Question

You win the lottery! Your choices are Take a single payment of $20 million today. Take 40 payments of $1 million; first payment today and then $1 million at the start of every year for the next 39 years a) If the interest rate is 2% compounded annually, which would you prefer? b) If the interest rate is 10% compounded annually, which would you prefer? c) At what annually compounded interest rate would you be indifferent between the two?

Answer 1

Option 1

PV of payment = $ 20 Million

a)

Option 2

Number of payments (nper) = 40 payments

Payment amount (PMT) = $ 1 million

Rate = 2% pa

PV of payment (PV) = = $ 27,902,588.83

So Option 2 would be selected due to higher present value

b)

Option 2

Number of payments (nper) = 40 payments

Payment amount (PMT) = $ 1 million

Rate = 10 % pa

PV of payment (PV) = = $ 10,756,955.79

So Option 1 will be selected due to higher PV

c)

To be indifferent between the two options,

PV of the payment = 20,000,000

nper = 40

PMT = 1,000,000

Annual compounded interest rate (rate) =

= 4.21% pa compounded annually (indifferent between the two options)