Fundamentalsof

Time Value of Money

Fundamentalsof

Time Value of Money

Time Value of Money (TVM) - Now is better than later and more is better than less. This is how we measure "How Much Better?"Time Value of Money (TVM) - Now is better than later and more is better than less. This is how we measure "How Much Better?"

Four Questions of Cash Flow Analysis

How much does it cost?

When do we pay it?

How much do we make?

When do we get it?

How much does it cost?

When do we pay it?

How much do we make?

When do we get it?

The Rules of Cash Flow Analysis

More is better than less

Sooner is better than later

Masters Level – something beats nothing

More is better than less

Sooner is better than later

Masters Level – something beats nothing

1. $1.00 Compounded into the future2. Present Value of $1.003. Present Value of $1.00 PER PERIOD4. Amount to Amortize $1.005. Future Value of $1.00 accumulating per

period.6. Amount to grow to $1.00 per period (Sinking

Fund Factor).

1. $1.00 Compounded into the future2. Present Value of $1.003. Present Value of $1.00 PER PERIOD4. Amount to Amortize $1.005. Future Value of $1.00 accumulating per

period.6. Amount to grow to $1.00 per period (Sinking

Fund Factor).

Six Functions of the Dollar

Compounding is calculating cash flows into the future.

Discounting calculates the present value today.

Compounding is calculating cash flows into the future.

Discounting calculates the present value today.

These calculations allow us to calculate the equivalent cash flows adjusted for time and amount. These calculations allow us to calculate the equivalent cash flows adjusted for time and amount.

Timing of Cash Flows

Formula:Formula:

Compounding

(1+i)(1+i) ^̂ nn

Where i is the interest rate and n is the period.Where i is the interest rate and n is the period.

For example: The “compounding factor” at an interest rate of 3% in Year 6 is:For example: The “compounding factor” at an interest rate of 3% in Year 6 is:

(1+.03)(1+.03) ^̂ 66 = 1.194052297= 1.194052297

Compounding refers to interest earned on an investment for given periods (FUTURE VALUE).Compounding refers to interest earned on an investment for given periods (FUTURE VALUE).

Say you invest $1,000,000 at 10% per year, compounded annually, for 4 years. How much would you have at the end of 4 years?

Investment Rate: 10%

Period Balance Factor0 $ 1,000,000.00 1 $ 1,100,000.00 1.100002 $ 1,210,000.00 1.210003 $ 1,331,000.00 1.331004 $ 1,464,100.00 1.46410

The compounding Factor Applies to each dollar. Your financial calculator calculates them for you.

Say you invest $1,000,000 at 10% per year, compounded annually, for 4 years. How much would you have at the end of 4 years?

Investment Rate: 10%

Period Balance Factor0 $ 1,000,000.00 1 $ 1,100,000.00 1.100002 $ 1,210,000.00 1.210003 $ 1,331,000.00 1.331004 $ 1,464,100.00 1.46410

The compounding Factor Applies to each dollar. Your financial calculator calculates them for you.

Compounding

Formula:Formula:

Discounting

(1+i)(1+i) ^̂ nn

Where i is the discount rate and n is the period.Where i is the discount rate and n is the period.

Discounting refers to calculating the PRESENT VALUE of cash flows, or stripping the interest from the principle.Discounting refers to calculating the PRESENT VALUE of cash flows, or stripping the interest from the principle.

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For example: The “discounting factor” at an discount rate of 10% in Year 6 is:For example: The “discounting factor” at an discount rate of 10% in Year 6 is:

(1+.10)(1+.10) ^̂ 66 = 0.56447393= 0.5644739311

For example, your opportunity cost of capital is 10% and you will receive a cash flow of $1,464,100 at the end of 4 years. What is the present value today?

For example, your opportunity cost of capital is 10% and you will receive a cash flow of $1,464,100 at the end of 4 years. What is the present value today?

Discounting

Discounting Example

i - The periodic interest rate (Interest Rate PER PERIOD).

n - The Number of compounding periods.

PV - The Lump sum present value amount.

PMT - the periodic payment at equal periods.

FV - The lump sum amount received in the future at the END of the last period.

i - The periodic interest rate (Interest Rate PER PERIOD).

n - The Number of compounding periods.

PV - The Lump sum present value amount.

PMT - the periodic payment at equal periods.

FV - The lump sum amount received in the future at the END of the last period.

Five Elements of Cash Flow

Annuities are an equal stream of cash flows, each period for a given time. Cash flows are assumed to be received at the end of each period.

Mortgage payments are an annuity.

Annuities are an equal stream of cash flows, each period for a given time. Cash flows are assumed to be received at the end of each period.

Mortgage payments are an annuity.

Annuities

The present value of an annuity is equal to the present value of each cash flow. So it is the sum of the factors.

Present Value of mortgage payments is the loan balance.

The present value of an annuity is equal to the present value of each cash flow. So it is the sum of the factors.

Present Value of mortgage payments is the loan balance.

Present Value of An Annuity

A loan balance is calculated as the present value of the remaining mortgage payments.

We know the discount rate is equal to the interest rate of the loan.

Given that discount rate, the lender is indifferent to receiving the present value of the remaining cash flows (mortgage payments) of the lump sum present value, the loan balance.

A loan balance is calculated as the present value of the remaining mortgage payments.

We know the discount rate is equal to the interest rate of the loan.

Given that discount rate, the lender is indifferent to receiving the present value of the remaining cash flows (mortgage payments) of the lump sum present value, the loan balance.

Loan Balance

i - The periodic interest rate (Interest Rate PER PERIOD).

n - The Number of compounding periods (Years, Quarters, Months).

PV - Present Value, also the loan amount.

PMT - the periodic payment at equal periods.

i - The periodic interest rate (Interest Rate PER PERIOD).

n - The Number of compounding periods (Years, Quarters, Months).

PV - Present Value, also the loan amount.

PMT - the periodic payment at equal periods.

Loan Calculations

What is the monthly loan payment for a $1,000,000 loan at 6.50% with a 25 year term?What is the monthly loan payment for a $1,000,000 loan at 6.50% with a 25 year term?

Example A

What is the loan balance of a mortgage at 7.00% interest, with 18.5 years remaining and monthly payments of $2,350.00?

What is the loan balance of a mortgage at 7.00% interest, with 18.5 years remaining and monthly payments of $2,350.00?

Example B

A property was acquired 6 years ago with a loan of $15,000,000 at 7.75% interest, monthly payments for 30 years. What is the balance today?

A property was acquired 6 years ago with a loan of $15,000,000 at 7.75% interest, monthly payments for 30 years. What is the balance today?

Example C

Internal Rate of Return (IRR): is the rate of return that is earned on each dollar that remains at risk in an investment. It can be calculated as the discount rate where the Net Present Value of a cash flow is equal to $0. The discount rate is sometimes called the "opportunity cost of capital." That is, the rate an investor would require on an investment.

Internal Rate of Return (IRR): is the rate of return that is earned on each dollar that remains at risk in an investment. It can be calculated as the discount rate where the Net Present Value of a cash flow is equal to $0. The discount rate is sometimes called the "opportunity cost of capital." That is, the rate an investor would require on an investment.

Internal Rate of Return

Rates of Return

IRR, Interest Rate, Discount Rate perform the exact same function in finance.

The appropriate return ‘name’ depends on if money is being invested to generate cash flow (IRR), money is being lent (interest rate), or if cash flow is being discounted (discount rate).

IRR, Interest Rate, Discount Rate perform the exact same function in finance.

The appropriate return ‘name’ depends on if money is being invested to generate cash flow (IRR), money is being lent (interest rate), or if cash flow is being discounted (discount rate).

Risk and Return (Alternative Investments)

T-Bills

Riskless Rate

RISK

RETURN

Municipal Bonds

Mortgage Backed Securities

Corporate Bonds

Real Estate

Common Stocks

Discount Rate

Equates risk with reward. The more risky an investment, the greater rate of return an investor will require (higher discount rate).

Three main concepts:

Equates risk with reward. The more risky an investment, the greater rate of return an investor will require (higher discount rate).

Three main concepts:

1. Opportunity Cost2. Inflation3. Risk

1. Opportunity Cost2. Inflation3. Risk

Real Estate Risks

Business Risk

Financial Risk

Liquidity Risk

Inflation Risk

Management Risk

Interest Rate Risk

Legislative Risk

Environmental Risk

Business Risk

Financial Risk

Liquidity Risk

Inflation Risk

Management Risk

Interest Rate Risk

Legislative Risk

Environmental Risk