Question

Marcia, age 56, is starting to think about retirement. She plans to retire at age 65 and she expects to liver to age 90. She estimates that she will need $50,000 per year, before tax in retirement to give her the lifestyle she wants. She will receive a non-indexed pension of $25,000 a year plus a combined $12,000 per year in CPP and OAS retirement income. She currently has $70,000 in her RRSP. For planning purposes, Marcia is using a 8% nominal rate of return on savings before retirement and a 6% nominal rate of return during retirement. Inflation is expected to remain at 2% per year throughout her lifetime.

4. What is Marcia’s real rate of return before and after retirement? (ROUND TO 4 DECIMAL

PLACES)

5. What is the present value at retirement of her required retirement income of $50,000 per

year, before tax?

6. What is the present value at retirement of her non-indexed pension?

7. What is the present value at retirement of her CPP and OAS retirement income?

8. Before she retires, Marcia decides that she will deposit $12,000 per year at the end of each year to her RRSP. How much will she have saved in her RRSP by the time she retires? Assume that Marcia will increase her annual deposit for inflation.

9. Based on your answers to the questions above, will Marcia have enough money for retirement? Explain.

Please show all calculations for all parts

Answer 1

GIVEN DATA-

Current age-56

Retirement age- 65

Expectation to live- 90

Estimation to save per yr- 50000$

Income from No-indexed pension- 25000$/yr

Income from CPP and OAS- 12000$/yr

Savings in RRSP- 70000$

Nominal Rate before retirement (N*)- 8%

Nominal Rate before retirement (N1)- 6%

Inflation (I*)- 2%

Q4.Solution-

Real rate of return-

before Retirement = ((1+N*)/(1+I*))-1 = ((1+8%)/(1+2%))-1= 0.0588235 OR 5.8823%

after Retirement = ((1+N1)/(1+I*))-1 = ((1+6%)/(1+2%))-1 = 0.0392156 OR 3.9215%

Q5. Solution-

Present Value at retirement will be treated like present value of amount at present whose formulae is-

P.V. = CF* ((1/(1+i)^n)

where,

CF- Cash flow per period (viz. required retirement income in this case- 50000$)

i- real rate of return before retirement (viz. 5.8823 as calculated earlier)

n- No. of terms (viz. 9 yrs from age 56 to age 65)

So, Present Value= 50000* (1/((1+5.8823%)^9))= 29892.33$

Q6. Solution-

Present Value at retirement will be treated like present value of amount at present whose formulae is-

P.V. = CF* ((1/(1+i)^n)

where,

CF- Cash flow per period (viz. non indexed pension in this case- 25000$)

i- real rate of return before retirement (viz. 5.8823 as calculated earlier)

n- No. of terms (viz. 9 yrs from age 56 to age 65)

So, Present Value= 25000* (1/((1+5.8823%)^9))= 14946.16$

Q7. Solution-

Present Value at retirement will be treated like present value of amount at present whose formulae is-

P.V. = CF* ((1/(1+i)^n)

where,

CF- Cash flow per period (viz. income from CPP and OAS in this case- 12000$)

i- real rate of return before retirement (viz. 5.8823 as calculated earlier)

n- No. of terms (viz. 9 yrs from age 56 to age 65)

So, Present Value= 12000* (1/((1+5.8823%)^9))= 7174.16$

Q8. Solution-

Savings of Marcia for RRSP-

Saving= Current Saving+ Deposit per yr*(_(1+i)^9 ) = 70000+ 12000* _{(1+5.8823%)^9}   = 215298$ at the age of retirement.

Q9. Solution-

As per the calculation above Marcia at present requires to save 29892.33$ per yr while she is saving 22120.32$ per yr (from non-indexed pension and CPP & OAS). So, there is a defficient amount of 7772.01$ per yr.

In case we consider the saving of RRSP and consider it diving on yearly basis then a amount of 70000$ for 9 years result in 7777.77$ per yr which is nearby equal to the amount defficient. So, if RRSP is considered then Marcia might reach the amount expected by her at the age of retirement which is 50000$ per yr.