5 Aug 2022

159

The Ultimate Guide to Cash Flow Management

Format: APA

Academic level: College

Paper type: Math Problem

Words: 723

Pages: 1

Downloads: 0

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. 

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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? 

Solution (See excel file attached) 

1QP       
Option A       
Receive a one-time gift of $10,000 today   
Year  Cash Flow ($)  Present Value ($) 

10,000 

10000 

 
Total Present Value   

10000 

 
       
Option B       
Receive $1400 each year     
Year  Cash Flows ($)  Present Value ($) 

1400 

1359.223301 

 

1400 

1319.634273 

 

1400 

1281.198323 

 

1400 

1243.881867 

 

1400 

1207.652298 

 

1400 

1172.477959 

 

1400 

1138.328116 

 

1400 

1105.172928 

 

1400 

1072.983425 

 

10 

1400 

1041.731481 

 
Total Present Value (PV)   

11942.28397 

 
       
Option C       
Receive a one-time gift of $17,000 10 year from today   
Year  Cash Flow ($)  Present Value ($) 

17,000 

12649.59655 

 
Total Present Value   

12649.59655 

 
       

Option A would be worth $10,000 today. 

Option B would be worth $11,942.28 today. 

Option C would be worth $12,649.60 today. 

Financial theory supports choosing Option C. This is because the PV of Option C is greater than that of Option A and Option B. 

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 $10,000 today. 

Option B would be worth $10,304.12 today. 

Option C would be worth $9,492.71 today. 

Financial theory supports choosing Option B. This is because the PV of Option B is greater than that of Option A and Option C. 

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 $10,000 today. 

Option B would be worth $8,984.72 today. 

Option C would be worth $7180.98 today. 

Financial theory supports choosing Option A. This is because the PV of Option A is greater than that of Option B and Option C. 

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 nothing for the next 10 years, then put $1800 per year away for the remaining 35 years? 

   
Rate 

0.075 

35 

PMT 

1800 

FV 

$277,652.89 

How much money will Erich and Mallory have in 10 years if they put $1800 per year away for the next 10 years? 

Rate 

0.075 

10 

PMT 

1800 

FV 

$25,464.76 

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? 

0.075 

35.00 

PV 

25,464.76 

FV 

$320,063.27 

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? 

0.075 

45 

PMT 

1800 

FV 

$597,716.13 

How much money will Erich and Mallory have in 45 years if they put away $150 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!) 

0.00625 

540 

PMT 

150 

FV 

$670,054.64 

$670,054.64 

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 $700,000 saved up on the first day of their retirement 45 years from today? 

FV 

700,000 

0.075 

20 

PMT 

$16,164.53 

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StudyBounty. (2023, September 16). The Ultimate Guide to Cash Flow Management.
https://studybounty.com/the-ultimate-guide-to-cash-flow-management-math-problem

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