which perpetuity do you prefer? annual payments of $10.00 starting a year from now with a...

which perpetuity do you prefer? annual payments of $10.00 starting a year from now with a time value of money of 12 percent per year compounded quarterly? or quarterly payments starting three months from now that will increase by one percent per quarter? the first payment is $1.50 and your time value of money is 12 percent per year. please show your work.

Expert Solution

Option 1
$10 starting a year from now
Interest rate	12.00%



PV of perpetuity
	Coupon/interest Rate
	10/0.12
	83.33







PV of perpetuity of $ 83.33

	PV_p/(1+r)^t

PV_p	Present Value of perpetuity of $10
	$83.33
	83.33/(1+0.12)¹
	74.40

Therefore the present value of this option is $74.40


Option 2
$1.5 per quarter increasing @1% per quarter
Quaterly Interest Rate	12/4
	3.00%
Annuity Growth rate	1.00%
PV of increasing annuity	Coupon payment/(interest rate - Growth Rate)
	1.5/(0.03-0.01)
	75
PV of today

PV of perpetuity of $ 75	PV_p/(1+r)^t
	75/(1+0.03)¹
	72.82

Therefore the present value of this option is $72.82

Thus the perpetuity of $10 per year one year from now should be preferred because its Present value is greater.

jeff jeffy answered 2 years ago

A perpetuity will make annual payments with the first payment coming 12 years from now. The...

A perpetuity will make annual payments with the first payment coming 12 years from now. The first payment is for $4500, and each payment that follows is $150 dollars more than the previous one. If the effective rate of interest is 4.8%, what is the present value of the perpetuity?

Jeff bought an increasing perpetuity due with annual payments starting at 100 and increasing by 10...

Jeff bought an increasing perpetuity due with annual payments starting at 100 and increasing by 10 each year until the payment reaches $250; the payments remain at $250 thereafter. The annual effective rate is 6%. Determine the present value of this perpetuity.

Your bank offers you a 10-year loan, with annual payments of $10,000 starting 1 year from...

Your bank offers you a 10-year loan, with annual payments of $10,000 starting 1 year from today. If the annual interest rate is 6.7%, compounded annually, what is the principal amount of the loan?

A perpetuity makes payments at the end of each year at an annual effective rate of...

A perpetuity makes payments at the end of each year at an annual effective rate of 3.4%. The payment pattern is 3,2,1 (at the end of years 1, 2 and 3) and this pattern repeats for the balance of the perpetuity. Calculate the present value of the perpetuity at the beginning of the rst year. Please show all work.

Charlotte will receive quarterly payments from a perpetuity, beginning now. The amount of the first payment...

Charlotte will receive quarterly payments from a perpetuity, beginning now. The amount of the first payment is 100, and each subsequent payment is larger than the previous payment by an amount X. Assuming an interest of 6% convertible monthly, the present value of this perpetuity is $20,000. Find X.

An individual makes six annual deposits in a savings account starting one year from now that...

An individual makes six annual deposits in a savings account starting one year from now that pays interest at a rate of 10% compounded quarterly. Ten years after the last deposit, a withdrawal of $10,000 per year for 10 years is withdrawn from the account. How much would be the six annual deposits? Solve step by step and draw cash flow diagram.

Gustav owns a perpetuity which pays 200 per year starting at the end of year 2....

Gustav owns a perpetuity which pays 200 per year starting at the end of year 2. Ingrid owns a perpetuity that pays deposits X at the end of each 6 months, beginning 6 months from now. Assume a nominal annual interest rate of 8%. For what value of X is the present value of the two perpetuities equal.

consider a financial asset that pays a perpetuity of $600 per year, starting one year from...

consider a financial asset that pays a perpetuity of $600 per year, starting one year from now. The discount rate is 9%. If the required investment today is $4000, what is the net present value of the investment

You will be receiving the following payments from a friend -- $100 one year from now,...

You will be receiving the following payments from a friend -- $100 one year from now, $145 two years from now, and $125 three years from now. Calculate the present value of these payments given that the rate of interest is 6% per year. Also, calculate the future value of the payments in year three.

A perpetuity will pay $1,025 per year, starting five years after the perpetuity is purchased

A perpetuity will pay $1,025 per year, starting five years after the perpetuity is purchased. What is the present value of this perpetuity on the date that it is purchased, given that the interest rate is 9%. Show your work or inputs.

Question