BDH+ed+3+Chapter+4+-+Questrom

# BDH+ed+3+Chapter+4+-+Questrom - FE101 Chapter 4 Time Value...

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FE101: Chapter 4 Time Value of Money: Valuing Cash Flow Streams

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Learning Objectives Value a series of many cash flows Value a perpetual series of regular cash flows called a perpetuity Value a common set of regular cash flows called an annuity Value both perpetuities and annuities when the cash flows grow at a constant rate Compute the number of periods, cash flow, or rate of return of a loan or investment 2
Valuing a Stream of Cash Flows 3

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Valuing a Stream of Cash Flows Applying the Rules of Valuing Cash Flows Suppose we plan to save \$1,000 today, and \$1,000 at the end of each of the next two years If we earn a fixed 10% interest rate on our savings, how much will we have three years from today? 4
Valuing a Stream of Cash Flows We can do this in several ways First, take the deposit at date 0 and move it forward to date 1 Combine those two amounts and move the combined total forward to date 2 5

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Valuing a Stream of Cash Flows Continuing in the same fashion, we can solve the problem as follows: 6
Valuing a Stream of Cash Flows Another approach is to compute the future value in year 3 of each cash flow separately Once all amounts are in year 3 dollars, combine them 7

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Valuing a Stream of Cash Flows Consider a stream of cash flows: C 0 at date 0, C 1 at date 1, and so on, up to C N at date N We compute the present value of this cash flow stream in two steps 8
Valuing a Stream of Cash Flows First, compute the present value of each cash flow Then combine the present values 9

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Present Value of a Stream of Cash Flows Problem: You have just graduated and need money to buy a new car. Your rich Uncle Henry will lend you the money so long as you agree to pay him back within four years. You offer to pay him the rate of interest that he would otherwise get by putting his money in a savings account. Based on your earnings and living expenses, you think you will be able to pay him \$5000 in one year, and then \$8000 each year for the next three years. If Uncle Henry would otherwise earn 6% per year on his savings, how much can you borrow from him? 10
Present Value of a Stream of Cash Flows Solution: Plan: The cash flows you can promise Uncle Henry are as follows: Uncle Henry should be willing to give you an amount equal to these payments in present value terms. 11

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Present Value of a Stream of Cash Flows Plan: We will: Solve the problem using the Present Value (PV) equation Verify our answer by calculating the future value of this amount. 12
Present Value of a Stream of Cash Flows Execute: We can calculate the PV as follows: 13 2 3 4 5000 8000 8000 8000 1.06 1.06 1.06 1.06 4716.98 7119.97 6716.95 6336.75 \$24,890.65 PV

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Present Value of a Stream of Cash Flows Execute: Verify our answer by calculating the future value (FV) of this amount Now, suppose that Uncle Henry gives you the money, and then deposits your payments in the bank each year.
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