MBA 621 Financial Management Lecture Notes

MBA 621: Financial Management Study Notes

Course Information

• Instructor: G. Chang

• Semester: Winter 2025

Time Value of Money

Basic Principles of Finance

• Three Key Principles:

  1. More is better than less.

  2. Sooner is better than later.

  3. Sure is better than risky.

Present Value Basics

Interest Rate (i)

• Definition: The interest rate transforms money today into money tomorrow.

• It represents the rate at which money grows when invested.

• Types of Interest Rates:

  • Simple Interest: Interest is paid only on the initial investment.

  • Compound Interest: Interest is paid on the initial investment and on any interest reinvested from previous periods.

Compound Interest

• Example of Compound Interest Rate at 10% per Annum:

  • At the end of one year, $100 grows to:

  • $100 imes (1 + 0.10) = 110$

  • At the end of two years, $100 grows to:

  • $100 imes (1 + 0.10)^2 = 121$

• General Formula for Future Value (FV):

  • If the compound interest rate is $i$, then the future value of $C$ dollars:

  • In one period: $FV_1 = C(1 + i)$

  • In two periods: $FV_2 = C(1 + i)^2$

  • In $t$ periods: $FV_t = C(1 + i)^t$

• Denote the present value (PV) of $C$ as PV and future value as $FV_t$.

Present Value of a Cash Flow

General Concept

• When the discount rate is $i$:

  • The present value of $C$ dollars obtained one period from today is:

  • $PV = \frac{C}{1 + i}$

  • Obtained two periods from today:

  • $PV = \frac{C}{(1 + i)^2}$

  • Obtained $t$ periods from today:

  • $PV = \frac{C}{(1 + i)^t}$

Example Calculations

• Example 1 (9% Discount Rate):

  • Present value of $100 obtained one year from today:

  • $PV = \frac{100}{1 + 0.09} = 91.74$

  • Present value of $100 obtained two years from today:

  • $PV = \frac{100}{(1 + 0.09)^2} = 84.17$

• Example 2 (8% Discount Rate, PV = $8000):

  • Future value after 7 years:

  • $FV_7 = 8000(1 + 0.08)^7 = 13,712$

  • Future value after 20 years:

  • $FV_{20} = 8000(1 + 0.08)^{20} = 37,287.66$

Historical Case Study: Manhattan Island Purchase

• Peter Minuet (1626):

  • Purchased Manhattan Island from Canarsee Indians for approximately $24.

• Considerations: What would $24 in 1626 be worth in 2016 if invested prudently at an interest rate of 8%?

  • Future value in the first year:

  • $FV_1 = 24(1.08) = 25.92$

  • Future value after two years:

  • $FV_2 = 24(1.08)^2 = 28.00$

  • Future value after 50 years:

  • $FV_{50} = 24(1.08)^{50} = 1,125.64$

  • Future value after 390 years?

Present Value of Multiple Cash Flows

General Concept

• Cash Flows Over Time (i = 10%):

  • If cash flows are:

  • Year 0: $100

  • Year 1: $225

  • Year 2: $140

• Each individual cash flow must be discounted back to present value:

  • Year 0: $PV_0 = 100$

  • Year 1: $PV_1 = \frac{225}{(1 + 0.10)} = 204.55$

  • Year 2: $PV_2 = \frac{140}{(1 + 0.10)^2} = 115.74$

  • Total present value:

  • $PV_{total} = 100 + 204.55 + 115.74 = 420.29$

Annuities and Perpetuities

Definition of Annuity

• An annuity is a constant payment $C$ every period until $t = n$.

  • Ordinary Annuity: Payments made at the end of each period.

  • Annuity Due: Payments made immediately at the start of each period.

• Present value determined by summing present discounted values of payments.

Present Value of an Annuity Formula

• General formula:
  [ PV = C imes rac{1 - (1 + i)^{-n}}{i} ]

Annuity Case Study

• Example (Cemetery Manager):

  • Offering 60-year care contracts estimating maintenance at $250/year, at a discount rate of 5.5%.

  • Calculation to find break-even charge:

Present Value of a Perpetuity

• A perpetuity is a constant payment of $C$ every period forever.

• Present value formula:
  [ PV = \frac{C}{i} ]

• Historical Example (British Consols):

  • 2.5% perpetuity promising to pay £25 each year.

  • Discount rate: 10.5%.

  • Price of a consol calculation:

  • $PV = \frac{25}{0.105} = 238.09$

Growth Perpetuity Definition

• A growth perpetuity starts with payment $C$ and grows at growth rate $g$ forever.

• Present value for growth perpetuity:
  [ PV = \frac{C}{i - g} ]

• Example (University of Iowa):

  • Donation proposal of $150,000 plus 5$30,000 for 30 years and an interest rate of 8%.

  Amortization Example

  • Loan of $6000 at 15% interest repaid in four equal installments.

    • Excel PMT function computation allows calculating annual payment: $PMT(15\%, 4, 6000, 0) = 2,101.58$

  • Loan Amortization Schedule:

    • Interest expense equals 15% of beginning year balance.

    • Ending balance must equal zero.

  • Key Takeaway: Compounding can occur on various intervals (e.g., quarterly), affecting growth rate calculations.