Answer each of the following independent questions. Alex Meir recently won a lot
ID: 2342518 • Letter: A
Question
Answer each of the following independent questions. Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: () $74,000 cash immediately, (2) $26,000 cash immediately and a six-period annuity of $8,300 beginning one year from today, or (3) a six-period annuity of $15,000 beginning one year from today. (FV of $1, PV of $1, EVA of S1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Assuming an interest rate of 6%, determine the present value for the above options, which option should Alex choose? 2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2027 Weimer will make annual deposits of $140,000 into a special bank account at the end of each of 10 years beginning December 31, 2018. Assuming that the bank account pays 7% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 20277 Complete this question by entering your answers in the tabs below. Assuming an interest rate of 6%, determine the present value for the above options, which option should Alex choose? (Round your final answers to nearest whole dollar amount.) PV Option Option 1 Option 2 Option 3Explanation / Answer
Answer to question No.1
Three options are given, we should have to choose the best option and best option can be chosen as which option has the higher Present value of cash inflow.
so we need to first calcualte the present value of cash inflow of every option -
1st Option - Receive $ 47000 cash immediately its present value is $ 47000.
2nd Option - $ 26000 cash immediately and annuity of $ 8300 beginning one year from today (at the end of the year), means ordinary annuity
formula of PV of annuity = annuity*[1- (1+i)^-n]/(i)
where - annuity value/periodic payment = $ 8300
i - interest rate per period
n - no. of periods
= 8300*[1 - (1+0.06)^-6]/(0.06)
= 8300*[(1- 0.704961)]/(0.06)
= 8300*0.295039/(0.06)
= 2448.828/0.06
= 40813.79
total cash inflow at time 0= 26000+40813.79
= 66813.79
Cash flow at time 0 under 3rd option -
here periodic payment = $ 15000
no. of period = 6 years
interest rate per period = 6%
PV = periodic payment*[(1-(1+i)^-n ]/(i)
= 15000*[1- (1+0.06)^-6]/(0.06)
= 15000*[1-0.704961)/(0.06)
= 15000*0.295039/0.06
= 4425.592/0.06
= 73759.86
Conclusion - Alex should choose option 3 as it has higher present value among three options.
Answer to Question No.2 -
As Weimer has deposited annuity at the end of the year so it has ordinary annuity.
started payment from 31st dec 2018 to end of 31 dec. 2027. total no. of payment = 10
formula of Ordinary annuity = Periodic payment*[(1+i)^n -1]/(i)
where periodic payment = $140000
interest rate per period = 7%
no. of period = 10 years
put the values in above ordinary annuity formula
= 140000*[(1+0.07)^10 -1]/(0.07)
= 140000*[1.96715136 - 1]/(0.07)
= 140000*0.96715136/(0.07)
= 135401.19/0.07
= 1934302.71
Please check with your answer and let me know.
Annuity payment PV Annuity Immediate cash PV option Option 1 + 47000 =' 47000 Option2 8300 40813.79 + 26000 =' 66814 Option 3 15000 73759.86 + 0 =' 73760