Calculations

Question 1

Hannah currently has $915,000 saved. She will retire in 10 years and wants to take $80,000 income for 25 years at the beginning of each year. She also wishes to have $1,000,000 35 years from now to leave to her heirs. What is the internal rate of return needed to accomplish this?

Answer 1

Enter cash flows before retirement, then cash flows in retirement, then one final cash flow after retirement

• 915 +/- CFj
• 0 CFj
• 9 ORANGE Nj [OS] means Orange Shift
• 80 Cfj
• 25 ORANGE Nj
• 1000 CFj
• ORANGE IRR/YR
• = 4.9649

Question 2

Monthly amount needed to contribute at the beginning of the month to a retirement plan to generate $1000 in income? Will retire in 10 years, earn 10% return, and live in retirement for 30 years

Answer 2

• Calculate amount needed at start of retirement to fund that payment in retirement
  
  • BEGIN
  • N = years in retirement x 12 = 30 x 12 = 360
  • i = 10/12
  • FV = 0
  • PV = ? = $114,900.41
• Calculate monthly savings to save that amount
  
  • N = years until retirement x 12 = 10 x 12 = 120
  • i = 10/12
  • FV = 114,900.41
  • PMT = ? = $556.24

Question 2

Monthly amount needed to contribute at the beginning of the month to a retirement plan to generate $1000 in income? Will retire in 10 years, earn 10% return, and live in retirement for 30 years

Answer 2

• Calculate amount needed at start of retirement to fund that payment in retirement
  
  • BEGIN
  • N = years in retirement x 12 = 30 x 12 = 360
  • i = 10/12
  • FV = 0
  • PV = ? = $114,900.41
• Calculate monthly savings to save that amount
  
  • N = years until retirement x 12 = 10 x 12 = 120
  • i = 10/12
  • FV = 114,900.41
  • PMT = ? = $556.24

Question 3

standard deviation on calculator

Answer 3

enter the first return → E+ → next return → E+ → etc → orange → Sx, Sy

Question 4

standard deviation (on formula sheet)

Answer 4

• problem:
  
  • 50/50 weighting
  • deviations of 10.5% and 23.8%
  • correlation 1.5
• square root of: (0.5²x0.105²)+(0.5²x0.238²)+2*0.5*0.5*.0105*0.238*0.15
• square root of 0.01879
• = 0.137 or 13.7%

Question 5

geometric average using time value

Answer 5

PV = -1

FV = (1+return)*(1+return)*(1+return)…etc

N = # periods

i = ?

Question 6

How much will be needed to cover post-secondary schooling

Answer 6

• STEP 1: Calculate what college costs will inflate to
  
  • N = years until college begins
  • I = college inflation rate
  • PV = annual cost of college today
  • PMT = 0
  • FV = ?
• STEP 2: Calculate how much will be needed to fund that for all 4 years using real rate of return
  
  • BEG mode
  • N = years of college (usually 4)
  • I = real rate of return [(1+return / 1+inflation)-1]x100
  • PV = ?
  • PMT = FV from step 1
  • FV = 0

Question 7

how much will be needed to fund retirement?

Answer 7

capital needs analysis approach

• STEP 1: calculate WRR (if not provided) in today’s dollars
• STEP 2: adjust retirement need for inflation
  
  • N = WLE
  • I = inflation rate
  • PV = retirement need in today’s dollars
  • FV = ?
• STEP 3: calculate need to fund for retirement years using real rate of return
  
  • BEG mode
  • N = RLE
  • I = real rate of return [(1+post-retirement rate of return/1+inflation)-1 x 100]
  • PV = ?
  • PMT = FV from step 2
• STEP 4: calculate annual savings need prior to retirement
  
  • N = WLE
  • I = pre-retirement rate of return
  • PV = current amount saved, if anything
  • PMT = ?
  • FV = PV from step 3