Part B/C Time value and discount rates Personal Finance s guaranteed by the stat
ID: 1172453 • Letter: P
Question
Part B/C Time value and discount rates Personal Finance s guaranteed by the state in which you live, opportunities eist to sell the claim today for an mmedale single cash payment Problem You just won a lottery that promises to pay you $1,600,000 exactly 15 years trom today Because the $1,600,000 payment What is the least you wi sell your claim for it you can earm the folowing rates of return on sinstar knestments during the 15 year peniod (1)6% (2) 10% O: 14% b. Rewon part a under the assumption that the $1,500 000 payment wi be received in 20 rather than 15 years ?.Onthe 8 of youtndrgs n parts a and b dsats the ened of boete soe ofthe rate cium and the bmhe un·receet of Daymert on thie Dresent value of attu" sum h(1) The t you wil see your aam tyou can eam a rate of of 6% drng he 20-year ossO ound to honearest cent) (2) The leat you wEel yor dam tr tyou can earn a rato ofreurn of 10% ang he 20year perossO (Randtots nerstr.) 0) The least you w" sal your damfotyou can earn a rate ofreun ot 14% aring 20-rear proced] (Rent tone nearest cent) d ?? best answer below ) greater tme over which the opportunity cost acoles greater tme over wich the 000ounty cost appleExplanation / Answer
Answer b.
If interest rate is 6%:
Cash Inflow = $1,600,000
Period = 20 years
Present Value = $1,600,000 / 1.06^20
Present Value = $498,887.56
The least you will sell your claim for if you can earn a rate of return of 6% during the 20-year period is $498,887.56
If interest rate is 10%:
Cash Inflow = $1,600,000
Period = 20 years
Present Value = $1,600,000 / 1.10^20
Present Value = $237,829.80
The least you will sell your claim for if you can earn a rate of return of 6% during the 20-year period is $237,829.80
If interest rate is 14%:
Cash Inflow = $1,600,000
Period = 20 years
Present Value = $1,600,000 / 1.14^20
Present Value = $116,418.76
The least you will sell your claim for if you can earn a rate of return of 6% during the 20-year period is $116,418.76
Answer c.
As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies.