Question

The present value of a stream of cash flows you expect to received will always increase when:

	a.	the interest rate is greater than zero and the number of compounding periods decrease.
	b.	the interest rate is zero and the number of compounding periods increase.
	c.	the interest rate is greater than zero and the number of compounding periods increase.
	d.	the interest rate is zero and the number of compounding periods decrease.

Answer 1

The correct option is a. The interest rate is greater that zero and the number of compounding period decreases.

Option b and d does not make sense as interest rates are 0, therefore the present value will always be equal to future cash flows. The compouding period will have no effect and the amount will neither decrease nor increase.

Let us understand other two options from example.

Suppose 100% is receivable at year 1, the compouding rate is 10%.

When compounded annually :

Present value = CashFlow/(1+Rate)^n = 100/(1+.10)^1 = 90.9091

When compounded semi-annualy, compounding period increases :

Present Value = Cash Flow/(1+Rate)^2 = 100/(1+.10)^2 = 82.64

Clearly, the present value of cash flow increases as the compouding period increases and interest rate is positive i.e. more than zero.

Hence, a is correct option.

If you have any doubt, you can ask me in the comment section.