Expected Rate Of Return And Risk: Carter Inc. Is Evaluating

Expected Rate Of Return And Risk Carter Inc Is Evaluating A Sec

Carter Inc. is evaluating a security. One year Treasury bills are currently paying 9.1 percent. The task is to calculate the security's expected return and its standard deviation, and determine if Carter should invest in this security based on these metrics. The given probabilities and returns are as follows:

  • Probability 15%, Return 6%
  • Probability 30%, Return 9%
  • Probability 40%, Return 10%
  • Probability 15%, Return 15%

Using this data, we will perform calculations to find the expected return and the standard deviation of this investment.

Additionally, the problem introduces two capital budgeting projects (Project A and Project B). Both projects have a 5-year life. Project A is a replacement project, and Project B is unrelated to current operations. The G. Wolfe Corporation employs the risk-adjusted discount rate method, grouping projects by purpose/risk class with preassigned required rates of return:

  • Replacement decision: 12%
  • Modification or expansion of existing product line: 15%
  • Project unrelated to current operations: 18%
  • Research and development operations: 20%

The expected cash flows for these projects are:

  • Initial investments: $250,000 for Project A, $400,000 for Project B
  • Year 1 inflow: $130,000 for Project A, $135,000 for Project B
  • Year 2 inflow: $40,000 for Project A; Year 3 inflow: $50,000; Year 4 inflow: $90,000; Year 5 inflow: $130,000 for both projects

The task is to determine each project's risk-adjusted net present value (NPV), considering the respective risk classes and required rate of returns, and prepare written responses analyzing whether to proceed with these projects based on the NPVs.

Paper For Above instruction

The assessment of expected return and risk for securities and projects is foundational in making informed investment decisions. In this paper, we analyze the expected rate of return and standard deviation of a security being evaluated by Carter Inc., followed by a discussion on risk-adjusted net present value (NPV) calculations for two distinct capital projects within the context of different risk classes and required rates of return. The objective is to evaluate whether Carter Inc. should proceed with these investments based on quantitative analysis and strategic considerations.

Expected Return and Standard Deviation of the Security

The expected return quantifies the average return an investor anticipates, considering the probabilities of different outcomes. The calculation involves multiplying each possible return by its probability, then summing these products:

Expected Return = (0.15 × 6%) + (0.30 × 9%) + (0.40 × 10%) + (0.15 × 15%)

= (0.15 × 0.06) + (0.30 × 0.09) + (0.40 × 0.10) + (0.15 × 0.15)

= 0.009 + 0.027 + 0.04 + 0.0225 = 0.0985 or 9.85%

This suggests that the security's expected annual return is approximately 9.85%, slightly below the current risk-free rate of 9.1%, indicating a potentially acceptable but modest return.

The standard deviation measures the total risk or variability of returns. It is computed as the square root of the variance, which involves summing the squared deviations of each outcome from the expected return, weighted by their probabilities:

Variance = Σ [Probability × (Return - Expected Return)²]

= 0.15 × (6% - 9.85%)² + 0.30 × (9% - 9.85%)² + 0.40 × (10% - 9.85%)² + 0.15 × (15% - 9.85%)²

Calculating each component:

  • 0.15 × (−3.85%)² = 0.15 × 0.001482 = 0.0002223
  • 0.30 × (−0.85%)² = 0.30 × 0.000072 = 0.0000216
  • 0.40 × (0.15%)² = 0.40 × 0.000000225 = 0.00000009
  • 0.15 × (5.15%)² = 0.15 × 0.002653 = 0.00039795

Summing these: 0.0002223 + 0.0000216 + 0.00000009 + 0.00039795 ≈ 0.00064195

Standard deviation = √0.00064195 ≈ 0.0253 or 2.53%

Thus, the security exhibits a standard deviation of about 2.53%, indicating relatively low volatility compared to the expected return, consistent with less risky assets like treasury bills.

Risk-Adjusted NPV of Projects A and B

Evaluating projects based on risk-adjusted NPV necessitates discounting their respective cash flows at the preassigned risk-adjusted rates of return, which align with their purpose and risk profile.

For Project A, a replacement project with a risk class of "replacement decision," the required rate of return is 12%. Similarly, Project B, which is unrelated to current operations, has a required return of 18%. The NPV calculation involves discounting each cash inflow and outflow at the respective rates and summing them to ascertain the project's profitability.

To illustrate, the formula for NPV is:

NPV = Σ (Cash flow in Year t / (1 + r)^t) – Initial Investment

Calculations for Project A:

  • Initial Investment: -$250,000
  • Year 1: $130,000 / (1 + 0.12)^1 ≈ $116,071
  • Year 2: $40,000 / (1 + 0.12)^2 ≈ $31,887
  • Year 3: $50,000 / (1 + 0.12)^3 ≈ $35,583
  • Year 4: $90,000 / (1 + 0.12)^4 ≈ $57,144
  • Year 5: $130,000 / (1 + 0.12)^5 ≈ $73,732

Summing the discounted cash inflows: $116,071 + $31,887 + $35,583 + $57,144 + $73,732 ≈ $314,417

Thus, NPV for Project A = $314,417 – $250,000 = $64,417, indicating a positive value and a potentially acceptable project.

Similarly, for Project B, requiring an 18% discount rate:

  • Initial Investment: -$400,000
  • Year 1: $135,000 / (1 + 0.18)^1 ≈ $114,406
  • Year 2: $40,000 / (1 + 0.18)^2 ≈ $28,746
  • Year 3: $50,000 / (1 + 0.18)^3 ≈ $30,340
  • Year 4: $90,000 / (1 + 0.18)^4 ≈ $48,519
  • Year 5: $130,000 / (1 + 0.18)^5 ≈ $58,651

Summing the inflows: approximately $280,662

Therefore, NPV = $280,662 – $400,000 ≈ -$119,338, suggesting that Project B would likely result in a loss based on the risk-adjusted discounting, and might not be a sound investment unless strategic benefits justify the negative NPV.

Strategic Implications and Decision-Making

The quantitative analysis indicates that Project A, with a positive NPV, aligns with the firm’s risk profile and provides value beyond the cost of capital, making it financially attractive. Conversely, Project B’s negative NPV suggests a poor financial return when discounted at the appropriate risk-adjusted rate, implying that the firm should approach the project cautiously, considering other qualitative factors or potential strategic benefits that might not be fully captured in the NPV calculation.

When evaluating securities or projects, firms must consider both quantitative metrics and strategic context. The low standard deviation of the security indicates relatively low risk, aligning with treasury bill-like assets, while the analysis of projects emphasizes the importance of matching project risk profiles with appropriate discount rates. Proper risk adjustments help in making balanced investment choices that optimize value creation and align with the firm's risk appetite.

Conclusion

In conclusion, the expected return of the evaluated security is approximately 9.85%, with a standard deviation of around 2.53%, indicating low volatility consistent with treasury securities. For capital projects, the risk-adjusted NPV analysis reveals that Project A is financially viable with a significant positive NPV, whereas Project B’s negative NPV raises concern about its profitability given the associated risk levels. These evaluations support strategic decision-making, emphasizing the importance of aligning projects and investments with the firm's risk profile and financial objectives.

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