Management and Organizational Studies 2310A/B Study Guide - Midterm Guide: Cash Flow, Compound Interest
5 Nov 2018
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MOS 2310 – Finance
Chapter 6 – Discounted Cash Flow Valuation
Introduction
- Most investments have multiple cash flows that need to be accounted for
6.1 Future and Present Values of Multiple Cash Flows
Future Value with Multiple Cash Flows
- The cash flow being invested presently is labelled as Time 0
- There are two ways to calculate future values for multiple cash flows:
1) Compound the accumulated balance forward one year at a time
▪ Ex: Suppose you decide to invest $100 today earning 8% interest, and in
one year you will deposit another $100
• [(Initial $100 x 1.08)+second $100] x 1.08
• = $208 x 1.08
• = $224.64
2) Calculate the future value of each cash flow first and then add them up
▪ Ex: Suppose you decide to invest $100 today earning 8% interest, and in
one year you will deposit another $100
• Initial $100 = Time 0
o $100 x 1.082 = Time 0 = $116.64
• Second $100 = Time 1
o $100 x 1.08 = Time 1 = $108
▪ Total Future Value = $116.64 + $108 = $224.64
IN CLASS EXAMPLE
- You currently have $7,000 in a bank account earning interest at an annual rate of 8%,
compounded annually. You think you will be able to deposit an additional $4,000 at the
end of the next three years – How much will you have in 3 years
o Find the value of each cash flow at year 3 and add them together:
▪ Ex: Year 0 = 7000(1.08)3
Present Value with Multiple Cash Flows
- There are two ways to calculate present values for multiple cash flows:
1) Calculate the present values individually and then add them up
▪ Ex: Suppose you need $1,000 in one year and $2,000 more in two years. If
you can early 9% on your money how much do you have to invest.
• PV of $2000 in two years: $2,000/1.092 = $1,683.36
• PV of $1000 in one year: $1,000/1.09 = $917.43
• Total PV = $1683.36 + $917.43 = $2,600.79
2) Discount back one period at a time
▪ Ex: Suppose you have a cash flow that is going to pay $1,000 at the end of
every year for the next 5 years, with a 6% discount rate
Find the Additions by taking ($1,000/1.06x)
IN CLASS EXAMPLE
- You are offered an investment that will pay you $200 in one year, and $400 in two years,
$600 in three years and $800 in four years. You can earn 12% per year on similar
investments. How much is this investment worth today?
o Find the value of each cash flow at year 3 and add them together:
▪ Ex: Year 0 = 200 / (1.12)1
▪ Year 1 = 400 / (1.12)2
A Note on Cash Flow Timing
- In most cases, it is assumed that the cash flows occur at the end of each period
o Always go with this assumption unless explicitly told otherwise
6.2 Valuing Level Cash Flows: Annuities and Perpetuities
- Common to encounter situations where we have multiple cash flows with same amounts
- Almost all consumer loans and home mortgages feature equal payments made monthly
- Annuity: A level stream of cash flows for a fixed time period
o All of the cash flows are the same
- Perpetuity: An annuity in which the cash flows continue forever
Present Value for Annuity Cash Flows
Document Summary
Most investments have multiple cash flows that need to be accounted for. 6. 1 future and present values of multiple cash flows. The cash flow being invested presently is labelled as time 0. Initial = time 0: x 1. 082 = time 0 = . 64, second = time 1, x 1. 08 = time 1 = , total future value = . 64 + = . 64. You currently have ,000 in a bank account earning interest at an annual rate of 8%, compounded annually. There are two ways to calculate present values for multiple cash flows: calculate the present values individually and then add them up, ex: suppose you need ,000 in one year and ,000 more in two years. You are offered an investment that will pay you in one year, and in two years, in three years and in four years. You can earn 12% per year on similar investments.
