91Ó°ÊÓ

(CMA, adapted) Whimsical Corporation is an international manufacturer of fragrances for women. Management at Whimsical is considering expanding the product line to men's fragrances. From the best estimates of the marketing and production managers, annual sales (all for cash) for this new line is 900,000 units at \(\$ 100\) per unit; cash variable cost is \(\$ 50\) per unit; and cash fixed costs is \(\$ 9,000,000\) per year. The investment project requires \(\$ 120,000,000\) of cash outflow and has a project life of seven years. At the end of the seven-year useful life, there will be no terminal disposal value. Assume all cash flows occur at year-end except for initial investment amounts. Men's fragrance is a new market for Whimsical, and management is concerned about the reliability of the estimates. The controller has proposed applying sensitivity analysis to selected factors. lgnore income taxes in your computations. Whimsical's required rate of return on this project is \(10 \%\). 1\. Calculate the net present value of this investment proposal. 2\. Calculate the effect on the net present value of the following two changes in assumptions. (Treat each item independently of the other. a. \(20 \%\) reduction in the selling price b. \(20 \%\) increase in the variable cost per unit 3\. Discuss how management would use the data developed in requirements 1 and 2 in its consideration of the proposed capital investment

Step by step solution

01

Calculate Initial Cash Flow

The initial investment required is given as \$120,000,000. This is the cash outflow at year 0. The initial cash flow (CF0) is \(-120,000,000\).

02

Determine Annual Net Cash Flow

Annual sales revenue is calculated as 900,000 units multiplied by \\(100 per unit, which equals \\)90,000,000. The total variable cost per year is 900,000 units times \\(50, giving \\)45,000,000. Annual fixed costs are \\(9,000,000. Therefore, annual net cash flow is: \(\\)90,000,000 - \\(45,000,000 - \\)9,000,000 = \$36,000,000\).

03

Calculate Net Present Value

The NPV is computed using the formula: \[ NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - CF_0 \], where \( CF_t \) is the annual net cash flow, \( r \) is the discount rate, and \( n \) is the project life in years. Substituting the values: \[ NPV = \sum_{t=1}^{7} \frac{36,000,000}{(1.1)^t} - 120,000,000 \]. Using financial tables or a calculator will find \( NPV = 14,486,342.96 \).

04

Adjust for 20% Reduction in Selling Price

If the selling price decreases by 20%, the new selling price is \(\\(100 \times 0.8 = \\)80\). New annual sales revenue becomes \(900,000 \times 80 = \\(72,000,000\). Keeping other costs as is, new annual net cash flow will be \(72,000,000 - 45,000,000 - 9,000,000 = \\)18,000,000\). Compute the new NPV using this adjusted cash flow: \[ NPV = \sum_{t=1}^{7} \frac{18,000,000}{(1.1)^t} - 120,000,000 \]. This results in NPV = \(-22,683,314.92\).

05

Adjust for 20% Increase in Variable Costs

With a 20% increase in variable costs, the new variable cost is \(\\(50 \times 1.2 = \\)60\) per unit. Total variable costs are \(900,000 \times 60 = \\(54,000,000\). Thus, the new annual net cash flow is \( 90,000,000 - 54,000,000 - 9,000,000 = \\)27,000,000 \). Calculate NPV with this adjusted cash flow: \[ NPV = \sum_{t=1}^{7} \frac{27,000,000}{(1.1)^t} - 120,000,000 \]. This gives an NPV = \(-4,674,491.19\).

06

Discuss Management Implications

The initial NPV result suggests the project is financially viable as it is positive. However, sensitivity analysis shows potential risk; a reduction in selling price or an increase in variable costs can make the project's NPV negative, indicating a loss. Management should use these insights to evaluate the reliability of their price and cost estimates, and consider how sensitive their profitability is to changes in key assumptions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sensitivity Analysis

When embarking on any major project, like introducing a new product line, it’s crucial to understand how changes in key variables might impact the overall viability of the project. This is where sensitivity analysis plays a vital role. By examining how sensitive the Net Present Value (NPV) is to changes in assumptions – such as selling price or variable costs – companies can gauge potential risks and make more informed decisions.

• For instance, if Whimsical Corporation reduces its selling price by 20%, the project's NPV drops significantly to a negative value, suggesting potential losses.
• Similarly, a 20% increase in variable costs can also turn the NPV negative.

This analysis helps management consider worst-case scenarios and their potential effects, ensuring they're well-prepared for different market conditions. It also highlights the importance of precise forecasting and the need for strategies to mitigate potential risks.

Capital Investment Decision

Capital investment decisions revolve around determining whether significant expenditures, like the $120 million investment proposed by Whimsical Corporation, will generate favorable returns. These decisions are critical as they affect the long-term financial health of a business.
A crucial component of capital investment decisions is the calculation of NPV, which measures the difference between the present value of cash inflows and outflows over the project's life. A positive NPV signifies that the project is expected to generate more cash than it consumes, thus adding value to the company. Conversely, a negative NPV warrants a reassessment of the investment decision.

• In Whimsical's case, the initial NPV calculation was positive, indicating potential profitability under the original assumptions.
• However, adjustments in price and cost estimates significantly impacted profitability, emphasizing the importance of accurate financial predictions.

Management uses these insights to evaluate whether the potential rewards justify the investment risks involved.

Discount Rate

The discount rate is pivotal in capital budgeting decisions as it reflects the company's required rate of return. It adjusts future cash flows to their present value, accounting for risk, inflation, and opportunity costs. For Whimsical Corporation, a discount rate of 10% was used to calculate the NPV of the new fragrance line project.
Choosing an appropriate discount rate is essential. It ensures that future cash inflows are not overvalued, which might lead to unwise investment decisions.

• The higher the discount rate, the lower the present value of future cash flows, meaning the company requires a higher return to justify its investment.
• Conversely, a lower discount rate increases the present value of future cash receipts, potentially making projects appear more attractive than they actually are.

Thus, setting the correct discount rate is crucial to accurately evaluate the profitability and viability of any proposed investment.

Variable and Fixed Costs

Understanding the distinction and influence of variable and fixed costs is fundamental for assessing the financial performance of a project.
Variable costs fluctuate with production volume. For Whimsical, the variable cost per unit of fragrance was $50, leading to total variable costs directly tied to the number of units produced. Changes to these costs, such as a 20% increase, could significantly affect profitability as seen in the sensitivity analysis.
Fixed costs, on the other hand, remain constant regardless of production output. In the exercise, Whimsical sustained fixed costs of $9,000,000 annually. While these costs stabilize the budget expectations, they add a burden that must be offset by sufficient revenue.

• Variable costs can offer flexibility, but they require close management since they directly impact the net cash flow.
• Fixed costs necessitate careful planning to ensure consistent coverage through sales revenue, especially in variable market conditions.

Both play a decisive role in determining the break-even point and profitability, crucial for effective financial planning.