Prob 1 Annuity Payments Discount rate Growth rate Price to ✓ Solved
Prob. 1 Annuity Payments Discount rate Growth rate Price to be paid Cash Flows: Alfonso Canella: Hint: use the perpetuity formula.
Prob. 2 Machine 1 Machine 2 Discount rate Growth rate NPV IRR Cash flows: Start Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 Month 13 Month 14 Month 15 Month 16 Month 17 Month 18 Month 19 Month 20 Month 21 Month 22 Month 23 Month 24 Month 25 Month 26 Month 27 Month 28 Month 29 Month 30 Month 31 Month 32 Month 33 Month 34 Month 35 Month 36 Month 37 Month 38 Month 39 Month 40 Month 41 Month 42 Month 43 Month 44 Month 45 Month 46 Month 47 Month 48 Month 49 Month 50 Month 51 Month 52 Month 53 Month 54 Month 55 Month 56 Month 57 Month 58 Month 59 Month 60 Month 61 Month 62 Month 63 Month 64 Month 65 Month 66 Month 67 Month 68 Month 69 Month 70 Month 71 Month 72 Month 73 Month 74 Month 75 Month 76 Month 77 Month 78 Month 79 Month 80 Month 81 Month 82 Month 83 Month 84 Month 85 Month 86 Month 87 Month 88 Month 89 Month 90 Month 91 Month 92 Month 93 Month 94 Month 95 Month 96 Month 97 Month 98 Month 99 Month 100 Month 101 Month 102 Month 103 Month 104 Month 105 Month 106 Month 107 Month 108 Month 109 Month 110 Month 111 Month 112 Month 113 Month 114 Month 115 Month 116 Month 117 Month 118 Month 119 Month 120 Month 121 Month 122 Month 123 Month 124 Month 125 Month 126 Month 127 Month 128 Month 129 Month 130 Month 131 Month 132 Month 133 Month 134 Month 135 Month 136 Month 137 Month 138 Month 139 Month 140 Month 141 Month 142 Month 143 Month 144
Prob. 3 July 2000 pay due Interest rate Future value of July 2000 pay on July 1, 2011 Enter text answer in the box below: Present value of 25 yearly payments Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15 Year 16 Year 17 Year 18 Year 19 Year 20 Year 21 Year 22 Year 23 Year 24 Year 25.
Prob. 4 Lease Implicit lease rate Cash flows: Start Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 Month 13 Month 14 Month 15 Month 16 Month 17 Month 18 Month 19 Month 20 Month 21 Month 22 Month 23 Month 24 Month 25 Month 26 Month 27 Month 28 Month 29 Month 30 Month 31 Month 32 Month 33 Month 34 Month 35 Month 36 Month 37 Month 38 Month 39 Month 40 Month 41 Month 42 Month 43 Month 44 Month 45 Month 46 Month 47 Month 48.
Prob. 5 Sale price (M euros)/plane Down payment (%) Cost per plane (M euros) Discount rate Years (in Million euros) # of planes sold Investments on R&D Revenues Production Costs Cash Flows NPV IRR v. JAN '22.
Paper For Above Instructions
An annuity is a series of equal payments made at regular intervals. The concept of annuities is widely used in various financial contexts, including retirement planning, loan amortization, insurance policies, and mortgages. To calculate the value of an annuity, we can use the perpetuity formula, which can help determine the present value of these cash flows.
Understanding Annuities
Annuities can either be ordinary annuities, where payments occur at the end of each period, or annuities due, where payments are made at the beginning of each period. The key variables in calculating the value of an annuity include the payment amount (PMT), the discount rate (r), and the number of periods (n). The present value (PV) of an ordinary annuity can be calculated using the formula:
PV = PMT × [(1 - (1 + r)-n) / r]
This formula provides the present value of a series of future payments discounted back to the present, accounting for the time value of money.
Application of the Perpetuity Formula
The perpetuity formula is used to calculate the present value of an infinite series of cash flows that are received at regular intervals. It is expressed as:
PV = PMT / r
In our case, the cash flows of Alfonso Canella can be analyzed using this formula to determine their present value if we assume they go on indefinitely.
Machine Cash Flows
Prob. 2 outlines cash flows from two machines where financial metrics such as Net Present Value (NPV) and Internal Rate of Return (IRR) are calculated. NPV helps assess the profitability of an investment and is calculated by finding the difference between the present value of cash inflows and the present value of cash outflows over time. IRR is the discount rate that makes NPV equal to zero and helps in comparing the profitability of different investments.
Future Value Calculations
In Prob. 3, the future value of a payment made in July 2000 on July 1, 2011, can be computed using the formula for future value (FV), which considers the interest rate over the time period involved:
FV = PV × (1 + r)n
This formula allows us to determine how much an initial investment grows over a defined period at a given interest rate.
Leasing and Implicit Rates
Prob. 4 deals with lease payments and the implicit lease rate. An implicit lease rate is often determined by the cost of lease payments compared to the fair market value of the leased asset. Understanding these financial implications is crucial for businesses when considering leasing versus purchasing assets.
Sales and Research Investments
Lastly, Prob. 5 provides insight into the relationship between sales prices, production costs, and investments in research and development (R&D). The interplay of these variables on cash flows greatly impacts the financial outcomes for an organization. Analyzing these components helps businesses make informed decisions regarding resource allocation and pricing strategies.
Conclusion
In summary, understanding annuities and the various financial computations surrounding them, including NPV, IRR, future value, and cash flow analysis, is essential for effective financial management. By applying these concepts, individuals and businesses can better evaluate investment opportunities and make strategic financial decisions.
References
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