Question

1. What effect does increasing the required return have on the present value of a future amount? Why?
2. How are present value and future value calculations related?
3. What is the difference between an ordinary annuity and an annuity due? Which is more valuable? Why?
4. What are the most efficient way to calculate the present value of an ordinary annuity?
5. How can the formula for the future value of an annuity be modified to find the future value of an annuity due?
6. How can the formula for the present value of an ordinary annuity be modified to find the present value of an annuity due?
7. What is a perpetuity? Why is the present value of a perpetuity equal to the annual cash payment divided by the interest rate?

Answer 1

Question:

What effect does increasing the required return have on the present value of a future amount? Why?

Answer:

By increasing the required return , the Present Value decreases/lowers

This is because

Present Value is calculated as

PV = Future Value/ (1+ required return)^time period

So, if required return is increased, the Present Value decreases.

In other words, as the required return increases, the amount of interest is increased and hence less money is required to achieve the same future value.

Question:

How are present value and future value calculations related?

Answer:

The present value (PV) and future value(FV) calculations are inversely related.

Because,

PV = FV/ [(1+ required return)^time period]

and

FV = PV*[ (1+ required return)^time period]

Question:

What is the difference between an ordinary annuity and an annuity due? Which is more valuable? Why?

Answer:

Ordinary annuities is the ones in which the payments are made/ cash flows occur at the end of the period.

Annuity due is the ones in which the payments are made/ cash flows take place at the beginning of the period.

Annuity due is of more value, because the annuity due has higher present value as the payments are made sooner.

Also, in identical circumstances, annuity due will have a higher future value because the interest is being collected for an entire period longer.

Question:

What are the most efficient way to calculate the present value of an ordinary annuity?

Answer:

The most efficient way to calculate the present value of an ordinary annuity is to take the annual cash flow and multiply it by the corresponding factor.

Question:

How can the formula for the future value of an annuity be modified to find the future value of an annuity due?

Answer:

FV of ordinary annuity = CF *[ {(1+i)^n -1}/i]

FV of annuity due = CF *[ {(1+i)^n -1}/i] * (1+i)

CF = cash flow

n = time period

i= interest rate

From the above formulae we can see that by multiplying the future value of ordinary annuity with (1+ interest rate) we can get the future value of an annuity due. This is done in order to compensate for the additional period of interest each year.

Question:

How can the formula for the present value of an ordinary annuity be modified to find the present value of an annuity due?

Answer:

PV of ordinary annuity = CF *[ {1- (1+i)^-n }/i]

PV of annuity due = CF *[ {1- (1+i)^-n }/i] * (1+i)

CF = cash flow

n = time period

i= interest rate

From the above formulae we can see that by multiplying the present value of ordinary annuity with (1+ interest rate) we can get the present value of an annuity due . This is done in order to compensate for the additional period of interest each year.

Question:

What is a perpetuity? Why is the present value of a perpetuity equal to the annual cash payment divided by the interest rate?

Answer:

Perpetuity is the annuity with infinite stream of cash flows, i.e., the annuity lasts forever.

The present value of a perpetuity equal to the annual cash payment divided by the interest rate

This is because, perpetuity had fixed annual cash flows which are paid at equal duration and the time period is infinite. So, PV = Cash flow/ interest rate