Question

1. Explain why cash flows occurring at different times must be adjusted to reflect their value as of a common date before they can be compared, and be able to calculate the present value and future value for problems with multiple cash flows.
2. Explain how an ordinary annuity differs from an annuity due and be able to calculate the present value and the future value of an ordinary annuity and annuity due.
3. Explain what a perpetuity is and where we see them in business and be able to calculate the value of a perpetuity.
4. Explain what are growing annuities and perpetuities, as well as their applications in business, and be able to calculate the present value and future value of growing annuities and the present value of perpetuities.
5. Explain the concept of the effective annual interest rate (EAR) and be able to calculate the EAR.

Answer 1

1.

In Finance, money have time value. which simply state the most basic financial principle dollar today is worth more than dollar tomorrow. So cash flow occuring at different points in time have different values which need to be converted to at one point in time ( usually dollar today) for comparison. In that way we can calculate present value of cash flow which means cash flow occuring at different points in future time converted in terms of dollar today. Future value is value of cash flow at some point in time of future in terms of dollar of at that point of time.

Present value = C/(1+r)^t

Future value = C*(1+r)^t

(c= cash flow)

2. Ordinary annuity and annuity due is different in occurence of their payment, which means in ordinary annuity payment occur at end of the period and in annuity due payment occur at begining of the period. So formula for caculating ordinary annuity and annuity due are as follows.

Present value of Annuity due is calculated by multiplying (1+r) with ordinary annuity.

3. perpetuity is a type of secuirty which pays an amount for infinite period of time.in technical financial terms a constant cash flow occuring for infinite period of time. British consols are most famous exampls fo perpetuity instrument. In today's business use of perpetuity calculation is in real estate sector, government bonds, preffered stocks, retirement plans, stocks etc. In calculation of stock price we use perpetuity formula for discounting as we assume business will go on forever.

Present value of perpetuity = C/r

4. when perpetuity is growing, which means payment occur at every subseqeunt period is increased from previous one. for exapmle 1 payment is 100, second is 104, third 108.16. so here groeth rate is 4%. Such kind of perpetuity is used for endowment doations. It is also used in calculatiing value of stocks which give dividend at growing rate.

Annuity growing is a series of payment for specified number of period which grow after every payment. Payment occur will grow over the years. It is applied  for lease payments, retirement plans and many other investment and saving plans.

For caculation of present value we can just multiply present value with (1+r)^t

5. Effective annual interest rate is real rate which take into account the effects of compounding over the period of time. when we compound yearly, effective annual interest rate is same but when we compound monthly, weekly, qarterly etc. effective annual interest rate differ. Formula of same is

i = nominal rate

n = compounding period