| Course | GF520 Corporate Finance |
|---|---|
| Unit | Unit 7 |
| Paper type | Capital structure case study |
| Length | About 1,140 words, 7 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | MS in Finance |
| Updated | October 2026 |
Free sample paper for GF520 Unit 7
How Much Should a Fitness Chain Borrow? A Unit 7 Capital Structure Case Study of a Proposed Buyback
[Student Name]
Purdue University Global
GF520: Corporate Finance
Unit 7 Capital Structure Case Study
[Instructor Name]
[Date]
The fitness chain, its management's proposal and every figure are composite and illustrative; the articles and textbook cited are real.
The Company and the Proposal
The chain operates 210 clubs in the Midwest and South, nearly all in leased buildings, with about 1.4 million members on monthly contracts. Its total value, debt plus equity at market, is about $1.5 billion, and its debt of $300 million is 20 percent of that. Cash flow has been steady for five years, and management believes the shares are undervalued. It proposes to borrow $375 million and use it to repurchase shares, taking debt to $675 million, or 45 percent of value.
The question for the case is not whether the shares are cheap but whether the company's value is higher with 45 percent debt than with 20 percent. Two forces pull in opposite directions: interest is tax deductible, which favors more debt, and heavy debt raises the chance and cost of financial distress, which favors less (Myers, 1984).
Table 1: The Cost of Capital at Six Debt Levels
To see how the discount rate changes with debt, the chain's equity beta is first unlevered to remove the effect of today's debt, giving an asset beta of 0.90, and then relevered at each debt ratio using a 25 percent tax rate. Each cost of equity starts from a 4.3 percent Treasury yield and adds beta times a 5.5-point premium for market risk. The cost of debt rises at each step because lenders would rate the company lower.
1. 10 percent debt: equity beta 0.98, cost of equity 9.66 percent, cost of debt 5.6 percent, weighted rate 9.12 percent.
2. 20 percent debt, today: equity beta 1.07, cost of equity 10.18 percent, cost of debt 5.9 percent, weighted rate 9.03 percent.
3. 30 percent debt: equity beta 1.19, cost of equity 10.84 percent, cost of debt 6.5 percent, weighted rate 9.05 percent.
4. 40 percent debt: equity beta 1.35, cost of equity 11.73 percent, cost of debt 7.6 percent, weighted rate 9.32 percent.
5. 45 percent debt, proposed: equity beta 1.45, cost of equity 12.29 percent, cost of debt 8.2 percent, weighted rate 9.53 percent.
6. 50 percent debt: equity beta 1.58, cost of equity 12.96 percent, cost of debt 9.2 percent, weighted rate 9.93 percent.
The weighted rate is lowest between 20 and 30 percent debt, at about 9.03 to 9.05 percent, and rises steadily beyond that. At the proposed 45 percent it is half a point higher than today. The rate flattens near its low because, in that range, cheaper after-tax debt is offset almost exactly by the rising cost of equity.
Table 2: Tax Shield Against Expected Distress Cost
The cost of capital approach captures distress only through the rising cost of debt. A second approach values the two forces directly. The tax shield is valued at the tax rate times the debt, treating debt as permanent (Brealey et al., 2023). The expected cost of distress is the probability of distress at each debt level times the cost if it happens.
For this company the cost of distress is set high, at 25 percent of its value, or $375 million. Two features of the business justify that figure. Its clubs are leased, so it owns little that could be sold to repay lenders, and lease obligations continue whatever happens. And its members are on month-to-month contracts: news of financial trouble could lead many to cancel, cutting revenue precisely when the company needs it. Research finds that highly indebted firms lose market share to rivals during industry downturns, because customers and suppliers avoid firms that may not survive (Opler & Titman, 1994).
1. 10 percent debt: tax shield $37.5 million, distress probability 1 percent, expected distress cost $3.8 million, net benefit $33.8 million.
2. 20 percent debt: $75.0 million, 3 percent, $11.3 million, net $63.8 million.
3. 30 percent debt: $112.5 million, 7 percent, $26.3 million, net $86.3 million.
4. 40 percent debt: $150.0 million, 17.6 percent, $66.0 million, net $84.0 million.
5. 45 percent debt: $168.8 million, 23.7 percent, $88.8 million, net $80.0 million.
6. 50 percent debt: $187.5 million, 32 percent, $120.0 million, net $67.5 million.
Probabilities are drawn from the implied credit rating at each level, with the steep rise after 30 percent reflecting the move from investment grade to speculative grade.
Both tables point to the same answer from different directions: the weighted rate is lowest and the net benefit of debt is highest near 30 percent, and the proposed 45 percent gives back about $6 million of net value while adding about 0.5 points to the blended rate.
What the Buyback Would Do to Value
Moving from 20 to 30 percent debt adds about $22.5 million of net value, from $63.8 million to $86.3 million. Moving on to 45 percent subtracts about $6.3 million from that peak. The difference is small relative to a $1.5 billion firm, which is typical of capital structure decisions: the curve is flat near its top. The danger lies less in the average outcome than in the tail, since at 45 percent the company would have nearly a one-in-four chance of distress, and in distress it would lose members and leases at once.
Management's Case for 45 Percent
Management argues that the shares are undervalued, so buying more of them is a good use of money regardless of the tax argument. If that is true, a buyback creates value for remaining shareholders. But it does not require 45 percent debt; a buyback funded to 30 percent captures most of the tax benefit and still retires a meaningful block of shares. The undervaluation argument supports buying back shares, not borrowing to the point where distress becomes likely.
Sensitivity
If distress costs were 15 percent of value rather than 25, the net benefit would keep rising to about $115 million at 45 to 50 percent debt, and management's proposal would look right. The whole disagreement therefore turns on one assumption. If the chain owned most of its buildings, that lower figure would be reasonable. Because it leases nearly all of them, the higher figure is the more honest assumption, and the recommendation is built on it.
Recommendation
Approve a buyback funded by $150 million of new borrowing, taking debt to about $450 million, or 30 percent of value, rather than the proposed $375 million. This captures about $22.5 million of net value from the tax shield, keeps the company near investment grade and preserves borrowing capacity for club openings. Revisit the decision if the chain begins buying rather than leasing its sites.
References
Brealey, R. A., Myers, S. C., & Allen, F. (2023). Principles of corporate finance (14th ed.). McGraw Hill.
Myers, S. C. (1984). The capital structure puzzle. The Journal of Finance, 39(3), 574-592. https://doi.org/10.1111/j.1540-6261.1984.tb03646.x
Opler, T. C., & Titman, S. (1994). Financial distress and corporate performance. The Journal of Finance, 49(3), 1015-1040. https://doi.org/10.1111/j.1540-6261.1994.tb00086.x
What the GF520 Unit 7 assignment asks for
The seventh GF520 unit asks you to analyze a firm's capital structure and judge a proposed change. Describe the company and the proposal, including how much would be borrowed and what the money would do. Recompute the cost of capital at several debt levels by unlevering the equity beta and relevering it at each ratio, with a cost of debt that rises as the rating falls. Then value the trade-off directly: the tax shield at each level against the expected cost of financial distress, with the distress cost justified from the firm's assets and customers. Compare what both methods say. Address management's own argument for the change. Test the assumption that matters most and show how the answer moves. Finish with a specific recommendation. Cite research on capital structure and distress in APA 7.
Inside the GF520 Unit 7 example
The case opens with the chain's 210 leased clubs, 1.4 million monthly members and the $375 million proposal, then frames the choice with Myers's account of the trade-off. Table 1 lists six debt levels with equity beta, cost of equity, cost of debt and weighted rate. Table 2 values the shield at the tax rate times debt and the distress cost at $375 million times a probability tied to the implied rating, citing Opler and Titman on firms losing customers in distress. The highlighted sentence shows both methods pointing to about 30 percent. A section measures what the full buyback would give up, about $6 million, and the tail risk. Management's undervaluation argument is answered, a sensitivity test shows a lower distress cost would favor 45 to 50 percent, and the recommendation sets new borrowing at $150 million.
Where the points sit in the GF520 Unit 7 rubric
GF520 graders weight this case toward correct mechanics and sound judgment about the trade-off. Relevered betas, rising debt costs and recomputed weighted rates must be accurate at every level, and the method must be explained. Valuing the tax shield and expected distress costs directly earns substantial credit, especially when the distress cost is argued from the firm's own features rather than assumed. Comparing the two approaches shows synthesis. Responding to management's stated reason demonstrates that the student can separate a good idea from a bad way of funding it. A sensitivity test on the decisive assumption is expected for the top band. A specific recommendation with a condition for revisiting it, clear tables and APA 7 references complete the rubric.
GF520 Unit 7 help: mistakes that cost points
The most common GF520 Unit 7 error is keeping the cost of debt flat as borrowing rises, which makes more debt look better without limit. Some students relever beta incorrectly, forgetting the tax term, or use book values for the debt ratio. Distress costs are often set without justification or left out entirely. Others compute the weighted rate at many levels but never value the trade-off in dollars. Management's argument is ignored, or accepted without testing whether it requires the proposed debt level. The recommendation repeats the table's minimum without a specific dollar amount. For any firm your case describes, the method holds: rates at several levels, shield against distress, two methods compared, the key assumption tested and a precise recommendation.
Get a GF520 Unit 7 example written to your instructions
Name the firm in your GF520 Unit 7 case and include the figures it supplies, along with the prompt and rubric. The study comes back with the cost of capital recomputed across debt levels, the shield weighed against distress for that firm specifically, and a target ratio stated. First custom sample: free. Typical return: 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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GF520 Unit 7 questions, answered
Where does the probability of distress come from?
Usually from the rating a firm would likely receive at each debt level, matched to published cumulative default rates for that rating over a relevant horizon. The sample states each probability with its rating band and source. Where a case supplies its own estimates, the custom version uses those, since graders check that the probabilities rise with debt and are sourced rather than invented.
Where can I find a free GF520 Unit 7 sample paper?
This page holds a complete GF520 Unit 7 capital structure case study of a composite fitness chain, with cost of capital at six debt levels, tax shield against distress costs, a sensitivity test and APA 7 references.
Why set distress costs as high as 25 percent of value?
The chain leases nearly all its clubs, so it owns little lenders could sell, and members on monthly contracts can leave quickly if trouble becomes known. Both features would make financial distress unusually costly for this business.
Does undervalued stock justify borrowing more?
It may justify a buyback, but not a particular amount of debt. A buyback funded to 30 percent debt captures most of the tax benefit and still retires a large block of shares without raising the risk of distress sharply.
What would change the recommendation?
If the chain began owning its buildings, distress costs would fall, and the sample shows that at 15 percent of value the net benefit keeps rising to about 45 to 50 percent debt, close to management's proposal.