Finance_Chap 2

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Questions and Answers

What is the formula for calculating the future value of an ordinary annuity?

$FV(A) = \frac{A(1 + r)^n}{r}$

$FV(A) = \frac{A(1 + r)^n - 1}{r}$ (correct)

$FV(A) = A \cdot (r + 1)^{n} - 1$

$FV(A) = \frac{A(r + 1)^n - 1}{r}$

In the context of present value calculations, what does an annuity due signify?

Payments are variable and depend on the interest rate.

Payments cannot be adjusted once set.

Payments are made at the beginning of each period. (correct)

Payments occur at the end of each period.

How does the present value formula for an annuity due differ from that of an ordinary annuity?

It uses a longer time frame.

It is the same as the ordinary annuity formula.

It has an additional factor of $1+r$ in the numerator. (correct)

It eliminates the interest rate variable.

When computing future value, how does one account for payments made at the beginning of the period?

By multiplying the last calculated value by $1 + r$. Signup and view all the answers

What is the characteristic of payments in a stream of cash flows considered as an annuity?

They are equal and occur regularly over specified periods. Signup and view all the answers

Which formula is used to calculate the present value of an ordinary annuity?

$PV(A) = A \cdot \frac{1 - (1 + r)^{-n}}{r}$ Signup and view all the answers

If you deposit $1,000 annually at the end of each year at an interest rate of 7 percent for five years, what do you calculate?

The future value of the annuity. Signup and view all the answers

Which of the following is NOT a common practice for calculating the future value of cash flows?

Using current cash flow amounts only. Signup and view all the answers

What differentiates a lump-sum investment from an annuity?

A lump sum is made once while annuities are periodic payments. Signup and view all the answers

What determines the value of an annuity?

The interest rate and total periods of cash flow. Signup and view all the answers

What is the main criterion to use when there is a conflict in ranking two projects?

Always go for the project with the higher NPV Signup and view all the answers

What is the correct interpretation of the principle of asset valuation?

An asset should be valued based on discounted future cash flows using the required rate of return Signup and view all the answers

What is the present value (PV) of an asset that provides $5,000 cash flow per year for 4 years at a 6% required rate of return?

$17,325 Signup and view all the answers

Which of the following best describes an annuity in financial terms?

A series of equal cash flows occurring at the end of each period Signup and view all the answers

Why should decisions not be based solely on the internal rate of return (IRR)?

IRR assumes reinvestment at a high rate which is unrealistic Signup and view all the answers

What will be the sales figure for the P.J.Cramer Company at the end of six years if it grows at a compound rate of 20 percent annually from $500,000?

$1,244,640 Signup and view all the answers

What is the present value of receiving $1,000 at the end of 10 years with an opportunity rate of 10 percent compounded annually?

$385.54 Signup and view all the answers

Vernal Equinox will borrow $10,000 and repay $16,000 after three years. What is the implicit compound annual interest rate rounded to the nearest whole percent?

20% Signup and view all the answers

What is the approximate compound annual interest rate if a $1,000 savings bond is worth $1 million in 100 years?

5% Signup and view all the answers

What is the effective annual interest rate for an investment paying a nominal annual rate of 9.6% compounded quarterly?

9.99% Signup and view all the answers

Study Notes

Asset Valuation

Asset valuation process is finding fair value of an asset, at which it should be purchased or sold
Key principle of asset valuation: Future cash flows of an asset are discounted to the present value, using investor's required rate of return
Asset Fair Value = Σ[ (Ct) / (1+r)^t]
- Ct = Cash flow at time t
- r = Required rate of return
- t = Number of years
Example:
- Asset provides $5,000 cash flow for 4 years at 6% required rate of return
- Fair Value is $17,325, which is the present value of all future cash flows

Annuity

Annuity is a series of equal cash flows occurring over a specified number of periods
- CF1 = CF2 = CF3 = ... = CFn = A
Ordinary Annuity has payments at the end of each period
- Future Value (FV) = A [(1+r)^n - 1] / r
  - A = Annuity payment
  - r = Interest rate
  - n = Number of periods
- Present Value (PV) = A [1 - 1/(1+r)^n] /r
Annuity Due has payments at the beginning of each period
- Future Value (FV) = A(1+r) [(1+r)^n - 1] / r
- Present Value (PV) = A(1+r) [1 - 1 / (1+r)^n] / r
- Annuity due PV and FV are higher than ordinary annuity
- This is because payments are made earlier and have more time to accumulate interest

Perpetuity

Perpetuity is an ordinary annuity with payments continuing forever
Present value (PV) = A / r
- A = Annuity payment
- r = Interest rate
- This formula is used to find the present value of a perpetual stream of cash flows

Growing Perpetuity

Growing perpetuity has payments growing at a constant rate forever
Present Value (PV) = C1 / (r-g)
- C1 = Cash flow at time t = 1
- r = Discount rate
- g = Annual growth rate of cash flow

Future Value (FV)

P.J.Cramer Company had sales of $500,000 this year.
Sales are expected to grow at a compounded rate of 20% for the next six years.
Determining future sales requires calculating FV for each year.

Present Value (PV)

You will receive $1,000 in 10 years.
Your opportunity rate is 10%.
Interest can be compounded annually, quarterly, or continuously.
Calculating PV for each compounding method is required.

Implicit Compound Annual Interest Rate

Vernal Equinox borrows $10,000 for three years.
He agrees to pay back $16,000 at the end of three years.
This represents an implicit interest rate that needs to be calculated.

Implied Compound Annual Interest Rate

A 1,000savingsbondisexpectedtobeworth1,000 savings bond is expected to be worth 1,000savingsbondisexpectedtobeworth1 million in 100 years.
Calculating the implied compound annual interest rate is necessary.

Effective Annual Interest Rate (EAR) and Annual Percentage Rate (APR)

An investment promises a nominal annual interest rate of 9.6%.
EAR needs to be calculated for different compounding frequencies: annually, semiannually, quarterly, monthly, daily, and continuously.
EAR represents the actual interest earned after accounting for compounding.

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Description

Test your understanding of asset valuation and annuities with this quiz. Explore key concepts such as future cash flows, present value calculations, and the differences between ordinary and annuity due. Challenge yourself with practical examples and formulas to solidify your knowledge.