MAF101 Lecture Notes - Lecture 3: Cash Flow, Mortgage Loan
13 Jun 2018
School
Department
Course
Professor
MAF101 FUNDAMENTALS OF FINANCE
Kieu Trang Nguyen
Study notes
TOPIC 2 Financial Mathematics (PART 2)
Lecture 3: Multiple Cash Flows and ANNUITIES
*PV OF MULTIPLE CASH FLOWS
•When there are multiple cash flows involved, not just one as previously, we can not just
add the amounts together due to the time value of money.
•$1 today is worth more than $1 in two years time.
•Thus need to convert to a common base: either Present Value or Future Value
*PRESENT VALUE OF MULTIPLE AMOUNTS
The present value of a stream of cash flows can be determined using the following equation
where:
PV = present value of future multiple cash flows
Xt = cash flow received in period t
r = the compound interest rate on an alternative comparable
investment
t = the number of periods before Xt is received
•
Constructing a timeline is very useful when there are multiple cash flows
• There is no need to use the previous formula
• Can just use formula 2.2 from last week to calculate the PV of each future cash flow and
then just add them up.
• Important to construct a timeline
Example:
You are offered an investment that promises $1000 in the first year, $2000 in the
second year, $3000 in the third year and $500 in the fourth year. If an investment
opportunity of similar risk pays 10% p.a. compounded annually, what is the maximum
amount that you would pay for this investment?
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Step 1: Construct a timeline:
Example (cont)
You are offered an investment that promises $1000 in the first year, $2000 in the
second year, $3000 in the third year and $500 in the fourth year. If an investment
opportunity of similar risk pays 10% p.a. compounded annually, what is the maximum
amount that you would pay for this investment?
______________________________________________
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The present value of a stream of cash flows can be determined using the following equation where: You are offered an investment that promises in the first year, in the second year, in the third year and in the fourth year. Step 2: determine the present value of each future cash flow by using formula 2. 2. Nina has just signed a contract for million to be paid ,000 now, ,000 in one years time, and ,000 in two years time. Nina has a choice to take the above arrangement or take ,000 now. Pv0 = 200,000 + 500,000 + 300,000 (1+0. 1)1 (1+0. 1)2. Again there is no need to use the previous formula just add them up: can just use formula 2. 1 from last week to calculate the fv of each cash flow and then, again, important to construct a timeline. Up till now the simple and compounded interest formulae deal mainly with one cash flow.
