VIEWS: 56 PAGES: 8 CATEGORY: Business POSTED ON: 7/7/2011 Public Domain
Acct 414 Prof. Teresa Gordon Time Value of Money Formulas: Types of problems Single Sum. One sum ($1) will be received or paid either in the Present (Present Value of a Single Sum or PV) Future (Future Value of a Single Sum or FV) PV FV There will always be at least four variables in any present or future value problem. Three of the four will be known and you will solve for the fourth. Single sum problems: n = number of compounding periods i = interest rate PV = Value today of a single sum ($1) FV = Value in the future of a single sum ($1) a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 1 Acct 414 Prof. Teresa Gordon Types of Annuity Problems Ordinary annuity (OA) A series of equal payments (or rents) received or paid at the end of a period, assuming a constant rate of interest. PV-OA (Present value of an ordinary annuity) PV-OA PMT PM PMT PMT PMT PMT PMT PMT T FV-OA (Future value of an ordinary annuity) FV-OA PMT PM PMT PMT PMT PMT PMT PMT T Annuity Due (AD) A series of equal payments (or rents) received or paid at the beginning of a period, assuming a constant rate of interest. V-AD (future value of an annuity due) V-AD (present value of an annuity due) PV-AD (Present value of an ordinary annuity) PV-AD PMT PMT PMT PMT PMT PMT PMT PMT FV-AD (Future value of an ordinary annuity) a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 2 Acct 414 Prof. Teresa Gordon FV-AD PMT PMT PM PMT PMT PMT PMT PMT T Annuity Due vs. Ordinary Annuity The difference between an ordinary annuity and an annuity due is that: Given the same i, n and periodic payment, the annuity due will always yield a greater present value (less interest removed) and a greater future value (more interest added). There will always be at least four variables in any present or future value problem. Three of the four will be known and you will solve for the fourth. Annuity Problems: n = number of payments or rents i = interest rate PMT = Periodic payment (rent) received or paid And either: FV of an annuity (OA or AD) = Value in the future of a series of future payments a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 3 Acct 414 Prof. Teresa Gordon OR PV of an annuity (OA or AD) = Value today of a series of payments in the future Note: To convert answer into an annuity due, multiply by (1 + n) a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 4 Acct 414 Prof. Teresa Gordon Types of Annuity Problems a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 5 Acct 414 Prof. Teresa Gordon Example Problems Ordinary Annuity Example Suppose I must make three payments of $500, each at the end of each of the next three years. The interest rate is 8%. How much should I set aside today to have the required payments? This is an ordinary annuity: What if the first payment comes immediately instead of at the end of the first year, how much would I need to set aside today in order to have the required payments? This is an annuity due: We can use one of the formulas to adjust the IF – the easiest to memorize is the “multiply by (1+i)” rule: Alternative adjustment to the IF table is even easier – at least if you write the method at the top of your table! Look up IF for (n-1) and add 1: This second method is also the “logical” decision you would make from looking at the time- line. a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 6 Acct 414 Prof. Teresa Gordon EXAMPLE PROBLEMS Deferred annuity: Assume that you are to receive three payments of $100 each beginning 3 years from now. What is this series of payments worth using a 12% discount rate? Draw time line: Analyze time-line: remember to identify the ordinary annuity involved before deciding the number of periods deferred. Alternative 1 – Work as two part problem Alternative 2 – Adjust the ordinary annuity table IF: Look up PV-OA IF for (d+n) and then subtract the PV-OA IF for d Alternative 3 – Adjust the ordinary annuity table IF: Look up PV-OA IF for n and then multiply by the PV IF for d a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 7 Acct 414 Prof. Teresa Gordon Using Time Value of Money Tables Let “IF” (interest factor) stand for the number from the appropriate time value of money table for n periods and interest rate “i” PV of a lump sum = FV * IF {from PV of $ table} FV of a lump sum = PV * IF {from FV of $ table} PV of Ordinary Annuity = PMT * IF {from PV of ord. annuity table} FV of Ordinary Annuity = PMT * IF {from FV of ord. annuity table} PMT = (PV of Ordinary Annuity) / IF {from PV of ord. annuity table} or (FV of Ordinary Annuity) / IF {from FV of ord. annuity table} ADJUSTMENTS to ordinary annuity tables CONVERSION TO ANNUITY DUE: To find IF for Future Value of an Annuity Due: Add one to the number of periods and look up IF on table. Then subtract one from the interest factor listed. To find IF for Present Value of an Annuity Due: Subtract one from the number of periods and look up IF on table. Add one to the interest factor. Or look up the IF on the appropriate table and multiply by (1 + i). CONVERSION TO DEFERRED ANNUITY Let d = number of periods deferred and n = number of periodic payments Look up (d+n) on the appropriate table. Look up d on the same table. Subtract the smaller interest factor from the larger to get the deferred annuity IF. Or look up interest factor for n periods on appropriate annuity table. Then look up interest factor from the corresponding “lump sum” table for d. Multiply the two interest factors together to get the deferred annuity IF. a9e0308a-f9e4-49df-b441-2a45f01f132c.doc 7/7/11 Page 8