Class notes

Class notes FIN401 (FIN401) (Cash Flow, Discounting, Annuities, & Perpetuties)

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Course
FIN401 (FIN401)

Institution
Ryerson University (Ru )

explanation of Cash flows, Discounting, Annuities, and Perpetuities with examples and step by step explanation on how to solve it.

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Uploaded on October 5, 2023
Number of pages 9
Written in 2023/2024
Type Class notes
Professor(s) Daniel tut
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FIN401: Lecture 1
Goal
● Understand more fully the role of capital budgeting, leasing, and mergers
and acquisitions in the corporate financial decision-making process.
● Understand the issue involved in the capital structure and dividend policy
decision, why the decisions are not irrelevant, and what types of financing
are available to firms.
● Understand the importance of risk management in the corporate financial
decision-making processes.
● Be able to recognize some of the ethical issues inherent in corporate
financial decision-making.
Time Value of Money (A review of Chapter 4,6,7)
● Money received soon rather than later allows you to:
○ Use the funds for investment and/or consumption purposes
○ Minimize Inflation
○ Minimize Uncertainty
The Importance of Time
● When valuing or comparing cash flows that occur at different points in
time, we cannot just combine them together
○ A dollar today and a dollar in one year are not equivalent!
● We need to convert the cash flows into the same units first by moving them
to the same point in time
○ To move a cash flow forward in time, we use compounding
○ To move a cash flow earlier in time, we use discounting
Compounding vs Discounting:
The case of single cash flow
Compounding
● Determining the future value of a cash flow (or set of cash flows)
● Compound interest: Interest is earned on the principal amount invested
and on any accrued interest
● The basic compounding equation (for a single CF):
● FV = Future Value, PV = Present Value, r = annual interest rate, n = number of
years, (1+r) = interest rate factor
Example 1: You worked tirelessly all summer and made $9,000 in cash. You would
like to invest this money today in a special bank account that pays 5% interest
per year for a locked-in 15-year term. How much will you have in the account after
those 15 years?
● Formula Approach:
15
𝐹𝑉15 = $9000 × (1 + 0. 05) = $18, 710. 35
● Financial Calculator Approach:
○ Casio: TVM > F2 (Compound Interest)
○ Number of Years: N = 15
○ Interest Rate: I% (or I/Y) = 5%
○ Deposit Today: PV = $9000

, ○ Additiona; deposits (PMT) = 0
○ Payments & Compounding Periods (P/Y & C/Y) = 1
○ Looking for future Value > Compute FV = $18,710.35
Example 2: Suppose instead that you were able to make only $1,200 over the
summer. You want to deposit it today in a different savings account that has an
interest rate of 8% locked in for 10 years. How much money will you have in the
account at the end of the:
a. First Year
1
𝐹𝑉 = (1, 200)(1. 08) = $1, 296
b. Fifth Year
5
𝐹𝑉 = (1, 200)(1. 08) = $1, 763. 19
c. Tenth Year
10
𝐹𝑉 = (1, 200)(1. 08) = $2, 590. 71
Example 3: Fill in the Missing Values

Discounting
● Discounting is the process of translating a future value (or a set of future
cash flow) into a present value
● In order to get the present value, we rearrange the formula seen under the
compounding to set:
𝐹𝑉𝑛
𝑃𝑉0 = 𝑛
(1+𝑟)
● Where 1/(1+r) = discount factor
Example 4: Just imagine that you are holding a big-winning LottoCash ticket. For
your winnings, you can choose to receive either $3.2 million today or $8.5 million
10 years from now.
a. If the interest rate is 11%, which option should you choose?
Solution: compare present (or future) values
● Formula Approach:
$8.5𝑚
𝑃𝑉 = 10 = $2, 993, 568 < $3. 2𝑚
(1.11)

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