Corporate Finance Show: Work And Discuss Results
Corporate Financeshow Work And Discuss Results18 Rita Gonzales Won T
Corporate Finance Show work and discuss results 18. Rita Gonzales won the $41 million lottery. She is to receive $1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14%. What is the current value of her winnings?
36. Morgan Jennings, a geography professor, invests $50,000 in a parcel of land that is expected to increase in value by 12% per year for the next five years. He will take the proceeds and provide himself with a 10-year annuity. Assuming a 12% interest rate, how much will this annuity be? 15.
The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years. Year Cash Flow 1……………….. $15,000 2………………... $25,000 3………………… $40,000 The firm will also be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10%, should the investment be undertaken?
16. Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the third year. From the end of the third year until the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of capital is 12%, should this project be undertaken? Find the net present value of Skyline's investment at its internal rate of return. Explain your answer.
Paper For Above instruction
Understanding the valuation of various investment opportunities and financial decisions is essential in corporate finance. This paper explores several scenarios involving present value calculations, investment appraisal, and project valuation, using established financial principles and formulas. The case studies demonstrate practical applications of discounted cash flow (DCF) analysis, annuity valuation, and net present value (NPV) assessment to guide investment decisions.
Valuation of Rita Gonzales’ Lottery Winnings
Rita Gonzales’ lottery winnings consist of a series of annual payments and a lump sum at the end of 19 years. To determine the current value of her winnings, we need to calculate the present value (PV) of the annuity of annual payments and the PV of the lump sum, then sum these amounts.
The annual payment is $1.5 million for 19 years, and the lump sum at year 19 is $12.5 million. The discount rate is 14%. The PV of an annuity is calculated as:
PV of annuity = P × [(1 - (1 + r)^-n) / r]
where P = annual payment, r = discount rate, n = number of years.
Calculating PV of the annuity:
PV_annuity = 1,500,000 × [(1 - (1 + 0.14)^-19) / 0.14]
Calculating PV of the lump sum:
PV_lump = 12,500,000 / (1 + 0.14)^19
After computing these, the total PV (present value) is the sum of both components, which provides the current valuation of her winnings. Numerical calculations indicate that PV of the annuity is approximately $12.24 million, and PV of the lump sum is approximately $2.46 million, totaling roughly $14.70 million. This shows the high value of the lottery due to the present value effect of future payments.
Investment Analysis of Morgan Jennings’ Land
Morgan Jennings invests $50,000 in land expected to grow at 12% annually over five years. First, we calculate the future value (FV) of the investment after five years using the compound interest formula:
FV = PV × (1 + r)^n
where PV = $50,000, r = 12%, n = 5.
FV = 50,000 × (1 + 0.12)^5 ≈ 50,000 × 1.7623 ≈ $88,115.
Subsequently, this amount is to be converted into an annuity, providing a consistent annual income over 10 years, with a 12% interest rate. The PV of an ordinary annuity is given by:
PV of annuity = PMT × [(1 - (1 + r)^-n) / r]
Rearranged to find the annual payment (PMT), which is:
PMT = FV × [r / (1 - (1 + r)^-n)]
Substituting the values: FV ≈ $88,115, r = 0.12, n = 10, we obtain:
PMT ≈ 88,115 × [0.12 / (1 - (1 + 0.12)^-10)] ≈ 88,115 × 0.1585 ≈ $13,964.
This indicates Jennings could receive approximately $13,964 annually from his land investment, assuming a 12% discount rate over 10 years. This calculation guides financial planning and illustrates the potential income stream from the land appreciation.
Project Evaluation for Horizon Company
Horizon Company evaluates a project requiring an initial investment of $60,000, with expected cash inflows of $15,000, $25,000, and $40,000 over three years, respectively. The firm also incurs a $10,000 expense at the end of the project.
The net cash flows each year are considered, and the decision hinges on the project's net present value. Using a discount rate of 10%, we calculate the PV of each inflow and the outflows.
PV of each year's inflow:
PV Year 1 = 15,000 / (1 + 0.10)^1 ≈ 13,636
PV Year 2 = 25,000 / (1 + 0.10)^2 ≈ 20,661
PV Year 3 = 40,000 / (1 + 0.10)^3 ≈ 30,052
Subtract the closure cost of $10,000 at the end of Year 3, discounted to present value:
PV of closure cost = 10,000 / (1 + 0.10)^3 ≈ 7,529
Calculating total PV of inflows and outflows:
Total PV inflows = 13,636 + 20,661 + 30,052 ≈ 64,349
Total PV outflows = 60,000 + 7,529 (PV of closing costs) ≈ 67,529
The net present value (NPV) is:
NPV = Total PV inflows - Total PV outflows ≈ 64,349 - 67,529 = -3,180
Since the NPV is negative, the project should not be undertaken under these conditions, as it would not add value to the firm.
Skyline Corp.’s Investment in a Long-Term Project
Skyline Corp plans to invest $130,000 in a project that generates annual cash flows of $34,000 from the end of Year 3 till Year 12 (10 years). The cash flows start only after Year 3, meaning there is a delay before the project begins producing returns. The discount rate is 12%. The calculation involves determining the present value of an annuity starting in Year 3 and then assessing the NPV.
First, calculate the PV of the annuity of $34,000 over 10 years at 12%:
PV_of_annuity = 34,000 × [(1 - (1 + 0.12)^-10) / 0.12] ≈ 34,000 × 6.3282 ≈ 215,294
Because the cash flows commence at the end of Year 3, discount the PV back to Year 0:
PV at Year 0 = 215,294 / (1 + 0.12)^3 ≈ 215,294 / 1.4049 ≈ 153,107
Finally, subtract the initial investment to find the NPV:
NPV = PV at Year 0 - initial investment = 153,107 - 130,000 ≈ 23,107
This positive NPV indicates the project is financially viable and should be undertaken. Moreover, the internal rate of return (IRR) can be approximated as the discount rate that makes the NPV zero, estimated to be slightly above 12%, reinforcing the project's profitability.
Conclusion
In conclusion, the assessment of these investment opportunities using discounted cash flow techniques highlights the importance of valuation methods in financial decision-making. The lottery winnings valuation emphasizes the significance of discount rates on future cash flows. The land investment underscores the potential of growth and annuity calculations. The project evaluations demonstrate how NPV analysis guides strategic investment choices, helping firms determine whether projects add value based on present value computations and internal rate of return considerations. These principles are central to sound financial management and capital budgeting strategies.
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