Question

Your Answers: Type your answers in the table and submit this worksheet.

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 $1600 gift each year for the next 10 years. The first $1600 would be received 1 year from today. Option C: Receive a one-time gift of $20,000 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?

1. Option A would be worth $__________ today.

2. Option B would be worth $__________ today.

3. Option C would be worth $__________ today.

4. 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?

5. Option A would be worth $__________ today. 6

. Option B would be worth $__________ today.

7. Option C would be worth $__________ today.

8. 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?

9. Option A would be worth $__________ today.

10. Option B would be worth $__________ today. 1

1. Option C would be worth $__________ today.

12. Financial theory supports choosing Option _______

Decision #2: Planning for Retirement Tom and Tricia 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. Tricia just told Tom, 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—than they would have if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do). Help Tom and Tricia make an informed decision. Assume that all payments are made at the end of a year, and that the rate of return on all yearly investments will be 9% annually. (Please do NOT ROUND when entering “Rates” for any of the questions below)

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

b) How much money will Tom and Tricia have in 10 years if they put $2400 per year away for the next 10 years?

c) 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?

d) How much money will Tom and Tricia have in 45 years if they put $2400 per year away for each of the next 45 years?

e) How much money will Tom and Tricia 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 the 9% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal.) example of rounding: .062134 = .06213 or 6.213%

f) If Tom and Tricia 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 $1,200,000 saved up on the first day of their retirement 45 years from today?

Answer 1

1. optionA
At T zero	10000

2. option B
PVIFA(10,3%)
1	0.970874	1600	1553.398
2	0.942596	1600	1508.153
3	0.915142	1600	1464.227
4	0.888487	1600	1421.579
5	0.862609	1600	1380.174
6	0.837484	1600	1339.975
7	0.813092	1600	1300.946
8	0.789409	1600	1263.055
9	0.766417	1600	1226.267
10	0.744094	1600	1190.55
	8.530203		13648.32

3.option C
PVIF(10,3%)	0.744094

PV of 20000 after 10 years = 20000*0.744094

= 14881.88

4. Financial theory would choose option 3.

5. at 7 % interest -

optionA
At T zero	10000
option B
PVIFA(10,3%)
1	0.934579	1600	1495.327
2	0.873439	1600	1397.502
3	0.816298	1600	1306.077
4	0.762895	1600	1220.632
5	0.712986	1600	1140.778
6	0.666342	1600	1066.148
7	0.62275	1600	996.3996
8	0.582009	1600	931.2146
9	0.543934	1600	870.294
10	0.508349	1600	813.3589
	7.023582		11237.73
option C
PVIF(10,3%)	0.508349
	10166.99

option B would be chosen as it has the highest present value.

For 9, 10, 11 -when interest rate would be 10%

optionA
At T zero	10000
option B
PVIFA(10,3%)
1	0.909091	1600	1454.545
2	0.826446	1600	1322.314
3	0.751315	1600	1202.104
4	0.683013	1600	1092.822
5	0.620921	1600	993.4741
6	0.564474	1600	903.1583
7	0.513158	1600	821.053
8	0.466507	1600	746.4118
9	0.424098	1600	678.5562
10	0.385543	1600	616.8693
	6.144567		9831.307
option C
PVIF(10,3%)	0.385543
	7710.866

option A would be chosen as per financial theory.

Decision 2 -

periodic payment = 2400

interest rate = 9%

all payment are made at the end of the year

(a) annuity formula = periodic payment * [(1+i)^n-1]/(i)

= 2400*[(1+0.09)^35-1]/(0.09)

= 517705.8

(b) future value of annuity = 2400*[(1+0.09)^10-1]/0.09

= 36463.03

(c) by the help of CAGR = principal*(1+i)^n

= 34463.03*(1+0.09)^35

= 744355.2

(d) future value of annuity = 2400*[(1+0.09)^45-1]/0.09

= 1262061

(e) now interest rate per month = 9/12

no. of years = 12*45 = 540 months

periodic payment = 200 per month

future value of annuity = periodic payment*[(1+i)^n-1]/(i)

= 200*[(1+0.09/12)^540-1]/(0.09/12)

= 200*[(1+0.0075)^540-1]/0.0075

= 200*[(56.53659-1)/0.0075

= 200*7404.878

= 1480976

(f) 1200000 = x*[(1+0.09)^20-1]/0.09

108000 = x*4.604411

x = 23455.77

Please note all value are in $.

In case of any clarification required please comment.