Part II: Making Investment Decisions Using NPV, ARR, And PA

Part Ii Making Investment Decisions Using Npv Arr Irr And Paybacki

Part II: Making Investment Decisions Using NPV, ARR, IRR, and Payback Investments Investment A Investment B Required Investment $50,000 $150,000 Annual Cash Flows 20,000 Annual Net Income 8,000 Project Life 5 years 5 years Cost of Capital 10% 10%

Paper For Above instruction

Introduction

Investment decision making is a fundamental aspect of corporate financial management, involving the selection of projects or investments that maximize shareholder value. Various financial appraisal techniques are employed in this process, including Net Present Value (NPV), Accounting Rate of Return (ARR), Internal Rate of Return (IRR), and Payback Period. This paper evaluates two investment options—Investment A and Investment B—using these methods to determine their viability and attractiveness based on the given data.

Overview of Investment Options

Investment A requires an initial outlay of $50,000, with annual cash flows amounting to $20,000, and has a project lifespan of five years. Investment B requires a larger initial investment of $150,000, but shares the same project duration, with an assumed annual cash flow of $20,000 (or adjusted to the net income figure if necessary). Both investments are evaluated using the company's cost of capital at 10%, serving as the discount rate in NPV calculations.

Net Present Value (NPV) Analysis

NPV measures the difference between the present value of cash inflows and outflows over the project's lifespan, discounted at the cost of capital. It helps determine whether an investment adds value to the firm. Using the formula:

\[ NPV = \sum_{t=1}^{n} \frac{Cash\ Inflows_t}{(1 + r)^t} - Initial\ Investment \]

where \( r \) is the discount rate and \( n \) is the project duration, the NPVs for both investments can be calculated. The present value of an annuity simplifies this calculation:

\[ PV = Cash\ Flows \times \frac{1 - (1 + r)^{-n}}{r} \]

For Investment A:

\[ PV_A = 20,000 \times \frac{1 - (1 + 0.10)^{-5}}{0.10} \approx 20,000 \times 3.7908 = \$75,816 \]

\[ NPV_A = 75,816 - 50,000 = \$25,816 \]

For Investment B:

\[ PV_B = 20,000 \times 3.7908 = \$75,816 \] (assuming similar annual cash flows for simplicity)

\[ NPV_B = 75,816 - 150,000 = -\$74,184 \]

The positive NPV for Investment A indicates it would add value to the company, whereas Investment B's negative NPV suggests it would diminish shareholder value.

Accounting Rate of Return (ARR) Analysis

ARR assesses profitability based on accounting net income relative to initial investment:

\[ ARR = \frac{Average\ Annual\ Accounting\ Income}{Initial\ Investment} \]

For Investment A:

\[ ARR_A = \frac{8,000}{50,000} = 0.16 = 16\% \]

For Investment B:

\[ ARR_B = \frac{8,000}{150,000} \approx 0.0533 = 5.33\% \]

If the company's required ARR threshold exceeds these figures, Investment A, with its higher ARR, appears more attractive.

Internal Rate of Return (IRR) Calculation

IRR is the discount rate at which the NPV equals zero. For an annuity:

\[ 0 = Initial\ Investment + Cash\ Flows \times \frac{1 - (1 + IRR)^{-n}}{IRR} \]

Solving for IRR:

For Investment A:

\[ 50,000 = 20,000 \times \frac{1 - (1 + IRR)^{-5}}{IRR} \]

Using trial and error or financial calculator:

\[ IRR_A \approx 24.6\% \]

For Investment B:

\[ 150,000 = 20,000 \times \frac{1 - (1 + IRR)^{-5}}{IRR} \]

\[ IRR_B \approx 16.4\% \]

Since both IRRs exceed the company's cost of capital (10%), these investments meet the IRR criterion, with Investment A being more profitable.

Payback Period Analysis

The payback period indicates how long it takes for the project to recover its initial investment through cash inflows:

For Investment A:

\[ Payback\ Period = \frac{Initial\ Investment}{Annual\ Cash\ Flows} = \frac{50,000}{20,000} = 2.5\ years \]

For Investment B:

\[ \frac{150,000}{20,000} = 7.5\ years \]

Given the project life is five years, Investment A recovers the initial investment within the project duration, making it a preferable option. Investment B's payback period exceeds the project length, indicating it does not recover investment within project lifespan, which is a considerable drawback.

Conclusion

The comprehensive financial analysis clearly favors Investment A over Investment B. NPV calculations demonstrate that Investment A adds substantial value (+$25,816), while Investment B diminishes value. The IRR for Investment A (approximately 24.6%) exceeds the company's required threshold and the cost of capital, indicating profitability. Similarly, ARR-related analysis supports Investment A’s attractiveness due to higher profitability ratio. The payback period of 2.5 years demonstrates quicker recoupment of initial investment, aligning favorably with standard investment criteria. Conversely, Investment B presents significant drawbacks, including a negative NPV and a payback period exceeding the project's duration, making it an unattractive investment under the given parameters.

Ultimately, firms should prioritize projects like Investment A, which demonstrate favorable financial metrics across multiple evaluation methods, ensuring value addition and strategic alignment with capital budgeting criteria.

References

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