Question

1.

Why is it not possible to determine the future value of a perpetual stream of cash flows? Can we determine the value of an annuity? Explain with an example

2.

You have just won first division in the State lottery andhave a choice betweenthree alternatives as to how your prize is to be received. You can get $100,000 now, or $10,000 per year in perpetuity, or $50,000 now and $150,000 at the end of 10 years. If the appropriate discount rate is 12% per annum, which option should you choose

Answer 1

1. Perpetuity means the stream of cash flow that has no end so it will not be ending at a specific point in the future, and hence the future value can only be calculated at a future date which is not available in case of perpetuity, and hence it is not possible to determine the future value of perpetual stream of cash flows.

YES, We can determine the value of an annuity as when it will be finishing of at a specific point in future like for example , it will be for 20 years and we will calculate the the future value at the end of the 20 year, but for Perpetual stream of cash flow does not have any end, and it will be received forever, so we cannot calculate the future value of perpetuity.

2. Value of perpetuity at present= (cash flow/interest)

= (10000/.12)=83333.33

Second alternative p.v= (150000/(1.12)^10= $54091.

I will select to receive 100000 now in first alternative.

I will select to receive 150,000 at the end of 10th year.