Decision #1: Which set of Cash Flows is worth more now? Assume that your grandmo
ID: 2810071 • Letter: D
Question
Decision #1: Which set of Cash Flows is worth more now?
Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive:
Option A: Receive a one-time gift of $ 10,000 today.
Option B: Receive a $1400 gift each year for the next 10 years. The first $1400 would be
received 1 year from today.
Option C: Receive a one-time gift of $17,000 10 years from today.
Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose?
Option A would be worth $__________ today.
Option B would be worth $__________ today.
Option C would be worth $__________ today.
Financial theory supports choosing Option _______
Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose?
Option A would be worth $__________ today.
Option B would be worth $__________ today.
Option C would be worth $__________ today.
Financial theory supports choosing Option _______
Compute the Present Value of each of these options if you expect to be able to earn 9% annually for the next 10 years. Which of these options does financial theory suggest you should choose?
Option A would be worth $__________ today.
Option B would be worth $__________ today.
Option C would be worth $__________ today.
Financial theory supports choosing Option _______
Decision #2 begins at the top of page 2!
Decision #2: Planning for Retirement
Erich and Mallory are 22, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $1800 per year to prepare for retirement. Mallory just told Erich, though, that she had heard that they would actually have more money the day they retire if they put $1800 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do). Please help Erich and Mallory make an informed decision:
Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.5% annually.
(Please do NOT ROUND when entering “Rates” for any of the questions below)
How much money will Erich and Mallory have in 45 years if they do nothingfor the next 10 years, then put $1800 per year away for the remaining 35 years?
How much money will Erich and Mallory have in 10 years if they put $1800 per year away for the next 10 years?
b2) How much will the amount you just computed grow to if it remains invested for the remaining
35 years, but without any additional yearly deposits being made?
c)How much money will Erich and Mallory have in 45 years if they put $1800 per year away for each of the next 45 years?
d) How much money will Erich and Mallory have in 45 years if they put away $150
e) per MONTHat the end of each month for the next 45 years? (Remember to adjust 7.5% annual rate to a Rate per month!)
f)If Erich and Mallory wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end ofeach yearfor 20 years in order to have $700,000 saved up on the first day of their retirement 45 years from today?
Explanation / Answer
OPTION A Present Value of Cash Flow $10,000 OPTION B Annualgift $1,400 Number of Years 10 Interest rate(0.03) 3% Present Value of cash flow $11,942.28 (using PV function of excel with Rate=3%,Nper=10, Pmt=-1400) OPTION C Future Value after 10 years $17,000 Annual interest=3%=0.03 Present Value of Cash Flow $ 12,649.60 (17000/(1.03^10) Option A would be worth $10,000 Today Option B would be worth $11,942 Today Option C would be worth $12,650 Today Financial theory supports choosing Option C If The Interest Rate is 6% per year OPTION A Present Value of Cash Flow $10,000 OPTION B Annualgift $1,400 Number of Years 10 Interest rate(0.06) 6% Present Value of cash flow $10,304.12 (using PV function of excel with Rate=6%,Nper=10, Pmt=-1400) OPTION C Future Value after 10 years $17,000 Annual interest=6%=0.06 Present Value of Cash Flow $ 9,492.71 (17000/(1.06^10) Option A would be worth $10,000 Today Option B would be worth $10,304 Today Option C would be worth $9,493 Today Financial theory supports choosing Option B IF THE INTEREST RATE IS 9% ANNUALLY OPTION A Present Value of Cash Flow $10,000 OPTION B Annualgift $1,400 Number of Years 10 Interest rate(0.09) 9% Present Value of cash flow $8,984.72 (using PV function of excel with Rate=9%,Nper=10, Pmt=-1400) OPTION C Future Value after 10 years $17,000 Annual interest=9%=0.09 Present Value of Cash Flow $ 7,180.98 (17000/(1.09^10) Option A would be worth $10,000 Today Option B would be worth $8,985 Today Option C would be worth $7,181 Today Financial theory supports choosing Option A Interest Rate=7.5%=0.075 OPTION A-WAIT FOR 10 YEARS Annual investment $1,800 Number of years of investment 35 (45-10) Interest rate 7.50% Amount available at the time of retirement $277,653 (Using FV function of excel with Rate=7.5%, Nper=35, Pmt=-1800) OPTION B-START SAVING NOW Annual investment $1,800 Number of years of investment 10 Interest rate 7.50% Amount available at the end of ten years $25,465 (Using FV function of excel with Rate=7.5%, Nper=10, Pmt=-1800) Years to retirement after stopping saving 35 Amount available at the time of retirement $ 320,063 (25465*(1.075^35) This can alsobe calculated using Excel FV function with Rate-7.5%, Nper=35, PV=-25465 SHE SHOULD SELECT : OPTION B-START SAVING NOW Save for 10 years and then stop If they save for 35 years $277,653 If they save for next 10 ,amount available after 10 years $ 25,465 Amount available after 45 years $ 320,063 Amount available if they save for 45 years $597,716 (Using FV function of excel with Rate=7.5%, Nper=45, Pmt=-1800) e) Saving per month $150 Number of month 540 (45*12) Monthly interest=(7.5/12)% Amount available after 45 years $670,055 (Using FV function of excel with Rate=(7.5/12)%, Nper=540, Pmt=-150) f) Amount of Future value Required $700,000 Number of Years 20 Interest rate 7.50% Annual Saving required $16,165 (Using PMT function of excel with Rate=7.5%, Nper=20, FV=-700000)
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