QUESTION 5: Ashley Wei is 50 and would like to retire at age 63. She is presentl
ID: 2656874 • Letter: Q
Question
QUESTION 5: Ashley Wei is 50 and would like to retire at age 63. She is presently earning $150,000 per year in today’s $s and would like to have 70% of that income per year during retirement. She expects to live till age 90. She is eligible to receive maximum CPP and OAS starting at age 65 in today’s $s. Use 2012 values from table 17.4. She will receive an employer pension of $70,000 per year in today’s $s. She would like CPP to start after she retires, and OAS and employer pension to start after she turns 65. Her marginal tax rate is 46%.She has $240,000 in RRSP now. She plans to deposit $6,000 per year in today’s $s into it each year until retirement, which is the limit she can contribute, because of her employer pension. She will deposit tax refund on the RRSP contribution into a Tax Free Savings Account (TFSA). She expects to earn a nominal rate of return of 6% per year on her portfolio. Inflation rate is expected to be 2% per year. Assume deposits into the RRSP and TFSA are made at the end of the year.Savings in TFSA provide no income tax deduction, but the principal and income in TFSA are never taxed, even when withdrawn. Therefore, to make the TFSA comparable with other before tax values in this problem, multiply the accumulated TFSA value by 1.4.a. Do Ashley’s savings provide enough to maintain the standard of living she desires if she lives to age 90. If not, how much will be the value of the shortfall in retirement savings at age 63. b.How much more she contributes to her TFSA each year to reach her goal. Remember for each year maximum contribution allowed is $5500.
Explanation / Answer
Solution to Part (a):
Earns = $150,000
Required = $150,000 - $150,000 * 70% = $105,000
CPP = Table is not given in the question so we take CPP to be zero.
Pension = $70,000
Income shortfall = $105,000 - $0 - $70,000 = $35,000
Real rate of return = (1.06/1.02) – 1 = 3.92%
PVA = P{[1 – (1 + r)-n] / r}
= $35,000 {[1 – (1 + 0.0392)-27] / 0.0392}
= $576,698 (This is pre-tax Real $)
Where,
Principal (P) = $35,000
Rate (r) = 3.92% = 0.0392
Years (n) = 27 years (90 years – 63 years)
RRSP accumulates to age 63:
PV = -$240,000
PMT = -$6,000
I = 3.92%
N = 13 (63 – 50)
FV = [(PMT * k) / i] – {(1 + i)n * [PV + (PMT * k) / i]}
= $494,900 (pre-tax Real$)
TFSA accumulates also at tax-free rate, but is never taxed.
PMT = $2,760 ($6000 * 46%)
I = 3.92%
N = 13
FV = PMT [(1 + i)n – 1] / i
= $45,660 (after-tax Real$)
Gross-up = $45,660 * 1.4 = $63,924
Total saved = $494,900 + $45,660 = $540,560
Shortfall = $576,698 - $540,560 = $36,138
Solution to part (b):
The $36,138 is in pre-tax real dollars, but the TFSA yields after-tax dollars. Therefore, reverse the gross-up process and divide by 1.4 to turn the goal into after-tax dollars.
Goal is $36,138/1.4 = $25,813
FV = $25,813
I = 3.92%
N = 13
PMT = FV / [(1 + i)n – 1] / i
= $1,560