortensen’s Estimation
Generally speaking, WACC indicates the firm’s overall required return and therefore it can determine if opportunities are feasible. Higher beta and rate of return on equity give higher WACC of a firm and therefore indicates the decrease in valuation and a higher risk.

ix. WACC and Cost of Equity Versus Debt Fraction
The plotted graphs are attached in the Appendix at the end of this report as Graph 2 and 3.
As is shown in Graph 2, WACC linearly decreases as D/D+E ratio gets bigger. However, Graph 3 suggests that cost of equity is less sensitive to D/D+E ratio until it reaches certain threshold (around 0.8) and then increases dramatically as D/D+E gets higher. Considering we prefer both WACC and cost of equity to be small, a proper D/D+E ratio should be chosen around 0.8, considering the trade-off between lower WACC and lower cost of equity.
What’s more, these analyses on the relationship of WACC and cost of equity between debts are based on the assumption that the cost of debt remains the same throughout the whole debt accumulating period from 0 to 100%. However, this assumption is unrealistic because of the fact that as the debt fraction coming up to some certain point, the quantity of debts will greatly affects the payback ability of the company. Thus, the cost of debt can increase and will plays an important role in WACC and cost of equity estimation.

x. Analysis of Comparable Companies & Estimating Midland
The values of un-levered asset beta for different comparable companies can be calculated by adopting data from Exhibit 5 into equation ④. The average asset beta then can be obtained by taking average values on those un-levered asset beta values. The results are summarized into Table 6 below. Exploration & Production | D/D+E | Un-levered Asset Beta | Jackson Energy, Inc | 10.07% | 0.80 | Wide Plain Petroleum | 46.06% | 0.65 | Corsicana Energy Crop. | 13.19% | 0.96 | Worthington Petroleum | 32.20% | 0.94 | | Average | 0.84 | | | | Refining & Marketing | | | Bexar Energy, Inc | 9.34% | 1.54 | Kirk Crop. | 16.25% | 0.79 | White Point Energy | 17.29% | 1.47 | Petrarch Fuel Services | -13.64% | 0.27 | Arkana Petroleum Corp. | 24.41% | 0.94 | Beaumont Energy, Inc | 17.08% | 0.86 | Dameron Fuel Services | 33.47% | 0.94 | | Average | 0.98 |
Table 6 Asset Beta Vales for Comparable Companies and Average Value
Thus, the newly estimated equity beta values of Midland’s E&P and R&M division can be calculated by taking these average asset values into equation ⑤ to re-lever them. And that is: λ2,E&P=46.0% βEquity,2,E&P=1(1-46%)*0.84=1.56 λ2,R&M=31.0% βEquity,2,R&M=1(1-31%)*0.98=1.41
So the estimated equity beta for Midland’s E&P division is 1.56 and for R&M is 1.41. Once obtained these equity beta values, we can take then into equation ② and ③ respectively in order to calculate the cost of equity and the WACC for each division under this estimation. As the result, the estimated cost of equity for Midland’s E&P division is 12.76% and for R&M division is 12.05%. The estimated WACC values for these two divisions are 9.92% and 8.89 respectively. A summery table (Table 7) is provided below. Midland Energy Resources | D/V | Estimated Equity Beta | Spread to Treasury | Exploration & Production | 46.0% | 1.56 | 1.60% | | Cost of Debt | Cost of Equity | WACC | | 6.58% | 12.76% | 9.92% | Midland Energy Resources | D/V | Estimated Equity Beta | Spread to Treasury | Refining & Marketing | 31.0% | 1.41 | 1.80% | | Cost of Debt | Cost of Equity | WACC | | 6.78% | 12.05% | 8.89% |
Table 7 Newly Estimated Business Divisions’ Cost of Equity and WACC
The newly estimated WACC value using the average result from companies in the market is higher than the Midland’s consolidated WACC which calculated in part vi. A higher WACC value means that the company basically needs a larger amount of money in order to raise capital. Thus, a higher WACC value indicates that this division is more risky.
Notice that the WACC value of the Midland’s E&P division is much larger than its R&M division. This suggests that the E&P market maybe more risky. Midland was originally anticipating to continually perform some heavy investment in E&P division because of the oil price is at historic highs. But on the contrary, with such a high WACC of the E&P division, we recommend Midland to better carefully reviews its on-coming investments to avoid possible risks.

xi. Discussion about Choosing Hurdle Rate
Regarding to this hurdler rate choosing problem, we recommend the Midland to use different hurdler rate (MARR) with respect to the different WACC values of each division. The reason why we made such a recommendation is based on the following two reasons: 1. It is shown in the previous parts of this report that the WACC values of Midland varies greatly from the consolidated company (8.55%) to the E&P division (9.92%). Recall that the relation lays between MARR and WACC is that the MARR should be better grater or equals to the WACC. That indicates additional values have been brought into the company. So one problem for using one single consolidated corporate MARR to evaluating investment is that it overlooks the different performances and risks due to the nature of the businesses each division is doing. So it would be hard to find one single reasonable MARR for every division. Thus, the evaluation could be very imprecise. 2. Another problem with evaluating an investment with a single MARR value is that this may leads to an overoptimistic expectation on the return of the investment. An incorrectly estimated on returns may lead to more serious problems like increasing the cost of capital or stressing the company’s cash chain.

xii. Conclusions
It is clear the data analysis on the Midland Inc. suggests that it is playing well in the past years and it is also seeking for development. However, there are still certain problems that Midland Inc. certainly will be facing with. As can be concluded from the WACC analysis, the risks of investment for some of the Midland’s business divisions are still high. So we suggest the leaderboard to review all possible investment deeper and more careful. And Midland, as well as Ms. Mortensen, should taking everything possible into consideration (such as different MARRs and WACCs) when doing estimations or making decisions in order to reduce unnecessary loss or risks caused by incorrect predictions.