Podcast
Questions and Answers
What are the two types of factors involved in single payment factor calculations?
What are the two types of factors involved in single payment factor calculations?
- Present value (P) and Future value (F) (correct)
- Future value (F) and Annual value (A)
- Present value (P) and Annual value (A)
- Interest rate (i) and number of periods (n)
In standard factor notation (P/F, i, n), the letter to the left of the slash represents what is given.
In standard factor notation (P/F, i, n), the letter to the left of the slash represents what is given.
False (B)
Using spreadsheet notation, what formula is used to calculate the present value P?
Using spreadsheet notation, what formula is used to calculate the present value P?
=PV(i%,n,,F)
An individual deposits $8,000 into an account that pays an interest rate of 6% per year. Approximately, how much will be in the account after 8 years?
An individual deposits $8,000 into an account that pays an interest rate of 6% per year. Approximately, how much will be in the account after 8 years?
The uniform series factors involve ___ and ___.
The uniform series factors involve ___ and ___.
What condition must be met for cash flow to be considered a uniform series?
What condition must be met for cash flow to be considered a uniform series?
When calculating P using the formula P = A(P/A, i, n), the present value P is two periods ahead of the first A value.
When calculating P using the formula P = A(P/A, i, n), the present value P is two periods ahead of the first A value.
A company anticipates earning an extra $3,000 per year by upgrading its equipment. At an interest rate of 7% per year, how much can the company afford to spend now to break even over a 4 year project period?
A company anticipates earning an extra $3,000 per year by upgrading its equipment. At an interest rate of 7% per year, how much can the company afford to spend now to break even over a 4 year project period?
When using uniform series factors involving F/A and A/F, how does the time of the future value, F, relate to the time of the last annuity payment, A?
When using uniform series factors involving F/A and A/F, how does the time of the future value, F, relate to the time of the last annuity payment, A?
Using linear interpolation will produce the most accurate result for untabulated values.
Using linear interpolation will produce the most accurate result for untabulated values.
An engineer implements a new strategy that saves $12,000 per year for the company. At an interest rate of 9% per year, how much will the savings amount to in 6 years?
An engineer implements a new strategy that saves $12,000 per year for the company. At an interest rate of 9% per year, how much will the savings amount to in 6 years?
Which of the following is NOT a way to find factor values when i or n are not in standard interest tables?
Which of the following is NOT a way to find factor values when i or n are not in standard interest tables?
In an arithmetic gradient series, by how much does the magnitude of the cash flows change each period?
In an arithmetic gradient series, by how much does the magnitude of the cash flows change each period?
The gradient, G, in an arithmetic gradient starts between periods 0 and 1.
The gradient, G, in an arithmetic gradient starts between periods 0 and 1.
The present value equation for an arithmetic gradient is P = G(P/G, i, n). What do P, G, and i represent in this equation?
The present value equation for an arithmetic gradient is P = G(P/G, i, n). What do P, G, and i represent in this equation?
An investment yields $500 in year 1, and increases by $50 each year through year 5. At an interest rate of 8% per year, what is the present worth of the investment?
An investment yields $500 in year 1, and increases by $50 each year through year 5. At an interest rate of 8% per year, what is the present worth of the investment?
Arithmetic gradients have two distinct parts, a _______ and a gradient amount.
Arithmetic gradients have two distinct parts, a _______ and a gradient amount.
Which of the following is true for geometric gradients?
Which of the following is true for geometric gradients?
Tables are provided for geometric factors.
Tables are provided for geometric factors.
At an interest rate of 9% per year, what is present worth if the income increases at a of rate of 2% through year 5. In year one, the income is $1000?
At an interest rate of 9% per year, what is present worth if the income increases at a of rate of 2% through year 5. In year one, the income is $1000?
In a geometric gradient, if g is negative you must change signs in front of both ___ values.
In a geometric gradient, if g is negative you must change signs in front of both ___ values.
Which equation is used to solve for an unknown interest rate, i?
Which equation is used to solve for an unknown interest rate, i?
To find an unknown n (number of periods), it is never necessary to use a trial and error solution or interpolation in interest tables.
To find an unknown n (number of periods), it is never necessary to use a trial and error solution or interpolation in interest tables.
With the increasing availability of powerful computation devices, why is it still important to understand the underlying concepts of time value of money calculations, rather than relying solely on software?
With the increasing availability of powerful computation devices, why is it still important to understand the underlying concepts of time value of money calculations, rather than relying solely on software?
Name at least two methods to find factor values for untabulated interest rates or number of periods.
Name at least two methods to find factor values for untabulated interest rates or number of periods.
What distinguishes an arithmetic gradient from a geometric gradient in the context of cash flow analysis?
What distinguishes an arithmetic gradient from a geometric gradient in the context of cash flow analysis?
In F/A and A/F factors, F is in ______ period as last A.
In F/A and A/F factors, F is in ______ period as last A.
Match the factor with the best description:
Match the factor with the best description:
A manufacturing company is considering an investment in new equipment that is expected to generate $25,000 of cost savings each year for the next 7 years. If the company's required rate of return is 11%, what is the maximum price the company should be willing to pay for the equipment?
A manufacturing company is considering an investment in new equipment that is expected to generate $25,000 of cost savings each year for the next 7 years. If the company's required rate of return is 11%, what is the maximum price the company should be willing to pay for the equipment?
In uniform series calculations, the cash flow amount can be different each period as long as the payments are consecutive.
In uniform series calculations, the cash flow amount can be different each period as long as the payments are consecutive.
When calculating the future value F using the formula F = A(F/A, i, n), where is F in relationship to the last payment A?
When calculating the future value F using the formula F = A(F/A, i, n), where is F in relationship to the last payment A?
Flashcards
Single Payment Factors
Single Payment Factors
Factors used when a single payment is involved and relate present & future values.
Factors
Factors
Terms in parentheses or brackets.
Standard Factor Notation
Standard Factor Notation
Factors represented in a format like (F/P, i, n).
Uniform Series
Uniform Series
Signup and view all the flashcards
Uniform Series Assumptions
Uniform Series Assumptions
Signup and view all the flashcards
P Relative to First A Value
P Relative to First A Value
Signup and view all the flashcards
F Relative to Last A Value
F Relative to Last A Value
Signup and view all the flashcards
Find Factor Values
Find Factor Values
Signup and view all the flashcards
Arithmetic Gradient
Arithmetic Gradient
Signup and view all the flashcards
Base Amount
Base Amount
Signup and view all the flashcards
Gradient Start Period
Gradient Start Period
Signup and view all the flashcards
Location of PG
Location of PG
Signup and view all the flashcards
Geometric Gradients
Geometric Gradients
Signup and view all the flashcards
Solve for unknown i and n
Solve for unknown i and n
Signup and view all the flashcards
Study Notes
Learning Outcomes
- The key topics in this chapter are F/P and P/F Factors, P/A and A/P Factors, F/A and A/F Factors, Factor Values, Arithmetic Gradient, Geometric Gradient, and finding i or n.
Single Payment Factors (F/P and P/F)
- Single payment factors involve only P (present value) and F (future value).
- Formulas Include:
- F = P(1 + i)^n
- P = F[1 / (1 + i )^n]
- Terms in parentheses or brackets are called factors; values are in tables for i and n values.
- Factors are shown using standard factor notation such as (F/P,i,n), with the letter to the left of the slash being what is sought, and the letter to the right is what is given.
F/P and P/F for Spreadsheets
- The future value F is calculated using the FV function: = FV(i%,n,,P).
- The present value P is calculated using the PV function: = PV(i%,n,,F).
- Double commas are needed in each function.
Uniform Series Involving P/A and A/P
- The uniform series factors that involve P and A are derived when:
- Cash flow occurs in consecutive interest periods.
- The cash flow amount is the same in each interest period.
- Formulas include:
- P = A(P/A,i,n)
- A = P(A/P,i,n)
- P is one period ahead of the first A value.
Uniform Series Involving F/A and A/F
- The uniform series factors that involve F and A are derived when:
- Cash flow occurs in consecutive interest periods.
- Last cash flow occurs in the same period as F.
- Formula Includes:
- F = A(F/A,i,n)
- A = F(A/F,i,n)
- F takes place in the same period as the last A.
Factor Values for Untabulated i or n
- Three ways to find factor values for untabulated i or n values:
- Use formula.
- Use spreadsheet function with corresponding P, F, or A value set to 1.
- Linearly interpolate in interest tables.
- Formula or spreadsheet function is fast and accurate, while interpolation is only approximate.
Arithmetic Gradients
- Arithmetic gradients change by the same amount each period.
- The cash flow diagram for the PG of an arithmetic gradient has G starting between periods 1 and 2, not between 0 and 1.
- Cash flow in year 1 is usually not equal to G and is handled separately as a base amount.
- PG is located two periods ahead of the first change that is equal to G.
Typical Arithmetic Gradient Cash Flow
- The total present worth (PT) of a cash flow with an arithmetic gradient and a base amount can be calculated as: PT = PA + PG = base amount(P/A,i%,n) + G(P/G,i%,n).
Converting Arithmetic Gradient to A
- An arithmetic gradient can be converted into an equivalent A value using G(A/G,i,n).
- The general equation when a base amount is involved is:
- A = base amount + G(A/G,i,n)
- For decreasing gradients:
- A = base amount - G(A/G,i,n).
Geometric Gradients
- Geometric gradients change by the same percentage each period.
- There are no tables for geometric gradients; use the following equation for g ≠ i: Pg = A₁{1- [(1+g)/(1+i)]^n}/(i-g), where A₁ = cash flow in period 1 and g = rate of increase.
- If g = i, Pg = A₁n/(1+i).
- Note: in g is negative, change signs in front of both g values.
Unknown Interest Rate i
- Unknown interest rate problems involve solving for i, given n and 2 other values (P, F, or A), often requiring a trial and error solution or interpolation in interest tables.
- Set up an equation with all symbols involved and solve for i.
Unknown Recovery Period n
- Unknown recovery period problems involve solving for n, given i and 2 other values (P, F, or A), and often require a trial & error solution or interpolation in interest tables.
- Set up the equation with all symbols and solve for n.
Summary of Important Points
- In P/A and A/P factors, P is one period ahead of the first A.
- In F/A and A/F factors, F is in the same period as the last A.
- The best way to find untabulated factor values is to use a formula or spreadsheet.
- For arithmetic gradients, gradient G starts between periods 1 and 2.
- An arithmetic gradient has 2 parts: a base amount (year 1) and a gradient amount.
- For geometric gradients, gradient g starts between periods 1 and 2.
- In the geometric gradient formula, A₁ is the amount in period 1.
- To find the unknown i or n, set up an equation involving all terms and solve for i or n.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
