Question

Project Details

John and Jane Doe are newlyweds with executive track careers at ACME Gadget Company. In five years, the Does would like to have a family, envisioning two young children, Jack and Jill. With an eye for the future, John and Jane are now looking to ensure that their future family has a place to call home, that their future children will have access to all the education they desire, and that they themselves will be able to enjoy retirement when the time comes. As such, they’ve come to your financial planning company for advice for purchasing a house, planning for retirement, setting up a RESP and for your perspective on a side venture. They’ve provided you with the background and questions below.

Retirement planning.

John and Jane will contribute to an RRSP until they are each 71. When they turn 71, CRA rules require them to switch their RRSPs to an annuity and begin receiving payments. John and Jane will receive their first payments on their (respective) 71st birthdays. Each wish to receive a payment of $10 000 per month until they die. If the annuity pays 5% interest compounded monthly, how much must they have saved in their RRSP if they live until their 81, 91 or 101 birthday? Both John and Jane have 10 000 which they will contribute to their new RRSP on their 31st birthday. Supposing that their RRSPs earn 12% compounded monthly what is John’s monthly contribution if he plans to live until 91? Similarly, what is Jane’s monthly contribution if she plans to live until 101? Saving for their children’s education To establish funds for a RESP (to be opened upon the birth of either Jack or Jill, whomever comes first) John has suggested purchasing bonds as a lower risk alternative to more volatile funds. John has identified a 20-year bond with a face value of $10,000 which pays a coupon rate of 9% compounded semi-annually. The bond has 15 years remaining until maturity and a current yield rate of 8%. John can purchase the bond for $10,125. Is this good value?

Answer 1

All amounts are in $

This contains many subquestions so answered briefly

1) If expected life upto 81 years

How much they must have invested to get 10,000 monthly having annuity interest at 5% compunded monthly. So monthly interest would be 0.4167% (5/12)

The term of annuity is 10 years payments receiving at beginning of each month

Savings = 10,000 x (1 + present value of annuity due at 0.4167% for 119 periods)

= 10,000 x (1+93.67417)

= 946,742

2)

If expected life time is 91 years

Savings = 10,000 x (1 + Present value factor at 0.4167% for 239 periods)

= 10,000 x ( 1 + 151.156618)

= 1,521,566.18

3)

If expected life time is 101 years

Savings = 10,000 x (1+present value of annuity factor for 0.4167% for 359 periods)

= 10,000 x (187.057706)

= $1,870,577.06

4)

If the life expectancy is 91

Savings must be 1,521,566.18

Current age = 31

Initial Contribution 10,000

Interest rate per month = 1%

Total monthly contribution = 40x12 - 1 = 479 periods

So we calculate future value annuity factor for 480 periods and minus 1

Let the monthly contribution be Y

1,521,566.18 = 10,000 (1.01)^480 + Y (Future value factor for 480 periods at 1% per period - 1)

1,521,566.18 = 1,186,477.25 + Y (11,764.7725-1)

Y (11,763.7725) = 335,088.93

Y = $28.4848

Monthly contribution should be $28.4848

5)

If life expectancy is 101

The the Savings must be $1,870,577.06

Let monthly contribution be Y

1,870,577.06 = 10,000 (1.01)^40 + Y (future value factor for 480 periods - 1)

1,870,577.06 = 1,186,477.25 + Y (11,764.7725-1)

Y (11,673.7725) = 684,099.81

Y = 58.6014

Monthly contribution must be $58.6014

6)

Bond face value = 10,000

Coupon payment = 9% and semi annual payment

Coupon payment = 10,000 x 9% x 1/2 = 450

Market rate = 8% or 4% per semi annual period

Remaining life 15 years

Bond price = 450 (present value annuity factor for 4% for 30 periods) + 10,000 (present value annuity factor for 30th period at 4%)

= 450 (17.29203) + 10,0000 (0.30832)

= 10,864.61

So the bond under priced at 10,125. So we recommend to buy it

Note :

Future value annuity and present value annuities are taken from annuity calculators.

We can also find them using formulas

Future value annuity ordinary = A x [ (1+r)^n - 1]/r

Present value of annuity ordinary

= P X [ { 1 - (1+r)^-n }/1]