Week 2 - finance

• Time Value of Money


  The concept that a dollar today is worth more than a dollar in the future due to the potential for earning interest or returns over time.
• Compounding's Effect on PV


  Compounding increases PV by adding interest to principal and accelerating growth, leading to a larger PV especially with more frequent compounding.
• Compounding Periods


  Continuous compounding yields the highest PV, annual compounding yields a lower PV, and monthly compounding yields a higher PV than annual compounding.
• Compounding's Effect on PV


  Compounding increases PV by accelerating growth, making higher-frequency compounding more valuable, especially for long-term investments.
• PV Formula


  Present Value (PV) = Future Value (FV) / (1 + Discount Rate (r))^Number of Periods (n)
• Perpetuity


  A financial instrument providing a constant stream of cash flows indefinitely, with no maturity date and no principal repayment.
• Perpetuities vs. Bonds


  Perpetuities have no maturity date, no principal repayment, and constant cash flows, while bonds have a specific maturity date, principal repayment, and a typical fixed interest rate and principal schedule.
• Perpetuity Valuation


  Perpetuities are valued using the perpetuity formula (PV = CF / r), considering the time value of money and constant cash flows with no maturity date.
• Perpetuity Cash Flow


  The perpetual cash flow is the constant and predictable interest payment or cash flow generated by a perpetuity, which has an infinite duration and is subject to some level of uncertainty.
• Present Value (PV) and Annuity


  The present value of a perpetuity is CF / r, while the present value of an annuity is the sum of the present values of each periodic cash flow, using the annuity formula.
• Applying Formulas


  To apply formulas, identify the formula, specify the variables, plug in the numbers, and solve for the answer.
• Applying Formulas to Annuities


  To apply formulas to annuities, identify the annuity formula, specify the variables, plug in the numbers, and solve for the answer.
• Discount Rate and Present Value


  The discount rate affects the present value of a future cash flow or annuity, with a higher discount rate resulting in a lower present value and a lower discount rate resulting in a higher present value.
• Discount Rate's Impact on Investment Decisions


  The discount rate affects investment decisions by impacting the present value of future cash flows, influencing the acceptability of projects, capital budgeting, capital structure, risk assessment, and international investments.
• Payback Period


  The payback period is the amount of time it takes for an investment to generate enough cash to equal its initial outlay, calculated by adding future cash flows to the initial outlay and finding the point where the cumulative cash flow reaches zero.
• Discounted Payback Period


  The discounted payback period is the amount of time it takes for an investment to generate enough present value cash flows to equal its initial outlay, taking into account the discount rate and the present value of future cash flows.
• Discount Rate's Impact on Payback Period


  The discount rate affects the payback period by shortening it with a higher discount rate and lengthening it with a lower discount rate, with the discount rate influencing the risk assessment, time value of money, and present value calculation.
• Net Present Value (NPV)


  The Net Present Value (NPV) is a financial metric that calculates the present value of a project's cash inflows and outflows to evaluate its attractiveness, using a discount rate to discount future cash flows to their present value.
• Capital Investment Appraisal


  Capital investment appraisal is the process of evaluating the financial feasibility of a business project or investment, using various methods such as payback period, discounted payback period, net present value, internal rate of return, and profitability index to determine the attractiveness of the project.
• NPV Formula Application


  NPV = Σ (CFt / (1 + r)^t) with CFt = [20000, 30000, 40000, 50000], r = 0.10, and t = [1, 2, 3, 4] yields an NPV of $32,178.78.
• Compounding Periods


  Compounding periods refer to the frequency at which interest is added to an investment or loan, and affect the time value of money, compound interest rate, and present value.
• Compounding and Loan Payments


  Compounding increases the amount of interest paid, leads to faster principal paydown, results in higher monthly payments, and more interest paid in the early years of the loan.
• Effective Annual Rate (EAR)


  The effective annual rate (EAR) is the rate of interest that takes into account the compounding frequency and the number of times interest is compounded per year, producing the same total interest paid over a year as the actual interest rate and compounding frequency.
• EAR Formula


  (1 + r/m)^\*m - 1
• Effective Annual Rate (EAR) Formula


  (1 + r/m)^\*m - 1
• Daily Compounding


  EAR = (1 + r/365)^\*365 - 1
• Monthly Compounding


  EAR = (1 + r/12)^\*12 - 1
• Quartenly Compounding


  EAR = (1 + r/4)^\*4 - 1
• Annual Compounding


  EAR = 1 + r - 1 (since annual compounding means adding interest only once)
• Annual Percentage Rate (APR)


  The APR is the total interest rate charged on a loan or credit account over a year, including compounding, calculated using the formula (1 + r/m)^\*m - 1.
• Continuous Compounding


  The formula for continuous compounding is A = P \* e^(rt), where A is the total amount, P is the principal, e is the base of the natural logarithm, r is the interest rate, and t is time.
• Growing Annuity


  The formula for a growing annuity is S = P \* [(1 + r)^n - 1] / r, where S is the sum, P is the periodic payment, r is the rate of return, and n is the number of periods.
• Decreasing Annuity


  The formula for a decreasing annuity is similar to the growing annuity formula, but with a negative rate of return (r), where S is the sum, P is the periodic payment, r is the rate of return, and n is the number of periods.
• Present Value of Annuity


  The formula for the present value of an annuity is PV = P [\frac{1 - (1 + r)^{-n}}{r}], where PV is the present value, P is the periodic payment, r is the rate of return, and n is the number of periods.
• Future Value of Annuity


  The formula for the future value of an annuity is FV = P \* [(1 + r)^n - 1] / r, where FV is the future value, P is the periodic payment, r is the rate of return, and n is the number of periods.
• Delayed Annuity


  A delayed annuity is an annuity that starts making payments after a certain number of periods, using the formula S = P \* [(1 + r)^n - 1] / r, where S is the sum, P is the periodic payment, r is the rate of return, and n is the number of periods.
• Annuity Date

  The annuity date is the date when the first payment is made in an annuity, and is calculated using the formula NA = PV / PMT, where NA is the number of annuity dates, PV is the present value of the annuity, and PMT is the periodic payment.
• Infrequent Annuity


  An infrequent annuity is an annuity that makes periodic payments at irregular intervals. To calculate the future value, use the formula FV = P \* [(1 + r)^n - 1] / r, where FV is the future value, P is the periodic payment, r is the rate of return, and n is the number of payments. Adjust the formula to account for the irregular payment schedule by converting it to an equivalent annual payment schedule.
• Equating PV of Two Annuities

  To equate the present value of two annuities, use the equation P1 \* [(1 + r1)^-n1] / r1 = P2 \* [(1 + r2)^-n2] / r2, where P1 and P2 are the periodic payments, r1 and r2 are the rates of return, and n1 and n2 are the number of periods. This allows you to find the equivalent periodic payment or interest rate that makes the present value of one annuity equal to the present value of the other.
• Applying Equation

  To apply the equation in practice, identify the two annuities, plug in the values, simplify the equation, find the equivalent periodic payment or interest rate, and check the solution to ensure it makes sense.