Question

BUSI 320 Comprehensive Problem 3 2018 Summer

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 $ 7500 today.    

Option B:  Receive a $1000 gift each year for the next 10 years.  The first $1000 would be

     received 1 year from today.             

Option C:  Receive a one-time gift of $14,000 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 $_7,500today.

       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 7% 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 10% 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

Luke and Olivia 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.   Olivia just told Luke, 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 Luke and Olivia 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 8.4% annually.

How much money will Luke and Olivia have in 45 years if they do nothingfor the next 10 years, then put $2400 per year away for the remaining 35 years?

How much money will Luke and Olivia have in 10 years if they put $2400 per year away for the next 10 years?

b2)  How much will that 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 Luke and Olivia have in 45 years if they put $2400 per year away for each of the next 45 years?  

d) How much money will Luke and Olivia have in 45 years if they put away $200 per MONTHat the end of each month for the next 45 years?  (Remember to adjust 8.4% annual rate to a Rate per month!)

e)If Luke and Olivia wait 25 years (after the kids are raised!) before they put anything away for retirement,  how much will they to put away at the end ofeach yearfor 20 years in order to have $1,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

	If interest rate is 3%
	Option A would be worth $ 7500 today
	Option B would be worth $ 8530.20
	Year	Cash flow	Discount factor @ 3%	Present Value
	1	1000	0.9709	970.8738
	2	1000	0.9426	942.5959
	3	1000	0.9151	915.1417
	4	1000	0.8885	888.487
	5	1000	0.8626	862.6088
	6	1000	0.8375	837.4843
	7	1000	0.8131	813.0915
	8	1000	0.7894	789.4092
	9	1000	0.7664	766.4167
	10	1000	0.7441	744.0939
				8530.203
	Option C would be worth $ 10417.40
		14000*0.7441		10417.4
	Financial theory suggests choosing Option C
	If interest rate is 7%
	Option A would be worth $ 7500 today
	Option B would be worth $ 7023.58
	Year	Cash flow	Discount factor @ 7%	Present Value
	1	1000	0.9346	934.5794
	2	1000	0.8734	873.4387
	3	1000	0.8163	816.2979
	4	1000	0.7629	762.8952
	5	1000	0.7130	712.9862
	6	1000	0.6663	666.3422
	7	1000	0.6227	622.7497
	8	1000	0.5820	582.0091
	9	1000	0.5439	543.9337
	10	1000	0.5083	508.3493
				7023.582
	Option C would be worth $ 7116.20
		14000*0.5083		7116.2
	Financial theory suggests choosing Option A
	If interest rate is 10%
	Option A would be worth $ 7500 today
	Option B would be worth $ 6144.57
	Year	Cash flow	Discount factor @ 10%	Present Value
	1	1000	0.9091	909.0909
	2	1000	0.8264	826.4463
	3	1000	0.7513	751.3148
	4	1000	0.6830	683.0135
	5	1000	0.6209	620.9213
	6	1000	0.5645	564.4739
	7	1000	0.5132	513.1581
	8	1000	0.4665	466.5074
	9	1000	0.4241	424.0976
	10	1000	0.3855	385.5433
				6144.567
	Option C would be worth $ 5397
		14000*0.3855		5397
	Financial theory suggests choosing Option A