TVM Preferences More vs. Less Sooner vs. Later More Now vs. Less Later Less Now vs. More Later ????
TVM Questions What will my investment grow to? How much do I need today? How fast must my investment grow? How long will it take?
Compare and Contrast 19702011 Cost of a first-class stamp: $ 0.06 $ 0.44 Cost of a gallon of gas: $ 0.36 $ 2.98 Cost of a dozen eggs: $ 0.62 $ 2.20 Cost of a gallon of Milk: $ 1.15 $ 3.69 TVM 4.98% 5.29% 3.14% 2.88%
TVM Basic Concepts Simple vs. Compound Interest Simple Interest = interest earned only on principal (amount loaned) Compound Interest = interest earned on principal and any unpaid interest earned in an earlier time period
Calculator Tips Set Calculator to 4 decimal points Set P/Yr to 1 and do not change Clear calculator before calculation Use recommended format Learn to use special features Read carefully Know the concepts of TVM
TVM Concepts Use a time line Use + or - to indicate cash flow Periodic Cash flows can be at Beginning or End of Period Calculators use Percentages Excel uses decimals
Lump Sum vs. Periodic Pmts Lump Sum –Single Payment –At time zero –Present Value OR –Single Payment –At end of time –Future Value Periodic Payment –Ordinary Annuity Pmt at end of periods For life of investment –Annuity Due Pmt at beg. of periods For life of investment –PMT
Annuities Must be –Equal Amounts –Occurring in every compounding period –Ordinary Annuity – End of Period –Annuity Due – Beginning of Period
Future Value of a Combination If you invest $10,000 today and $1,000 at the end of each year in a mutual fund that is expected to earn a 12% compound after-tax return, how much will you have at the end of 5 years?
Present Value of a Combination What would you pay for the right to collect $800 at the end of each year for 7 years and an additional $10,000 at the end of the period, if your required return is 7.25%?
Alternative Two – Use the CF Register 1.Draw Time Line 2.Input Cash Flows into CF Register 3.Go to NPV Register 1.Input Rate of Return 2.Compute NPV
Uneven Cash Flows Example 1 – Alternative Two 1.Draw Time Line 2.Push CF button 3.Clear CF register 2 nd CLR Work 4.Input Cash Flows
Cash Flow Register Inputs –CF 0 = Investment, Price, Cost at Time 0 We are solving for PV so CF 0 should be 0 Since CF0 already = 0, –C01 = Cash Flow at the end of Period 1 –F01 = Frequency of C01 The number of times that C01 occurred consecutively
Uneven Cash Flows Example 1 1.Check Inputs 2.Go To NPV Register 3.Input I 9 ENTER, 4.CPT NPV = 5,009.83
Uneven Cash Flows Example 2 What would you be willing to pay for a real estate investment that has the following expected cash flows: Yr. 1 $500, Yrs. 2-6 $1,000, Yr. 7-10 $1,500, and Yr. 11 $30,000? Assume your required return for this type of investment is 17.0%.