Lecture Week3

Week Overview

• Course: MAF 101 - Fundamentals of Finance

• Topic: Present Value and Future Value of Multiple Cash Flows

• Institution: Deakin Business School

• Accreditations: AACSB, EFMD EQUIS

Learning Objectives

• Calculate Present Value (PV) and Future Value (FV) for multiple cash flows.

• Describe calculations for ordinary annuities and annuities due.

• Explain and calculate Present Value of growing perpetuities.

Announcements

• PASS Sessions:

  • Days: Monday at 11 AM, Tuesday at 8 PM

  • Purpose: Complement lectures and seminars.

• Quiz 1: Instructions available in Content -> Assessment Resources.

  • Important to read instructions carefully.

Examples of Cash Flows

• Higher Education Loans Program (HELP):

  • Covers tuition costs without attracting interest.

  • Indexes to inflation using the Consumer Price Index (CPI) or wage growth.

• Example: Ruth Gottesman’s donation of $1 billion to cover future student tuition at Albert Einstein College of Medicine.

Future Value of Multiple Cash Flows

• Definition: FV is the sum of the future values of each cash flow.

• Steps to Calculate FV:

  1. Draw a timeline marking each cash flow and the period's end.

  2. Calculate FV for each cash flow based on its time period.

  3. Sum all future values.

Example of Mixed Cash Flows

• John's Project:

  • Cash flows of $300, $600, $700, and $400 received over 4 years at an interest rate of 8%.

  • FV Calculation:

    • FV = 300 * (1+0.08)^3 + 600 * (1+0.08)^2 + 700 * (1+0.08)^1 + 400

    • Final FV = $2233.75

Present Value of Multiple Cash Flows

• Definition: PV is the sum of the present values of each cash flow.

• Steps to Calculate PV:

  1. Draw timeline for cash flows.

  2. Calculate PV for each cash flow.

  3. Sum all present values.

Example of Mixed Cash Flows

• Burwood Ltd's Cash Flows:

  • $3000, $6000, $4000, $9000 at the end of each year over 4 years at an 8% discount rate.

  • PV Calculation:

    • PV = 9000/(1+0.08)^4 + 4000/(1+0.08)^3 + 6000/(1+0.08)^2 + 3000/(1+0.08)^1

    • Final PV = $17712.41

Annuities

• Definition: A stream of cash flows spaced equally in time and of the same amount over a finite number of periods.

• Types:

  • Ordinary Annuity: Payments at the end of each period (e.g., mortgage repayments, salaries).

  • Annuity Due: Payments at the beginning of each period (e.g., rent, tuition).

Future Value of an Ordinary Annuity

• Calculation Formula:

  • FV = CF * [(1+i)^n - 1]/i

  • Example: John invests $1000/year for 4 years at a 6% return.

  • Final FV = $4374.62

Future Value of Annuity Due

• Calculation:

  • Each cash flow earns one more period of interest.

  • Final FV is always higher than an ordinary annuity of the same cash flow and time length.

Example of Future Value of Annuity Due

• John invests $1000 at the beginning of each year for 4 years at a 6% return.

  • Final FV = $4637.09.

Present Value of Annuities

• Ordinary Annuity PV Calculation:

  • PV = PMT * [1 - (1 + i)^-n] / i

  • Example: Payment of $5000 for 5 years at 6% rate results in PV = $21,061.82.

Present Value of Annuity Due

• Calculation:

  • The present value is always higher than an ordinary annuity.

Example of Present Value of Annuity Due

• Investment with 5 payments of $5000 starting now at 6% rate results in PV = $22,325.53.

Perpetuities

• Definition: A perpetuity is a constant stream of cash flows that lasts indefinitely.

• Present Value Calculation:

  • PV = CF / i

  • Example: If grandfather wants to receive $11,309/year, with a 9.9% rate, he needs $114,232.32 today.

Growing Perpetuities

• Definition: Cash flows that grow at a constant rate indefinitely.

• Present Value Calculation:

  • PV = CF1 / (i - g)

  • Example with CF growing at 2% and a discount rate of 10% gives a PV of $125,000.

Recap and Next Steps

• Key Steps:

  1. Draw timelines for cash flows.

  2. Identify required calculations.

  3. Use keywords for PV, FV, discount rates, and cash flow levels.

  4. Utilize Excel or financial calculators for calculations.

• Next Steps:

  • Review lecture slides and notes.

  • Attempt seminar problems.

  • Prepare for Quiz 1 by revising previous lectures.