Midland Energy Resources — Cost of Capital
A How-To Guide: Calculating and Understanding the WACC
This guide walks through every choice behind the WACC numbers, the logic for each input, and how
to use the accompanying Excel model. Approach the case as a consultant hired by Midland's board
to rebuild Mortensen's estimates from scratch and judge which estimate fits which use.
1. Framing: what the case is really asking
The case is about computing Midland's cost of capital and deciding which estimate is best. The
key insight is that there is no single “best” number — the right rate depends on the decision it
serves. Mortensen's estimates are used for five distinct purposes:
• Capital budgeting / asset appraisals — discount rates for project DCF
• Financial-accounting valuations
• Performance assessment via EVA (the WACC is the capital charge)
• M&A proposals
• Stock-repurchase decisions (valuing the firm to judge whether shares are cheap)
Does the use affect the estimate? Yes. Project and divisional decisions (capital budgeting, EVA)
require a divisional rate matched to the risk of those cash flows. Only whole-firm decisions — valuing
Midland for a share repurchase — justify a single corporate WACC. Using one blended rate
everywhere is the classic error: it over-accepts risky projects and over-rejects safe ones (the AES
cautionary tale from lecture).
2. The engine: the WACC formula
WACC = (E/V)·re + (D/V)·rd·(1 − t)
where D and E are the market values of debt and equity, V = D + E, re and rd are the costs of equity
and debt, and t is the tax rate. The cost of equity comes from the CAPM:
re = rf + β · MRP
Leverage enters the WACC twice — through the equity/debt weights and through beta (a more
levered firm has a higher equity beta). That is why beta must be adjusted whenever leverage
changes.
3. Choosing each input (and justifying it)
3.1 Tax rate — 40%
Computed as taxes ÷ pre-tax income from the income statement, averaged over three years: 41.4%
(2004), 39.2% (2005), 38.6% (2006) → average ≈ 39.7%, rounded to 40%. A multi-year average
smooths year-to-year noise in the effective rate.
3.2 Risk-free rate — match maturity to asset life
Use long-term Treasury yields, not bills: cost of capital is estimated for long-lived projects, and bill
yields are far more volatile. Match the maturity to the life of the division's assets:
Division
Rate used
Why
Consolidated & E&P
4.98% (30-yr)
Very long-lived reserves and PP&E
R&M & Petrochemicals
4.66% (10-yr)
Shorter reinvestment cycle; assets replaced
This is a judgment call — some solutions use the 30-year rate throughout. The model lets you switch
the maturity per segment.
3.3 Market risk premium — 5.0%
Use Midland's adopted figure of 5.0%. The evidence is genuinely split: long historical windows
support 6–6.5%, but the Duke CFO survey points to ~3.3% and recent research argues the post-war
premium will not repeat. 5.0% is the defensible middle that Midland chose after consulting its
bankers and analysts. This is the single biggest lever in the whole model — moving it to 6%
adds roughly a full point to every cost of equity.
3.4 Beta — unlever, then re-lever (Hamada)
Beta depends on leverage, so an observed equity beta is only comparable at the leverage that
produced it. To move a beta to a different capital structure, strip out leverage to get the asset
(unlevered) beta, then add the target leverage back:
βunlevered = βequity / [1 + (1 − t)(D/E)]
βrelevered = βunlevered × [1 + (1 − t)(D/E)target]
This is the tax-adjusted Hamada equation (debt beta assumed zero). It is used in two places: to
move Midland's consolidated beta from its current leverage to its target, and to translate
comparable-company betas onto each division's target structure.
3.5 Cost of debt — risk-free rate plus a credit spread
Each division has its own credit rating and therefore its own spread over Treasuries (E&P 1.60%,
R&M 1.80%, Petrochemicals 1.35%, Consolidated 1.62%). Pre-tax cost of debt = matched risk-free
rate + spread; the after-tax figure multiplies by (1 − t).
3.6 Weights — target, at market value
Use each division's target debt ratio (Table 1), measured at market value, not the current or book
ratio. Targets reflect the capital structure the firm manages toward.
4. Corporate WACC — worked example
Midland's published equity beta is 1.25 at its current market leverage (D/E = 79,508 / 134,114 =
0.593). Unlever it, then re-lever to the 42.2% target (D/E = 0.730):
• Asset beta = 1.25 / [1 + 0.6×0.593] = 0.922
• Re-levered beta = 0.922 × [1 + 0.6×0.730] = 1.326
• Cost of equity = 4.98% + 1.326×5.0% = 11.61%
• Cost of debt (after-tax) = (4.98% + 1.62%)×(1−0.40) = 3.96%
• WACC = 0.578×11.61% + 0.422×3.96% ≈ 8.4%
If you treat the given 1.25 as already at target (skipping the re-lever step), WACC ≈ 8.2%. Both are
defensible; state your assumption.
5. Divisional WACCs — and why they differ
For E&P and R&M, take the comparable companies in Exhibit 5, unlever each at its own D/E,
average the asset betas, and re-lever at the division's target. Combined with each division's own
risk-free rate, spread, and weights, the results are:
Asset β
Re-lev β
Cost eq.
WACC
E&P
0.93
1.41
12.0%
8.3%
R&M
1.05
1.33
11.3%
9.0%
Petrochemicals
0.45
0.63
7.8%
6.1%
Division
They differ because every input differs: the asset betas differ (R&M's comparables include
several high-beta refiners, so its unlevered beta sits above E&P's); the target leverage differs
(reshaping both the weights and the re-levered beta); the credit spreads differ; and the matched riskfree rate differs. The ~3-point spread across divisions is exactly why one corporate rate cannot serve
all three.
6. Petrochemicals — no data provided
Preferred method: find publicly traded petrochemical pure-plays, pull their betas and leverage, and
run the same unlever–average–re-lever procedure used for the other divisions.
Residual method (used here, since the case gives no peers): the consolidated asset beta is the
asset-weighted average of the three divisional asset betas, so solve for the missing one:
βu,Petro = (βu,consol − wE&P·βu,E&P − wR&M·βu,R&M) / wPetro
Using 2006 segment assets as weights (E&P 53%, R&M 36%, Petrochem 11%) gives an asset beta
of ≈ 0.45, a re-levered beta of ≈ 0.63, and a WACC of ≈ 6.1%.
Caution: this residual is highly sensitive to the inputs. Unlever the consolidated beta at the target
ratio instead of the current one, or shift the weights, and the implied Petrochemical beta can collapse
toward zero or go negative — an unrealistic result. That fragility is the lesson: the back-out is a last
resort, and real comparables are far more reliable.
7. Caveats to be ready to defend
• The corporate WACC swings ~0.2 pt on whether you re-lever the 1.25 beta.
• Divisional WACCs move with the risk-free-rate maturity choice; using 30-year throughout is a
defensible alternative.
• The MRP is the dominant assumption — a 1-point change shifts every cost of equity by
roughly a point.
• The Petrochemicals residual is fragile; treat it as illustrative, not precise.
Be ready to justify each choice rather than defend a single “correct” decimal.
8. Using the Excel model
The accompanying workbook is fully formula-driven across four tabs:
• Inputs — all blue cells are editable. The two yellow cells (tax rate and MRP) are the key
sensitivity drivers.
• Comparables — unlevers each Exhibit 5 company and averages the asset betas for E&P and
R&M.
• WACC — the full build-up by division; every cell links back to Inputs and Comparables.
• Summary — the headline betas, costs, and WACCs.
Change the MRP or tax rate on the Inputs tab and the entire model recalculates. To test the 30-yearthroughout alternative, switch the “Risk-free used” cells for R&M and Petrochemicals to the 30-year
rate.