CHAPTER 4
THE TIME VALUE OF MONEY AND DISCOUNTED CASH FLOW ANALYSIS
Objectives
∙To explain the concepts of compounding and discounting, future value and prent value.
∙To show how the concepts are applied to making financial decisions.
Outline
4.1 Compounding
4.2 The Frequency of Compounding
4.3 Prent Value and Discounting
4.4 Alternative Discounted Cash Flow Decision Rules
4.5 Multiple Cash Flows
4.6 Annuities
4.7 Perpetual Annuities
4.8 Loan Amortization
4.9 Exchange Rates and Time Value of Money
4.10 Inflation and Discounted Cash Flow Analysis
4.11 Taxes and Investment Decisions
Summary
∙Compounding is the process of going from prent value (PV) to future value (FV). The future value of $1 earning interest at rate i per period for n periods is (1+i)n.
∙Discounting is finding the prent value of some future amount. The prent value of $1 discounted at rate i per period for n periods is 1/(1+i)n.
∙One can make financial decisions by comparing the prent values of streams of expected future cash flows resulting from alternative cours of action. The prent value of cash inflows less the prent value of cash outflows is called net prent value (NPV). If a cour of action has a positive NPV, it is worth undertaking.
∙In any time value of money calculation, the cash flows and the interest rate must be denominated in the same currency.
∙Never u a nominal interest rate when discounting real cash flows or a real interest rate when discounting nominal cash flows.
How to Do TVM Calculations in MS Excel
Assume you have the following cash flows t up in a spreadsheet:
| A | B |
1 | t | CF |
2 | 0 | -100 |
3 | 1 | 50 |
4 | 2 | 60 |
| 钱财造句 5 | 3 | 70 |
6 | NPV | |
哲学意义摩登时代7 | IRR | |
| | |
Move the cursor to cell B6 in the spreadsheet. Click the function wizard fx in the tool bar and when a menu appears, lect financial and then NPV. Then follow the instructions for inputting the discount rate and cash flows. You can input the column of cash flows by lecting and moving it with your mou. Ultimately cell B6 should contain the following:
=NPV(0.1,B3:B5)+B2
The first variable in parenthesis is the discount rate. Make sure to input the discount rate as a decimal fraction (i.e., 10% is .1). Note that the NPV function in Excel treats the cash flows as occurring at the end of each period, and therefore the initial cash flow of 100 in cell B2 is added after the closing parenthesis. When you hit the ENTER key, the result should be $47.63.
Now move the cursor to cell B7 to compute IRR. This time lect IRR from the list of financial functions appearing in the menu. Ultimately cell B7 should contain the following:
=IRR(B2:B5)
When you hit the ENTER key, the result should be 34%.
Your spreadsheet should look like this when you have finished:
| A | B |
1 | t | CF |
2 | 0 | -100 |
3 | 1 | 50 |
4 | 2 | 60 |
5 | 3 | 70 |
己所不欲勿施于人的意思6 | NPV | 47.63 |
7 | IRR | 34% |
| | |
Solutions to Problems at End of Chapter
1. If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now, assuming no withdrawals in the interim?
SOLUTION:
n | i | PV | FV | PMT | Result |
20 | 10 | 1000 | ? | 0 | FV =6,727.50 |
| | | | | |
2. a. If you invest $100 every year for the next 20 years, starting one year from today and you earn interest of 10% per year, how much will you have at the end of the 20 years?
b. How much must you invest each year if you want to have $50,000 at the end of the 20 years?
SOLUTION:
n | i | PV | FV | PMT | Result |
a. 20 | 10 | 0 | ? | 100 | FV = 5,727.50 |
b. 20 | 10 办公楼设计规范 | 0 | 50,000 | ? | PMT = 872.98 |
| | | | | |
3. What is the prent value of the following cash flows at an interest rate of 10% per year?
a. $100 received five years from now.
b. $100 received 60 years from now.
c. $100 received each year beginning one year from now and ending 10 years from now.
d. $100 received each year for 10 years beginning now.
e. $100 each year beginning one year from now and continuing forever.
SOLUTION:
n | i | PV | FV | PMT | Result |
a. 5 | 10 | 国庆假期作文 ? | 100 | 0 | PV = $62.09课题研究计划 |
b. 60 | 10 | ? | 100 | 0 | PV = $.3284 |
c. 10 | 10 | ? | 0 | 100 ordinary | PV = $614.46 |
d. 10 | 10 | ? | 0 | 100 immediate | PV = $675.90 |
e. Perpetuity | 10 | ? | 0 | 100 ordinary | See below |
| | | | | |
e. PV = $100 = $1,000
.10
4. You want to establish a “wasting” fund which will provide you with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year?
SOLUTION:
n | i | PV | FV | PMT | Result |
生产批号4 | 10 | ? | 0 | 1,000 | PV =$3,169.87 |
| | | | | |
5. You take a one-year installment loan of $1000 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments.
a. What is the monthly payment?
b. What is the total amount of interest paid over the 12-month term of the loan?
SOLUTION:
n | i | PV | FV | PMT | Result |
12 | 1 | 1,000 | 0 | ? | PMT = $88.85 |
| | | | | |
a. PMT = $88.85
