Question

BUSI 320 Comprehensive Problem 3

Use what you have learned about the time value of money to analyze each of the following decisions:

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 received 1 year from today.   

Option C: Wait exactly 10 years from today and then receive a one-time gift of $17,000.

Compute the Present Value of each of these options if you expect the interest rate to be 2% 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 5% 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 8% 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: 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 $2400 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 $2400 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)

a) How much money will Erich and Mallory have in 45 years if they do nothing for the next 10 years, then put $2400 per year away for the remaining 35 years?

b1) How much money will Erich and Mallory have in 10 years if they put $2400 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 $2400 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 $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust 7.5% annual rate to a Rate per month! (do NOT round!)

e) 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 of each year for 20 years in order to have $800,000 saved up on the first day of their retirement 45 years from today?

Answer 1

a..Future value of annuity of $ 2400 from yrs. 11 to 35 will be =

FVOA of $ 2400 for FULL yrs. 1 to 45 MINUS FVOA of $ 2400 for yrs.1-10 (both at at 7.5 % p.a.)

Using FVOA formula

(2400*((1+0.075)^45-1)/0.075)-(2400*((1+0.075)^10-1)/0.075)

763002

b-1.

Future value of $ 2400 annuity for next 10 yrs. At 7.5% p.a.=

(2400*((1+0.075)^10-1)/0.075)

33953

b-2..

Future value of the above single sum of $ 33953 at end of 35 yrs.

using FV of single sum formula,

33953*(1+0.075)^25=

207057

c. Future value of $ 2400 annuity for next 45 yrs. At 7.5% p.a.=

(2400*((1+0.075)^45-1)/0.075)=

796955

d... Future value of $ 200 annuity per month for next 45*12= 540 months at 7.5%/12 p.m

(200*((1+(0.075/12))^540-1)/(0.075/12))=

893406

e. Amt.they have to put away at the end of each year for 20 years in order to have $800,000

can be found out by

Using the same formula as in   a. having the FV as $ 800000 & solving for $ X set-aside at end of 20 yrs. At 7.5% p.a.

800000=(X*((1+0.075)^45-1)/0.075)-(X*((1+0.075)^25-1)/0.075)

X= 3029.31

3029

The amt. to be saved at end of each yr. from yrs. 26-45   at 7.5% p.a.= $ 3029