电子科技大学：《金融学基础》（英文版）Chapter 4: Time Value of Money

Finance School of management Chapter 4: Time Value of Money Objective Explain the concept of compounding and discounting and to provide examples of real life applications ue sTc

1 Finance School of Management Objective Explain the concept of compounding and discounting and to provide examples of real life applications Chapter 4: Time Value of Money

Finance School of management Chapter 4 Contents Compounding Perpetual Annuities Frequency of Compounding Loan Amortization Present Value and Exchange rates and Time Discounting Value of money Alternative discounted Inflation and discounted Cash Flow Decision Rules Cash Flow Analysis Multiple cash Flows Taxes and investment Annuities Decisions uesTc

2 Finance School of Management Chapter 4 Contents ❖ Compounding ❖ Frequency of Compounding ❖ Present Value and Discounting ❖ Alternative Discounted Cash Flow Decision Rules ❖ Multiple Cash Flows ❖ Annuities ❖ Perpetual Annuities ❖ Loan Amortization ❖ Exchange Rates and Time Value of Money ❖ Inflation and Discounted Cash Flow Analysis ❖ Taxes and Investment Decisions

Finance School of management Financial decisions Costs and benefits being spread out over time The values of sums of money at different dates The same amounts of money at different dates have different values uesTc

3 Finance School of Management Financial Decisions – Costs and benefits being spread out over time – The values of sums of money at different dates – The same amounts of money at different dates have different values

Finance School of management Time Value of Money Interest Purchasing power Uncertainty uesTc

4 Finance School of Management Time Value of Money – Interest – Purchasing power – Uncertainty

Finance School of management impounding Present value(PV Future value(Fv) Simple interest: the interest on the original principal Compound interest: the interest on the interest Future value factor uesTc

5 Finance School of Management Compounding – Present value (PV) – Future value (FV) – Simple interest: the interest on the original principal – Compound interest: the interest on the interest – Future value factor

Finance School of management Value of Investing $1 at an Interest Rate of 10% Continuing in this manner you will find that the following amounts will be earned 1 Year Simple interest: 0.1 2 Years $1.21 Simple interest: 0.1+0.1=0.2 Compound interest: 0 3 Years $331 4 Years$1.4641 uesTc

6 Finance School of Management Value of Investing $1 at an Interest Rate of 10% – Continuing in this manner you will find that the following amounts will be earned: 1 Year $1.1 Simple interest: 0.1 2 Years $1.21 Simple interest: 0.1+0.1=0.2 Compound interest: 0.01 3 Years $1.331 4 Years $1.4641

Finance School of management Value of s5 Invested More generally, with an investment of $5 at 10% we obtain 1Year$5*(1+0.10) $5.5 2 years$5.5*(1+0.10) 6.05 3 years$6.05*(1+0.10) $6655 4 Years$6.65*(1+0.10) $7.3205 uesTc

7 Finance School of Management Value of $5 Invested – More generally, with an investment of $5 at 10% we obtain 1 Year $5*(1+0.10) $5.5 2 years $5.5*(1+0.10) $6.05 3 years $6.05*(1+0.10) $6.655 4 Years $6.655*(1+0.10) $7.3205

Finance School of management Value of S5 Invested If we can earn 10% interest on the principal $5 en after 4 years F=5×(+0.1)4=72305 uesTc

8 Finance School of Management Value of $5 Invested – If we can earn 10% interest on the principal $5, then after 4 years 5 (1 0.1) 7.2305 4 FV =  + =

Finance School of management Future Value of a Lump Sum F=P*(1+) FV with growths from -6%to +6% 3,500 3.000 4% > 1.500 2 Years uesTc

9 Finance School of Management Future Value of a Lump Sum n FV = PV * (1 + i) FV w ith grow ths from -6% to +6% 0 500 1,000 1,500 2,000 2,500 3,000 3,500 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 Y ears Future Value of $1000 6 % 4 % 2 % 0 % -2 % -4 % -6 %

Finance School of management Example: Future Value of a Lump sum Your bank offers a cd F=P*(1+i) Certificate of Deposit $1500*(1+0.03) with an interest rate of 3% for a 5 year =$1738.1111245 investments n You wish to invest $1, 500 for 5 years, how PV 1500 much Will your FV investment be worth? Result1738911111 uesTc 10

10 Finance School of Management Example: Future Value of a Lump Sum ❖ Your bank offers a CD (Certificate of Deposit) with an interest rate of 3% for a 5 year investments. ❖ You wish to invest $1,500 for 5 years, how much will your investment be worth? $1738 .1111145 $1500 * (1 0.03) * (1 ) 5 = = + = + n FV PV i n 5 i 3% PV 1,500 FV ? Result 1738.911111