FIN 370 Week 4 Risk, Return and Financial Planning Example

Patio Heaters or More Chairs? Expected Return, Risk and the Capital Asset Pricing Model in an Outdoor Furniture Maker's Expansion Choice, and the Outside Funding Its Growth Will Need

[Student Name]

University of Phoenix

FIN/370: Finance for Business

Week 4 Assignment

[Instructor Name]

[Date]

The furniture maker, its options and all figures are composites written for a model paper; methods and research findings come from the sources listed.

A composite company makes aluminum and teak outdoor furniture sold through specialty retailers and online, with sales of $24 million. Its owners plan 25% growth next year and must choose between two uses of a $3 million investment: launching a line of gas patio heaters or expanding production of its best-selling dining chairs. A project's expected return says what the owners hope for; its spread of outcomes says what they could lose and who would absorb it. This paper compares the options and plans the funding.

Expected Returns

Management estimated each option's return under three economic conditions. For the patio heaters, a strong economy would bring a 30% return, a normal one 14% and a recession a loss of 10%, with probabilities of 25%, 50% and 25%. The expected return is the probability-weighted average: 0.25 times 30%, plus 0.50 times 14%, plus 0.25 times negative 10%, or 12%. For the chair expansion, returns would be 18%, 12% and 4%, for an expected return of 11.5%.

Measuring Risk

Standard deviation measures how widely outcomes spread around the expected return. For the heaters, the squared deviations from 12% are 324, 4 and 484, weighted by probability to give a variance of 204 and a standard deviation of about 14.3%. For the chairs, the variance is about 24.8 and the standard deviation about 5.0%. The heaters offer half a point more expected return for nearly three times the risk.

The coefficient of variation, standard deviation divided by expected return, compares risk per unit of return: about 1.19 for the heaters and 0.43 for the chairs. By that measure, the chair expansion offers far more return for its risk (Brigham & Houston, 2022).

Whose Risk Matters

Markowitz (1952) showed that combining assets whose returns are not perfectly correlated reduces portfolio risk, so part of any single investment's risk can be diversified away. A diversified investor cares only about the part that remains, market risk. The furniture maker's owners, however, hold most of their wealth in the company, so the heaters' total risk would fall directly on them. A recession in which patio heaters lose money is also a recession in which furniture sales fall, so the heaters would add risk rather than diversify it.

A Required Return From the Capital Asset Pricing Model

Sharpe (1964) developed the capital asset pricing model, in which a security's required return equals the risk-free rate plus its beta times the market risk premium. The company is private, so it uses the average beta of publicly traded furniture and home furnishings companies, about 1.2. With a 4.3% risk-free rate and an assumed 5.5% premium for bearing market risk, the required return on equity is 4.3% plus 1.2 times 5.5%, or about 10.9%. Both options' expected returns exceed that, but the heaters' return exceeds it by less than one standard deviation, and their recession loss would be severe.

Planning the Funding for Growth

Whichever option is chosen, 25% growth requires more assets. The percent-of-sales method assumes that assets and spontaneous liabilities, such as accounts payable and accruals, grow in proportion to sales. The company's operating assets are 60% of sales, so they must rise from $14.4 million to $18.0 million, an increase of $3.6 million. Spontaneous liabilities are 12% of sales, rising from $2.88 million to $3.6 million, providing $720,000. Projected net income is 5% of $30 million, $1.5 million, and the company pays out 40% as dividends to the owners, retaining $900,000.

Additional funds needed equal the $3.6 million increase in assets, less $720,000 of spontaneous liabilities and $900,000 of retained earnings, or about $1.98 million. The company must borrow or raise that amount, in addition to financing the $3 million investment if it is not already included in operating assets.

Sensitivity of the Funding Need

The forecast is sensitive to margin and payout. If net margin falls to 4% because of higher aluminum prices, retained earnings drop to $720,000 and the funding need rises to about $2.16 million. If growth is 15% instead of 25%, the asset increase falls to about $2.16 million and the need to under $600,000. The owners should therefore arrange a credit line sized for the high case but draw on it only as sales materialize, rather than borrowing the full amount at the start of the year.

Checking the Plan

The forecast assumes that the company's asset needs grow proportionally with sales. Some assets, such as the factory building, have spare capacity, so actual needs may be lower. The company could reduce the funding gap by cutting the dividend payout to 20% for a year, which would retain an extra $300,000, or by negotiating longer supplier terms.

What the Lender Will Look At

A lender considering the credit line will look at the same measures: the chair expansion's predictable returns, the company's interest coverage and whether growth in receivables and inventory is funded with short-term borrowing that will be repaid as sales are collected. Presenting the risk comparison alongside the funding forecast helps the owners show that they chose the lower-risk path.

Recommendation

The company should expand the chair line. It offers nearly the same expected return with a much lower coefficient of variation, and its risk does not compound the owners' exposure to the economy. The company should arrange a credit line of about $2 million to fund the growth in working capital, and fund the $3 million expansion with an equipment loan. If the owners still want to enter patio heaters, a smaller test launch through one retailer would limit the downside while revealing demand.

Conclusion

The patio heaters promised a 12% expected return with a standard deviation of 14.3%, while the chair expansion offered 11.5% with 5.0%. Measured per unit of return, the chairs carry far less risk, and for owners whose wealth is concentrated in the company, total risk matters. The capital asset pricing model set a 10.9% hurdle, and the funding plan showed that 25% growth will require about $2 million of new financing before the investment itself.

References

Brigham, E. F., & Houston, J. F. (2022). Fundamentals of financial management (16th ed.). Cengage.

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x