Question

Assume a 35 year-old client comes to you with the following goals:

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.

To buy a vacation home worth $150,000 in ten years.

To leave $2.5 million to charity at the end of their life.

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

The above Question completely based on NPV ( Net present Value) method basis calculation. NPV formula = Cash flow/( 1+r)T

Cash flow represents -= Net cash Inflow + cash outflow ,. r = Discount factor , t = Time period . NPV mainly represents = Present Value of Future cash flow .

In the above example, Client present age 35 , Retirement age =65 . He has some plan of cash out flow in different age bracket . We need to calculate NPV of all future age cash outflow in to present age 35 .

In the above Question, two discount rate being used , 1) discount rate at 8.50% - rate of return until retirement =35 age

2) Discount rate of return at retirement - 6% =65 age .

Any age which will exceed retirement age , we need to use two discount factor to determine value at 65 as well as 35 age .

NPV first case - Plan to Buy Home ( 10 years from now =35+10=45 Yr < 65Yr) - discount rate- 8.5% , Present value = Cash flow /(1+r)t = $1,50,000/(1+8.5%)*(45-35) = $ 66343 (A)

NPV 2nd  case - College for one child  ( 15 years from now =35+15=50 Yr < 65Yr) - discount rate- 8.5% , Present value = Cash flow /(1+r)t = $45,000/(1+8.5%)*(50-35) = $ 13236 ( B)

NPV 3rd case - Leave for charity ( 95 years from now => 65Yr) - discount rate will change . As per Question , one discount rate at 65 Year and others one rate of return till retirement .

NPV at 65 Years as Cash flow /(1+r)t = $2500,000/(1+6%)*(95-65) = $ 435275 (a)

NPV at 35 Years as Cash flow /(1+r)t = $435275/(1+8.5%)*(65-35) = $ 37659 (C)

NPV 4th case - For normal living after retirement need $135000 => 65Yr). Assuming we used at least 8.50% growth on yearly basis to get Present value of Living expenses would be = $1,35000(1+8.50%) =$ 146,475(D)

IF we add up all PV calculated as above = A+B+C+D = $ 263,723

Last part we need to find out about yearly Investment from Now to meet all future cash outflow .

The NOV value if Investment must be natch with NPV for future cash outflow calculated as above

I think Client needs to invest Yearly -$263723/12 = $ 21976 ( approx) to meet cash outflow