Question

Scenario:

Your 21-year old niece, who is graduating from college next month, asked for your advice – should she:

Invest $5,000 per year into her retirement fund (9 payments) from age 22 – 30?

Or wait until she turns 31 and invest $5,000 every year through age 65 (35 payments)?

Share your niece's age 65 balance from part A. for both scenarios with the class. What did you find? Share your findings from part B. What did you find? Discuss the implications for her goal of becoming financially independent.

Answer 1

The Question focuses on Study of Two Scenarios viz.,

1. Invest $5,000 per year into her retirement fund (9 payments) from age 22 – 30

Or

2. Wait until she turns 31 and invest $5,000 every year through age 65 (35 payments)

This should be decided based on the Present value of the Cash Outflow at different point of time and reaching at a conclusion Based on Net Cash Outflow.

Present value is the current worth of a future sum of money or stream of cash flow given a specified rate of return.

Future cash flows are discounted at the discount rate.

Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they are earnings or obligations.Let us Assume the discount rate as 10% for Simplified Calculation purpose and for Study of Given two Scenarios.

1. Invest $5,000 per year into her retirement fund (9 payments) from age 22 – 30 :

Since in the absence of information related to timing of investment, it is assumed that it is done in the beginning of the year.

The Calculation as per Discounted Cash Outflow is presented as follows:

Age	Investment(Cash Outflow)($)(i)	PVF @ 10%(ii)	(i)*(ii)
22	5000	0.909	4545.45
23	5000	0.826	4132.23
24	5000	0.751	3756.57
25	5000	0.683	3415.07
26	5000	0.621	3104.61
27	5000	0.564	2822.37
28	5000	0.513	2565.79
29	5000	0.467	2332.54
30	5000	0.424	2120.49
Total	45000	5.759	28795.12

PVF = Present Value factor at rate of 10%. formula for calculating PVF = 1/(1+r)ⁿ Where, r = discount rate and n = year

For first year 22, PVAF @ 10% = 1/(1.1)¹ = 0.909

For Second Year 23, PVAF @ 10% = 1/(1.1)² = 0.826

The Total Cash outflow discounted as on today(at the time, when Cousin age is 21 years) in above case is $28,795.12

The Above Amount of Present cash flows can also be calculated by using Cumulative Factor of Present value from year 22 to 30 as follows (This calculation can only done when the amount of investment p.a. is constant):

Present value of cash outflow from 22 to 30 years as on today = $5000 * 5.759 (As calculated above in the total of PVAF)

= $28,759.12

2. Wait until she turns 31 and invest $5,000 every year through age 65 (35 payments) :

Now, in this scenario, we can directly calculate Present value of future cash flows from year 31 to 65 (total 35 payments) ny using Cumulative Present Value factor from tenth Year from now(i.e. 31 years minus 21 years) upto Fourty-Fourth year(i.e. 65 year minus 21 years) which comes to 4.090 (Refer Working Note at the end of this answer)

Present value of cash outflow from 31 to 45 years as on today = $5000 * 4.090

= $20,450

Conclusion:

Since the Present value of cash flow is less in scenario 2 by $ 8,309 (i.e. 28,759-20,450), It is advised to choose for Scenario 2 i.e. wait until she turns 31 and invest $5,000 every year through age 65 (35 payments)

The implications for her goal of becoming financially independent:

Since the Present value of cash flow is less in scenario 2 by $ 8,309 as calculated above.There is a huge difference in amount invested.in first scenario, the total cash outflow in terms of $5000 per annum of 9 payments is calculated as 45000 while it is 175000 (5000*35 payments). Therefore, as becoming financially independent criteria as concerned, Choosing Scenario 2 i.e. to wait until she turns 31 and invest $5,000 every year through age 65 (35 payments) is more beneficial as more funds are invested which Directly results into increase in returns.

Working note:

Age	Investment(i)	PVAF @ 10%(ii)	(i)*(ii)
31	5000	0.385543	1927.716
32	5000	0.350494	1752.469
33	5000	0.318631	1593.154
34	5000	0.289664	1448.322
35	5000	0.263331	1316.656
36	5000	0.239392	1196.96
37	5000	0.217629	1088.146
38	5000	0.197845	989.2233
39	5000	0.179859	899.2939
40	5000	0.163508	817.54
41	5000	0.148644	743.2181
42	5000	0.135131	675.6529
43	5000	0.122846	614.2299
44	5000	0.111678	558.3908
45	5000	0.101526	507.628
46	5000	0.092296	461.48
47	5000	0.083905	419.5273
48	5000	0.076278	381.3884
49	5000	0.069343	346.7167
50	5000	0.063039	315.197
51	5000	0.057309	286.5428
52	5000	0.052099	260.4934
53	5000	0.047362	236.8122
54	5000	0.043057	215.2838
55	5000	0.039143	195.7126
56	5000	0.035584	177.9205
57	5000	0.032349	161.7459
58	5000	0.029408	147.0417
59	5000	0.026735	133.6743
60	5000	0.024304	121.5221
61	5000	0.022095	110.4746
62	5000	0.020086	100.4315
63	5000	0.01826	91.30136
64	5000	0.0166	83.00123
65	5000	0.015091	75.45567
Total	175000	4.090065	20450.32