Time Value of Money Cheat Sheet, Cheat Sheet of Law

Download Time Value of Money Cheat Sheet and more Cheat Sheet Law in PDF only on Docsity! Time value of money Cheat Sheet by Natalie Moore (NatalieMoore) via cheatography.com/19119/cs/11141/ Variable key Where: FV = Future value of an investment PV = Present value of an investment (the lump sum) r = Return or interest rate per period (typically 1 year) n = Number of periods (typically years) that the lump sum is invested PMT = Payment amount CFn = Cash flow steam number m = # of times per year r compounds Equation guide Future value of a lump sum: FV = PV x (1 + r) - Future​​-value factor (FVF) table - Excel future value formula FV= - Compound interest. Formula for simple interest is PV + (n x (PV x r)) Future Value of an Ordinary Annuity FV = PMT x { [ ( 1 + r ) - 1 ] / r} Future Value of an Annuity Due FV (annuity due) = PMT x { [ ( 1 + r) -1 ] / r } x (1 + r) Future Value of Cash Flow Streams FV = CF1 x (1 +r) + CF2 x (1 + r) + ... + CFn x (1 + r) Present value of a lump sum in future PV = FV / (1 + r) = FV x [ 1 / (1+ r) ] - Presen​t-value factor (FVF) table - Excel present value formula PV= Equation guide (cont) Present Value of a Mixed Stream PV = [CF1 x 1 / (1 + r) ] + [CF2 x 1 / (1 + r) ] + ... + [CFn x 1 / (1 + r) ] Present Value of an Ordinary Annuity PV = PMT/r x [1 - 1 / (1 + r) ] Present Value of Annuity Due PV (annuity due) = PMT/r x [1 - 1 / (1 + r) ] x (1 + r) Lump sum future value in excel Present Value of a Growing Perpetuity Most cash flows grow over time This formula adjusts the present value of a perpetuity formula to account for expected growth in future cash flows Calculate present value (PV) of a stream of cash flows growing forever (n = ∞) at the constant annual rate g PV = CF1 / r - g r > g Loan Amorti​zation​ A borrower makes equal periodic payments over time to fully repay a loan E.g. home loan Uses - Total $ of loan - Term of loan Loan Amorti​zation (cont)​ - Frequency of payments - Interest rate Finding a level stream of payments (over the term of the loan) with a present value calculated at the loan interest rate equal to the amount borrowed Loan amorti​zation schedule​ Used to determine loan amorti​sation payments and the allocation of each payment to interest and principal Portion of payment repres​enting interest​ declines over the repayment period, and the portion going to principal repayment increases PMT = PV / {1 / r x [ 1 - 1 / (1 + r) ] } Deposits Needed to Accumulate a Future Sum Determine the annual deposit necessary to accumulate a certain amount of money at some point in the future E.g. house deposit Can be derived from the equation for fi nding the future value of an ordinary annuity Can also be used to calc required deposit PMT = FV {[( 1 + r) - 1 ] / r} Once this is done substitute the known values of FV, r, and n into the righthand side of the equation to find the annual deposit required. Stated Versus Effective Annual Interest Rates Make objective compar​isons of loan costs or investment returns over different compou​nding periods Stated annual rate is the contra​ctual annual rate charged by a lender or promised by a borrower By Natalie Moore (NatalieMoore) cheatography.com/nataliemoore/ www.jchmedia.com/ Published 19th March, 2017. Last updated 19th March, 2017. Page 1 of 4. Sponsored by Readable.com Measure your website readability! https://readable.com n n n n-1 n-2 n-n n n 1 1 1 n n n n Time value of money Cheat Sheet by Natalie Moore (NatalieMoore) via cheatography.com/19119/cs/11141/ Stated Versus Effective Annual Interest Rates (cont) Effective annual rate (EAR) AKA the true annual return, is the annual rate of interest actually paid or earned - Reflects the effect of compou​nding frequency - Stated annual rate does not Maximum effective annual rate for a stated annual rate occurs when interest compounds contin​uously EAR = ( 1 + r/m ) - 1 Compou​nding contin​uously: EAR (conti​‐​ nuous compou​nding) = e​ - 1 Concept of future value Apply simple interest, or compound interest to a sum over a specified period of time. Interest might compound: annually, semian​‐ nual, quarterly, and even continuous compou​nding periods Future value value of an investment made today measured at a specific future date using compound interest. Compound interest is earned both on principal amount and on interest earned Principal refers to amount of money on which interest is paid. Important to understand After 30 years @ 5% a $100 principle account has: - Simple Interest: balance of $250. - Compound interest: balance of $432.19 FV = PV x (1 + r) The Power of Compound Interest Future Value of One Dollar Present value Used to determine what an investor is willing to pay today to receive a given cash flow at some point in future. Calcul​ating present value of a single future cash payment Depends largely on investment opport​‐ unities of recipient and timing of future cash flow Discou​nting​ describes process of calcul​‐ ating present values - Determines present value of a future amount, assuming an opport​unity to earn a return (r) - Determine PV that must be invested at r today to have FV, n from now - Determines present value of a future amount, assuming an opport​unity to earn a given return (r) on money. We lose opport​unity to earn interest on money until we receive it To solve, inverse of compou​nding interest PV of future cash payment declines longer investors wait to receive Present value (cont) Present value declines as the return (discount) rises. E.g. value now of $100 cash flow that will come at some future date is less than $100 PV = FV / (1 + r) = FV x [ 1 / (1+ r) ] The Power of Discou​nting​ Special applic​ations of time value​ Use the formulas to solve for other variables - Cash flow CF or PMT - Interest / Discount rate r - Number of periods n Common applic​ations and refine​ments - Compou​nding more frequently than annually - Stated versus effective annual interest rates - Calcul​ation of deposits needed to accumulate a future sum - Loan amorti​sation By Natalie Moore (NatalieMoore) cheatography.com/nataliemoore/ www.jchmedia.com/ Published 19th March, 2017. Last updated 19th March, 2017. Page 2 of 4. 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