Question

Macroeconomics

Christina wins the lottery and seeks your advice as to whether or not she should take a lump sum payment or smaller payments over many years. The lump sum is a check for $20M today. The payments are $40M paid out as $1.5M per year for 20 years. Financially, which is the better deal if the interest rate is 5.2%? Show your work and then interpret your results.

Answer 1

Payment done in one lump sum = $20 M

Annual payment per year for 20 years = $1.5 M

Time = 20 years

R = 5.2%

Then,

PW of the annual payment = 1.5*(1-1/(1+5.2%)^20)/5.2%

PW of the annual payment = $18.38 M

Since PW of annual payment of $1.5 M for 20 years is only $18.38 M and it is less than the $20 M, paid as one time lump sum payment done at present, then it is wise and good to opt for the $20 M one time lump sum payment.

It is not justified to go for the annual payment as it has lower value of PW than that of one time lump sum payment.