Question

Critical Thinking Questions

1. What is the Rule of 72?
2. What is Compounding/Discounting?
3. What is an annuity? Give one example of an annuity and of one which is not.
4. Explain the meaning of this statement: Annuity due differs from ordinary annuity. In case of annuity due, show the required change in the future value and present value equations.
5. Construct an amortization schedule that includes all the required information and illustrate the relationship between the elements in this schedule.
6. Why are cash management and cash budgeting important to a company’s survival?
7. In what ways can a company handle temporary shortfalls in cash balances?
8. What can the companies do when they have surplus cash?
9. When does the cash conversion cycle of a firm start and when does it end?
10. A common method that we use to determine the appropriate inventory levels is the economic order quantity (EOQ) model. Explain what this model is.

Answer 1

1]

As per rule of 72, the number of years required for $1 to double in value is approximately (72 / interest rate).

For example, at 8% interest rate, the number of years required for $1 to double in value is (72 / 8%) = 9 years

This is verified as below :

future value = present value * (1 + interest rate)^{number of years}

$2 = $1 * (1 + 8%)⁹

2   = 2

2]

Compounding is when the interest in each period is added to the original principal such that the principal at the end of each period is increased. That is, the original principal does not remain fixed (as in the case of simple interest) but keeps increasing as the interest in each period is added to the original principal. This leads to "compound growth" which results in a much higher interest in each subsequent year.

Discounting is the opposite of compounding. A future value is discounted such that its present value is calculated after the effect of compound interest. That is, the present value, if invested at compound interest, results in the ending future value

3]

An annuity is a series of payments that occur periodically (yearly, monthly, weekly etc).

For example, a sum of $100 received after 1 year is not an annuity, but a lump sum.

A series of $100 payments received every month for 12 months is an annuity

4]

In an ordinary annuity, each payment is received at the end of the period.

In an annuity due, each payment is received at the beginning of the period.

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

Future value of annuity due = P * (1 + r) * [(1 + r)ⁿ - 1] / r,

PV of annuity = P * [1 - (1 + r)^-n] / r,

PV of annuity due = P + [P * [1 - (1 + r)^-(n-1)] / r]

where P = periodic payment

r = interest rate per period

n = number of periods