Questions and Answers
The term 'nominal return' is synonymous with money income.
False
Compounding refers to the process of earning interest on previously earned interest.
True
The rule of 72 is used to determine how long it takes for an investment to triple in value.
False
A loan's APR is referred to as the total cost of borrowing expressed as a percentage.
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An annuity is defined as a lump sum payment received in the future.
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The IRR is the interest rate that makes the NPV of cash flows equal to zero.
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Financial calculators require special keys for performing simple TVM calculations.
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The internal rate of return does not take into account the time valuation of money.
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The present value of a future sum decreases as the discount rate increases.
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A $20,000 sum to be received in 6 years at an 8 percent discount rate has a present value of $20,000.
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The future value of an investment of $18,000 at 6 percent for 7 years will be approximately $27,065.
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The formula used in Excel to calculate present value does not require future cash flow as an input.
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Compounding results in a greater accumulated sum than simple return methods.
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Present value reflects the value today of future sums.
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Raising the discount rate increases the present value of a future sum.
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Future value is calculated by discounting cash flows to the present.
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The lump sum today is considered more valuable than a future sum due to fewer compounding periods.
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A regular annuity involves payments made at the beginning of the period.
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An annuity due has a lower value than a regular annuity because it has less compounding.
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The Rule of 72 estimates how long it takes for an investment return to double based on the investment return percentage.
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Future value is calculated using today's dollars adjusted for inflation.
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Failing to account for inflation can lead to a decrease in the purchasing power of money over time.
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Jason's investment of $14,000 today will yield a compounded annual return of 13% in 10 years.
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It would take approximately 19 years for an investment to triple in value at a 6 percent annual return.
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Marcy invests $3,000 a year for her daughter's college education, assuming a return of 5 percent per year.
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The present value of $3 when earning a 6 percent rate for 19 years is $1.
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If Jason waits 10 years to receive his $48,000, he will have lost money compared to his initial investment due to inflation.
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Inflation decreases the purchasing power of money over time.
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Investing a fixed sum annually into an annuity will result in a lower total amount compared to a lump sum investment.
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Jason's compounded annual return from his $14,000 investment will be 6% after 10 years.
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The future value of a present sum of money grows at a constant rate over time.
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The internal rate of return does not consider the timing of cash flows.
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The present value of a future cash flow decreases as inflation increases.
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An annuity due involves payments made at the end of each period.
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The internal rate of return is the interest rate that equates the present value of cash inflows to the present value of cash outflows.
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Future value calculations consider the effects of compounding interest over time.
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An investment earning 6 percent for 7 years would result in a future value that is less than the original sum invested.
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What annual return would Jason achieve if he invests $14,000 today to receive $48,000 in 10 years?
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How many years would it take for an investment of $1 to triple at an annual return of 6%?
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Which of the following best describes the process of earning interest on previously earned interest?
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If Marcy deposits $3,000 annually into an investment with a return of 9%, what type of investment is she making?
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What does the internal rate of return represent?
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What effect does inflation have on the purchasing power of money over time?
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How do annuities generally differ from lump sum investments?
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What does the internal rate of return (IRR) indicate?
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What is the future value of an investment?
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If the discount rate increases, what happens to the present value of a future cash sum?
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Study Notes
Time Value of Money Concepts
- "Money income" is also referred to as nominal income, which includes both purchasing power and inflation impact.
- The Rule of 72 serves as a quick formula to estimate the time needed for an investment to double, by dividing 72 by the annual rate of return.
- Annuity refers to a series of payments received over time, typically at regular intervals, such as monthly or quarterly.
- Internal Rate of Return (IRR) is defined as the interest rate that makes the net present value (NPV) of all cash flows equal to zero.
- A loan's annual percentage rate (APR) indicates the total cost of borrowing, expressed as a percentage of the loan amount, including interest and fees.
Financial Calculators and Terminology
- The hp12c is a popular financial calculator known for its efficiency in computing time value of money (TVM) problems.
- Basic keys on financial calculators typically include N (number of periods), I/Y (interest rate per year), PV (present value), PMT (payment amount), and FV (future value).
- Compound interest is calculated at intervals, meaning it accumulates on both the original principal and previously earned interest.
Overview of Time Value of Money
- Compounding involves earning interest on both the initial principal and the accumulated interest, leading to enhanced future values over time.
- Assessing the value of money at different points is crucial for making informed investment decisions, as it incorporates expected returns and mitigates erroneous assumptions.
Present and Future Value
- Present Value (PV) represents today's worth of cash flows to be received in the future, calculated by discounting future cash flows at an appropriate rate of return.
- Future Value (FV) refers to the accumulated amount at the end of a specific time period, derived from compounding existing cash flows.
Important Concepts
- The required rate of return reflects the expected earnings from investments with similar risk profiles.
- Increasing the discount rate leads to a decrease in present value, as alternative investments may yield better returns, reducing the attractiveness of future sums.
Financial Calculations and Scenarios
- PV Example: To find the present value of a 20,000sumreceivedafter6yearsatan820,000 sum received after 6 years at an 8% discount rate, PV calculates to 20,000sumreceivedafter6yearsatan812,603.
- FV Example: An investment of 18,000at618,000 at 6% interest for 7 years grows to 18,000at627,065.
- Annual Return Calculation: Depositing 14,000todaycouldyield14,000 today could yield 14,000todaycouldyield48,000 in 10 years, resulting in an annual return of 13%.
- Time to Triple Value: At a 6% return, it takes approximately 19 years for $1 to triple in value.
- Accumulation Example: If Marcy deposits 3,000annuallyat93,000 annually at 9% for 16 years, she will accumulate about 3,000annuallyat999,010 for her daughter's education.
Valuing Annuities and Payments
- Investment Bid: For receiving 1,500annuallyfor40yearswithan111,500 annually for 40 years with an 11% required return, the present value is calculated at 1,500annuallyfor40yearswithan1113,427.
- Annuity Assessment: Ann can expect a 10.5% return on an investment costing 180,000fora180,000 for a 180,000fora20,000 annual payment over her expected lifespan of 29 years.
- Savings Timeline: It takes 18 years for 2,000annuallyat62,000 annually at 6% interest to reach 2,000annuallyat660,000 total savings.
Debt Payment Calculation
- For a $50,000 debt with 12% interest to be repaid over 4 years, annual payment requirements must account for both principal and interest obligations.
Investment Concepts
- Money has a lower present value in the future than today; investing today yields a higher future value.
- Regular annuities involve payments at the end of each period; annuity dues have payments due at the beginning, benefiting from an extra period of compounding.
Annuities
- Annuity due example: annual retirement contributions on January 1.
- Regular annuity example: payments received on December 31.
- Annuities due generally hold higher values due to additional compounding.
Rate of Return
- Rate of return reflects the gains received from an investment.
- Inflation-adjusted returns take into account the cost of living, crucial for financial planning to ensure future purchases retain their value.
The Rule of 72
- A quick tool to estimate how long it will take for an investment to double based on the interest rate.
Future Value Calculation
- Future value represents what a set amount of money will be worth, factoring in inflation.
- Future Value Formula: Cash Flow x (1 + interest rate) ^ number of periods.
Inflation Impact
- Failing to account for inflation can lead to a significant decrease in purchasing power over time.
Compounding Examples
- In a case study, 14,000investedtodaypromises14,000 invested today promises 14,000investedtodaypromises48,000 in 10 years with an annual return of 13%.
- To triple a dollar at a 6% return takes approximately 19 years.
Yearly Contributions
- For a college fund, contributions of $3,000 annually at a 9% return supports growth.
- Differences in future value are evident when comparing contributions at the beginning vs. end of the period due to compounding timing.
Compounding Frequency
- 10,000at1210,000 at 12% interest yields 10,000at1211,200 compounded annually and 11,268.25compoundedmonthly;adifferenceof11,268.25 compounded monthly; a difference of 11,268.25compoundedmonthly;adifferenceof68.25.
Net Present Value (NPV)
- NPV considers future cash flows discounted back to present value for investment decisions.
- Example: A cash flow series from an investment indicated a net present value of -$5,882 at an 8% discount rate.
Nominal vs. Real Returns
- Salary growth at 4% versus 3% inflation results in a 1% real rate of return over five years.
- Future salary projections demonstrate increases in both nominal and real values.
Investment Returns
- A 30,000investmentreturned30,000 investment returned 30,000investmentreturned10,000 in Year 2, 8,000inYear3,8,000 in Year 3, 8,000inYear3,11,000 in Year 4, and $9,000 in Year 5, demonstrating the importance of tracking returns over investment lifespans.
Internal Rate of Return (IRR)
- Considers the time value of money and cash flows.
- Often used to evaluate the profitability of capital expenditures.
Present Value Calculation
- Present Value of 20,000tobereceivedin6yearsatan820,000 to be received in 6 years at an 8% discount rate is 20,000tobereceivedin6yearsatan812,603.
Future Value Calculation
- An investment of 18,000ata618,000 at a 6% interest rate compounded over 7 years grows to 18,000ata627,065.
Compounded Annual Return
- To receive 48,000in10yearsfroma48,000 in 10 years from a 48,000in10yearsfroma14,000 deposit today, the compounded annual return is 13%.
Time to Triple Investment
- With a 6% rate of return, it takes approximately 19 years for an investment of $1 to triple in value.
Savings for Education
- Marcy deposits 3,000annuallyintoaninvestmentat93,000 annually into an investment at 9% for 29 years to save 3,000annuallyintoaninvestmentat920,000 for her daughter's college, achieving a return of 10.5%.
Years to Accumulate Savings
- Saving 2,000ayearata62,000 a year at a 6% interest rate will accumulate to 2,000ayearata660,000 in about 18 years.
Debt Payment Calculation
- Aaron's $50,000 debt at a 12% interest rate, paid off over 4 years, requires annual payments that account for both interest and principal.
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Test your knowledge of the Time Value of Money with this engaging crossword puzzle. Challenge yourself with terms and concepts related to financial income and returns. Suitable for students studying finance or anyone interested in economic principles.
