Time Value of Money

Overview

Concept: "A peso today is worth more than a peso tomorrow."

• Basic Finance Problems:
  1. Where to put money? (Investment Decision)
  2. Where to get money? (Financing Decision)

Investment Decisions

• Real Assets:
  • Equipment and machinery for revenue generation.
  • Expanding facilities (e.g., office buildings, factories).
  • Acquiring licenses and brands.
• Financial Assets:
  • Investing in shares of other companies.
  • Lending money.
  • Purchasing fixed income instruments (e.g., treasury securities, corporate bonds).

The Concept of Interest

Formula: I = P × r × t

Where:

• I = Interest
• P = Principal
• r = Interest Rate
• t = Time Period

Example

Borrowed Amount: P1,000
Interest Rate: 9%
Time Period: 1 year

Calculation: I = 1,000 × 0.09 × 1 = P90

Types of Interest

Simple Interest

Based on the original principal.

Formula: I = P × r × t

Example

• Invested Amount: P10,000
• Interest Rate: 9%
• Time: 3 years
• Total Interest: I = 10,000 × 0.09 × 3 = P2,700

Compound Interest

Interest earned on interest.

Formula: FV = PV × (1 + r/n)^{nt}

Example

• Invested Amount (PV): P10,000
• Interest Rate (r): 9% or 0.09
• Time (t): 3 years
• Compounded: Annually (n = 1)
• Total Future Value: FV = 10,000 × (1 + 0.09/1)^{1*3} = P12,404.01

Future Value of Money

Formula: FV = PV × (1 + r)^{t}

Where:

• PV = Present Value
• r = interest rate
• t = time period

Example

Given:
Present Value (PV): P10,000
Rate (r): 9% or 0.09
Time (t): 3 years

Calculation: FV = 10,000 × (1 + 0.09)^{3} = P12,404.01

Present Value of Money

Formula: PV = \frac{FV}{(1 + r)^{t}}

Example

Options:

1. P200,000 now
2. P500,000 in 10 years at 10% return.

Present Value Calculation: PV = \frac{500,000}{(1 + 0.10)^{10}} ≈ P193,484.30

Comparison:
P200,000 > P193,484.30 → Prefer to receive P200,000 now.

Compounding on Different Periods

Example:
Invested Amount: P10,000
Interest Rate: 9% or 0.09
Compounded Quarterly (n = 4).
Calculation: FV = PV × (1 + r/n)^{nt}

Multiple Cash Flows and Annuities

Ordinary Annuity

Payments at the end of each period.

Formula for PV: PV = C × \left( \frac{1 - (1 + r)^{-n}}{r} \right)

Example

• Annual Payment (C): P50,000
• Rate (r): 10% or 0.10
• n: 3 years
• PV: P50,000 × \left( \frac{1 - (1 + 0.10)^{-3}}{0.10} \right) ≈ P124,345.48

Annuity Due

Payments at the beginning of each period.

PV and FV Formulas adjust accordingly.

Perpetuity

An annuity that continues indefinitely.

Formula: PV = \frac{C}{r}

Example

Annual Payment (C): P12,000
Rate (r): 10% or 0.10
PV: PV = \frac{12,000}{0.10} = P120,000

The present value of all the payments to the supplier of P12,000 indefinitely is P120,000.