Find The NPV And PI Of A Project That Costs 1500 And Returns

Find The Npv And Pi Of A Project That Costs 1500 And Returns 800 In

Calculate the Net Present Value (NPV) and Profitability Index (PI) of a project with an initial investment of $1,500 and cash inflows of $800 in Year 1 and $850 in Year 2, assuming a discount rate of 8%. Additionally, determine the NPV and PI for an annuity that pays $500 annually for eight years, costs $2,500, and has a discount rate of 6%. Furthermore, evaluate Nutrex Corporation's weighted average cost of capital (WACC) based on its target capital structure, cost of debt, tax rate, risk-free rate, market return, and beta. The specific tasks are as follows:

• Calculate the NPV and PI for the project with given cash flows and discount rate.
• Calculate the NPV and PI for the eight-year annuity with specified cash flows and purchase price.
• Determine Nutrex’s cost of debt based on the given parameters.
• Estimate Nutrex’s expected return on equity using the security market line.
• Calculate Nutrex’s after-tax weighted average cost of capital (WACC).

Paper For Above instruction

Calculating the Net Present Value (NPV) and Profitability Index (PI) of investment projects and understanding corporate finance metrics such as the weighted average cost of capital (WACC) are essential skills in financial management. These calculations enable investors and managers to assess the viability and profitability of projects and investment opportunities, facilitating informed decision-making that enhances shareholder value.

NPV and PI of a Two-Year Investment Project

The project under examination requires an initial investment of $1,500, with expected cash inflows of $800 in Year 1 and $850 in Year 2. To evaluate the project's profitability, the first step involves calculating the present value (PV) of the future cash inflows, discounted at the project’s cost of capital of 8%. The formula for PV of each cash flow is expressed as:

PV = Future Cash Flow / (1 + r)^t

where r is the discount rate, and t is the year.

For Year 1:

PV = $800 / (1 + 0.08)^1 ≈ $740.74

For Year 2:

PV = $850 / (1 + 0.08)^2 ≈ $730.07

The total present value of inflows is approximately $1,470.81. The NPV is calculated by subtracting the initial investment from this total:

NPV = Total PV of inflows - Initial Investment = $1,470.81 - $1,500 ≈ -$29.19

The negative NPV suggests that, based on an 8% discount rate, the project would not be profitable.

The Profitability Index (PI) is the ratio of the PV of inflows to the initial investment:

PI = Total PV of inflows / Initial Investment ≈ $1,470.81 / $1,500 ≈ 0.98

A PI below 1 indicates that the project's present value of inflows does not cover the initial cost, further suggesting that it is not a favorable investment under these assumptions.

NPV and PI of an Eight-Year Annuity

The second scenario involves an annuity paying $500 annually over eight years, costing $2,500, with a discount rate of 6%. The present value of an annuity can be computed using the standard annuity formula:

PV = P × [(1 - (1 + r)^-n) / r]

where P is the annual payment, r is the discount rate per period, and n is the number of periods.

Applying the values:

PV = $500 × [(1 - (1 + 0.06)^-8) / 0.06] ≈ $500 × 6.222

PV ≈ $3,111.00

The NPV is then calculated as:

NPV = PV of inflows - initial cost = $3,111.00 - $2,500 = $611.00

The profitability index is:

PI = PV of inflows / initial cost = $3,111.00 / $2,500 ≈ 1.24

Since the PI exceeds 1 and the NPV is positive, this project appears financially favorable.

Calculating Nutrex Corporation’s WACC

a. Cost of debt

Nutrex's target capital structure comprises 40% long-term debt and 60% equity. The before-tax cost of debt is 10%. The after-tax cost of debt is adjusted for the corporate tax rate (40%) as follows:

Cost of debt (after tax) = 10% × (1 - 0.40) = 6%

b. Expected return on common equity using the security market line

The expected return on equity (Re) from the Capital Asset Pricing Model (CAPM) is calculated as:

Re = Rf + β × (Rm - Rf)

where Rf is the risk-free rate (8%), β is the stock beta (1.8), and Rm is the expected market return (13%). Thus:

Re = 8% + 1.8 × (13% - 8%) = 8% + 1.8 × 5% = 8% + 9% = 17%

c. After-tax WACC

The weighted average cost of capital (WACC) combines the costs of debt and equity, weighted by their respective proportions in the capital structure:

WACC = (wd × rd × (1 - Tax Rate)) + (we × Re)

where wd is the weight of debt (40%), rd is the before-tax cost of debt (10%), we is the weight of equity (60%), and Re is the expected return on equity (17%). Substituting the values:

WACC = 0.40 × 10% × (1 - 0.40) + 0.60 × 17% = 0.40 × 6% + 0.60 × 17% = 2.4% + 10.2% = 12.6%

Therefore, Nutrex’s after-tax weighted average cost of capital is approximately 12.6%, which can be utilized as the discount rate for investment appraisal and valuation purposes.

Conclusion

Evaluating investment opportunities through the calculation of NPV, PI, and WACC provides vital insights into the profitability and risk profile of projects. The analyses indicate that the project with the cash flows provided is technically unprofitable at an 8% discount rate but would be viable at a lower rate or with improved cash flows. Similarly, the annuity investment demonstrates a positive NPV and PI exceeding 1, making it economically advantageous. Nutrex's WACC of approximately 12.6% reflects the firm's cost of capital, essential for making informed financing and investment decisions that align with its risk appetite and strategic goals.

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