BUSN 1330: John and Jane Doe are Newlyweds with Executive Track Careers at ACME: Business Mathematics Assignment, DC, Canada

University Douglas College (DC)
Subject BUSN 1330: Business Mathematics

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 an RESP, and for your perspective on a side venture. They’ve provided you with the background and questions below.

Purchase of a new home

John and Jane had planned to save $50,000 dollars over the next five years as a down payment on a house.  Jane assured John that if they contributed $850 each month to a savings account that pays an annual rate of interest of 2.5% compounded monthly that they would have enough money to put a down payment of $50,000 on their new house.  Wanting their daughter to have a house sooner than later, Jane’s parents (The Henrys) have offered to lend John and Jane $60,000, which they have suggested(perhaps naively) John and Jane payback by contributing to a savings account in the Henrys’ name as per Jane’s original savings plan. John’s worried this is not fair to his in-laws.  Is he correct? If so, devise a fair repayment plan that would see the Henrys repaid at a rate of 2.5% compounded monthly over the 5 years.

The Does have qualified for a mortgage of $500,000 to be amortized over 25 years.

Their mortgage broker has offered them the following options:

  1. Two consecutive 5-year terms with a fixed rate with monthly payments at an annual interest rate of prime+1% compounded monthly
  2. A single 10-year fixed rate term with biweekly payments at an annual interest rate of prime+1.25% compounded annually

Prime is currently at 1.5% and projected to increase by 0.25% every year for the next 10 years.  Note: the interest rate for fixed-rate mortgages is set at the beginning of the term using the current prime rate and remains fixed for the duration of the term; the interest rate for variable-rate mortgages is set at the beginning of each year using the current prime rate. Which Mortgage terms should they accept given that their goal is to pay as much principle as possible over the next 10 years?

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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 wishes to receive a payment of $15 000 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 $5000 which they will contribute to their new RRSP on their 31st birthday. Supposing that their RRSPs earn 8% 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 an RESP (to be opened upon the birth of either Jack or Jill, whoever 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 a good value?

A side-venture

Jane is an inventor, working for the ACME Gadget Company in research and development.  She recently proposed the development of advanced technology, but it was deemed too risky for R&D at ACME.  However, ACME has agreed that if Jane successfully develops the technology on her own, ACME will acquire a license to use the technology for a period of 10 years.  To develop the technology will require an initial expenditure of $250,000 now and an additional expenditure of $150,000 at the beginning of each of the next 2 years. When the patent is approved at the beginning of Year 4 (end of year 3), it is expected to be licensed to the ACME Gadget Company for an upfront fee of 100,000 plus an additional fee of $90,000/year for the next 9 years. At that time the product that uses the technology will be replaced by a new model.

Determine the net present value if the discount rate is 1)  and 2).  Calculate the internal rate of return on the investment.  You may use the linked IRR calculator.  Under what circumstances should Jane proceed with the side venture?

Prepare a written report to provide to John and Jane Doe.

  • An introduction that provides an overview of why the report was requisitioned and explaining why each analysis is conducted
  • An analysis of the personal loan between the Henrys and Does that provides an overview of how the analysis was conducted and provides sample calculations so the work can be verified
  • An analysis of the Does’ Mortgage options that provides an overview of how the analysis was conducted and provides sample calculations so the work can be verified
  • An analysis of the Does retirement needs and the development of a contribution plan to meet these needs.  Again, provide an overview of how the analysis was conducted and provides sample calculations so the work can be verified
  • An analysis of Bond purchasing option that provides an overview of how the analysis was conducted and provides sample calculations so the work can be verified
  • An analysis of Jane’s side venture opportunity that provides an overview of how the analysis was conducted and provides sample calculations so the work can be verified
  • A conclusion that summarizes how John and Jane’s Net worth will change through the next 10 years given that they follow your plan.

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