2Contents Compounding The Frequency of Compounding Present Value and DiscountingDiscounted Cash Flow Decision RulesMultiple Cash FlowsAnnuities, PerpetuitiesLoan AmortizationExchange Rates and Time Value of MoneyInflation and DCF AnalysisTaxes and Investment Decisions
21Perpetual Annuities / Perpetuities Recall the annuity formula:Let n -> infinity with i > 0:
22Alternative Discounted Cash Flow Decision Rules NPV rule: the NPV is the difference between the present value of all future cash inflows minus the present value of all current and future cash outflows. Accept a project if its NPV is positive.
23DCF rulesExample: You have the opportunity to buy a piece of land for $10,000. You are sure that 5 years from now it will be worth $20,000. If you can earn 8% per year by investing your money in bank, is this investment in the land worthwhile?
37Exchange Rate and TVM Time U.S.A. Japan 0.01 $/¥ 3% ¥ / ¥ ? $/¥ $10,0001,000,000¥10% $/$ (direct)3% ¥ / ¥? $/¥1,030,000¥$11,000 ¥TimeU.S.A.Japan
38Exchange Rate and TVM Time U.S.A. Japan 0.01 $/¥ 3% ¥/¥ 0.0108 $/¥ $10,0001,000,000¥10% $/$ (direct)3% ¥/¥$/¥1,030,000¥$11,124$11,000 ¥TimeU.S.A.Japan
39Exchange Rate and TVM Time U.S.A. Japan 0.01 $/¥ 3% ¥ / ¥ 0.0106 $/¥ $10,0001,000,000¥10% $/$ (direct)3% ¥ / ¥$/¥1,030,000¥$10,918 ¥$11,000 ¥TimeU.S.A.Japan
40Exchange Rate and TVM Time U.S.A. Japan 0.01 $/¥ 3% ¥ / ¥ 0.01068 $/¥ $10,0001,000,000¥10% $/$ (direct)3% ¥ / ¥$/¥1,030,000¥$11,000 ¥TimeU.S.A.Japan
41Computing NPV in Different Currencies In any TVM calculation, the cash flows and the interest rate must be denominated in the same currency.
42Inflation and Future Values Example: At age 20 you save $100 and invest it at a dollar interest rate of 8% per year, and you do not take it until age 65. If the inflation is estimated 5% per year, how much will you have accumulated in the account at that time in terms of real purchasing power?
45Inflation and Present Values Example: Your daughter is 10 years old, and you are planning to open an account to provide for her college education. Tuition for a year of college is now $15,000. How much must you invest now in order to have enough to pay for her first year’s tuition 8 years from now, if you think you can earn a rate of interest that is 3% more than the inflation rate of 5%?