Units 6 and 7

Time Value of Money (TVM)

Concept that money has different values at different points in time due to earning potential.

Present Value (PV)

Value today of future cash flows discounted at an appropriate rate.

Future Value (FV)

Value in the future of a present amount after earning a rate of return.

TVM Variables

N, I/YR, PV, PMT, FV.

N

Number of compounding periods.

I/YR

Interest rate or rate of return per year.

PV

Present value of an amount today.

PMT

Recurring payment amount.

FV

Future value of cash flows.

TVM Sign Convention

Cash inflows are positive; cash outflows are negative.

TVM Problem-Solving Process

Create timeline, identify variables, clear calculator, enter values.

Purpose of a Timeline

Shows cash flow timing, amount, and direction.

Future Value of Lump Sum

Amount a deposit grows to after compounding.

Present Value of Lump Sum

Amount needed today to achieve a future goal.

Effect of More Frequent Compounding

Produces a higher future value.

Annual Compounding

Interest credited once per year.

Semiannual Compounding

Interest credited twice per year.

Quarterly Compounding

Interest credited four times per year.

Monthly Compounding

Interest credited twelve times per year.

Ordinary Annuity

Series of equal payments occurring at the end of each period.

Annuity Due

Series of equal payments occurring at the beginning of each period.

Ordinary Annuity First Payment

Time period 1.

Annuity Due First Payment

Time period 0.

Annuity Due Future Value

Greater than equivalent ordinary annuity.

Begin Mode

Calculator setting used for annuity due calculations.

End Mode

Calculator setting used for ordinary annuity calculations.

MLB Rule

Mortgages, loans, and bonds are generally calculated in END mode.

Examples of Ordinary Annuities

Most loan payments and retirement contributions.

Examples of Annuity Due

Rent, tuition payments, retirement income.

Ordinary Annuity Payment from Lump Sum

Periodic payment generated from a lump-sum deposit.

Annuity Due Payment from Lump Sum

Periodic payment received at beginning of periods from a lump sum.

Term (N) Calculation

Determines how long a goal takes to achieve.

Term Calculation Uses

Time to double investments or repay debt.

Rule of 72

Approximate doubling time = 72 ÷ interest rate.

Rule of 72 Example

At 9%, money doubles in about 8 years.

Interest Rate (I) Calculation

Determines required rate of return to achieve a goal.

Interest Rate Use

Calculating loan rates and required investment returns.

Lottery Lump Sum vs Annuity

Compare using IRR or required rate of return.

Required Return for Lottery Example

Approximately 3.15%.

Debt Repayment Calculation

Determines payment necessary to retire debt.

Mortgage Payment Calculation

TVM application used to determine monthly mortgage payments.

Mortgage Amortization

Schedule showing principal and interest paid over time.

Closing Costs in Mortgage Problem

Only included if explicitly stated.

Mortgage Interest Savings Techniques

Double payment, extra annual payment, higher monthly payment.

Benefit of Extra Mortgage Payments

Reduces interest and shortens loan term.

Cash Rebate vs 0% Financing

TVM analysis compares total financing costs.

Payment of Mortgage Points

Paying upfront fees to lower interest rates.

Mortgage Point Break-Even Analysis

Time required for savings to exceed upfront point cost.

Nominal Return

Stated investment return before inflation.

Real Return

Inflation-adjusted rate of return.

Real Return Formula

[(1+Nominal Return)/(1+Inflation)] − 1.

Purpose of Real Return

Measures actual increase in purchasing power.

When to Use Real Return

When returns and expenses grow at different rates.

Education Funding Real Return Example

Use investment return adjusted for tuition inflation.

Retirement Funding Real Return Example

Use investment return adjusted for inflation.

Serial Payments

Payments that increase periodically, usually with inflation.

Difference Between Serial and Annuity Payments

Serial payments increase; annuity payments remain level.

Serial Payment Use

Education and long-term goal funding.

Uneven Cash Flows

Cash flows that vary by amount and timing.

CFj

HP calculator key used to enter cash flows.

Nj

HP calculator key used to enter repeated cash flows.

Net Present Value (NPV)

Difference between present value of inflows and investment cost.

Positive NPV

Investment exceeds required rate of return.

Negative NPV

Investment fails to meet required return.

NPV Equal to Zero

Investment exactly earns required rate of return.

NPV Formula

PV of future cash flows minus investment cost.

Purpose of NPV

Evaluate investment profitability.

Internal Rate of Return (IRR)

Discount rate that makes NPV equal zero.

IRR Decision Rule

Accept if IRR exceeds required return.

IRR Assumption

Cash flows are reinvested at the IRR.

Positive Relationship Between IRR and Attractiveness

Higher IRR generally indicates better investment.

Inflation-Adjusted Education Funding

Uses real return rather than nominal return.

Most Common TVM Exam Error

Using incorrect BEGIN or END mode.