Question

In 250 words, describe the differences to valuing the FV and PV of lump sums, ordinary annuities, annuities due, and unequal cash flows. What happens to the PV and FV of each type of cash flow when interest rates rise or the time periods decrease? Please be very descriptive in how the FV and PV are different of a lump sums, ordinary annuities, annuities due, and unequal cash flow.

Answer 1

	Future value	Present value
Lump sum	The lump sum amount is itself the future value.	The lump sum is discounted at given discount rate to arrive at present value. Let say n be time horizon r be the rate so present value of cash flow will be:- CFn =CFn/(1+r)^n
Ordinary annuity	For computing future value we compute the future value of given cash flows. Let say n be time horizon r be the rate so future value of cash flow will be:- CF1 = CF1*(1+r)^(n-1) CF2 = CF2*(1+r)^(n-2) And so on. All the future value are added to arrive at total future value.	For computing the present value we discount the cash flow to present value. Let say n be time horizon r be the rate so present value of cash flow will be:- CF1 = CF1/(1+r)^1 CF2 = CF2*(1+r)^2 And so on. All the present value are added to arrive at total future value.
Annuity due	In annuity due the first cash flow is made today. So future value will be calculated as follows:- Let say n be time horizon r be the rate so future value of cash flow will be:- CF0 = CF1*(1+r)^(n-0) CF1 = CF2*(1+r)^(n-1) And so on. All the future value are added to arrive at total future value.	In annuity due the first cash flow is made today. Let say n be time horizon r be the rate so present value of cash flow will be:- CF0 = CF0/(1+r)^0 CF1 = CF1/(1+r)^1 CF2 = CF2*(1+r)^2 And so on. All the present value are added to arrive at total future value.
Unequal cash flows	Future value is calculated for each cash flows. CFt = CFt *(1+r)^(n-t) n= total time horizon t= cash flow at time t All the future value are added to arrive at total future value.	Present value is calculated for each cash flow. CFt = CFt/(1+r)^t n= total time horizon t= cash flow at time t All the present value are added to arrive at total present value.

Interest rate rises

When interest rate rises the future value will increase and present value will fall in all the case.

Time period decrease

When time period decrease the future value will decrease and present value will rise in all the case.