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 3 years ago

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