Question

Assume a 35 year-old client comes to you with the following goals: 1. To retire at the age of 65 and be able to live off $135,000 per year. They will begin taking this out in monthly increments the day they retire. 2. To buy a vacation home worth $150,000 in ten years. 3. To leave $2.5 million to charity at the end of their life. 4. To send their only child to college fifteen years from now. Because most of the child's college expenses will be covered by the grandparents, the total cost to the client fifteen years from now will be $45,000. Use the following facts in order to determine how much the client must save each month from now until they retire: • Their rate of return until they retire is 8.5%. • Their rate of return in retirement is 6%. • Their life expectancy is to live to 95 years old.

Answer 1

To solve this question we will be using the NPV methodology.

Firstly let us understand what is NPV or Net Present Value. NPV basically aims to calculate the present value of all future cash flows (including cash outflows as well as Inflows) thereby helping us make comparisons today. Few terms that need to be known for this calculation are:

1. Cash Inflows & time period of cash Inflows

2. Cash Outflows & time period of cash outflows

3. Rate of Return which will be used for discounting

NPV Formula = Cash / ((1+Rr)^t) where

Cash = Cash Inflow or Cash Outflow

Rr = Rate of Return

t = Number of years over which we want to discount

Coming to the specific problem mentioned above, today our client is at 35 years of age & hence if we have to recommend how much he needs to save today, we need to do present value calculations till 35. Cash outflows have been stated clearly at the ages of 45, 50 & 65 till 95 of $150000, $45000 & $150000 / year respectively. He has also mentioned a salvage value (value of net savings at age of 95) of $2500000. First we need to use NPV to calculate the present value of all these expenses mentioned. To do this let us begin with the first investment at age of 45:

NPV = 150000 / (1+8.5%)^(45-35) = $66,343

Here we have taken 8.5% as the rate of return which will be the prevalent rate prior to retirement. Also t = Cash flow Age - Current age which gives the number of years over which the cash flow needs to be discounted. Similarly NPV for the $ 45000 payment at the age of 50 is:

NPV = 45000 / (1+8.5%)^(50-35) = $13,236

Now things change a bit for the payments that need to be made post retirement as the rate of return post 65 years of age changes from 8.5% to 6.5%. Hence our discounting needs to be done in 2 parts for which I will take the example of the $2,500,000 salvage value at the age of 95:

1. NPV till 65 using 6.5% as the discount rate

2. NPV till 35 using 8.5% as the discount rate

Step 1: NPV till 65

NPV = 2500000/(1+6.5%)^(95-65) = $377,965

Step 2: NPV till 35 - Here we begin from the result of Step 1

NPV = 377965 / (1+8.5%)^(65-35) = $32,701

The $135,000 which the client will take out each year for their expenses on a monthly basis is the last part of our NPV cash outflow calculation. Here also NPV will be done in 2 steps like done previously. However this is best done in excel as for each year NPV needs to be calculated till 65 years & then to 35. Also discount rate till 65 years will be 6.5%. from 65 to 35 it will be 8.5%.

For Example, NPV for 150,000 taken out at 70 years of age:

Step 1: NPV till 65

NPV = 150000 / (1+6.5%)^(70-65) = $98,534

Step 2 : NPV till 35

NPV = 98534 / (1+8.5%)^(65-35) = $8,525

Cumulatively the NPV for these payments comes out to $162,439

Sum of all our cash outflows in present value terms are $162,439 + $32,701 +$66,343 + $13,236 = $274,719

Now we need to calculate how much money needs to be invested each year to match the NPV of cash outflows. This too is best attempted in excel as each year's investment needs to be discounted. For instance if we invest $20,000 by the end of the year, then that needs to be discounted only for year 1. Taking example of NPV for investment made at age of 40:

NPV=20000/(1+8.5%)^(40-35) = 13301

The NPV value for all investments need to match the NPV for expenses i.e. $274,719. This happens at an annual investment value of $23,400 which is $1,950 / month.