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, theyve 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. Theyve 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, Janes parents (The Henrys) have offered to lend John and Jane $60,000, which they have suggested (perhaps naively) John and Jane pay back by contributing to a savings account in the Henrys name as per Janes original savings plan. Johns 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?

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 $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 31^st birthday. Supposing that their RRSPs earn 8% compounded monthly what is Johns monthly contribution if he plans to live until 91? Similarly, what is Janes monthly contribution if she plans to live until 101?

Saving for their childrens 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?

A side-venture

Jane is an inventor, working for the ACME Gadget Company in research and development. She recently proposed the development of an 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) i=5% and 2) i=10%. 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?

BELOW ARE THE FORMULA SHEETS

Simple interest I = Prt Future Value (moving money ahead in time) S = P(1+rt) moves a lump sum of money P ahead in time Present Value (moving money back in time) S P= (1 + r) moves a lump sum of money S back in time Finding equivalent values of Money If the interest rate is simple interest use the simple interest formulas, if the interest rate is compound interest use the compound interest formulas. At the focal date: New debts (paying) = Old debts (owing) at the current interest rate All monies, both all the old debts and all new debts, must move to the conversion or focal date. The procedure, then, in solving such problems is as follows. Step 1. Find the original maturity value of the original debts using the original rates of interest on the original loans. Step 2. Set up a time line to help you visualize the solution of the problem. Step 3. Move all the amounts to the focal date (conversion date) at the current rate of interest. At the focal date: New debts (paying) = Old debts (owing) at the current rate Business Mathematics 8 Note that whenever the statement says simply "due in," it means that the original amount borrowed plus interest is included in the value stated. On the other hand, if the statement says "due in with interest," "with interest," or "plus interest," then the interest on the amount must be calculated to get the maturity value. Compound Interest, Annuities, Bands, Sinking Funds, Net Present Value How much work to show for these concepts If you are not using a financial calculator, make sure on assignments and exams you show the formulas you used and the substitutions made into the formulas. If you are using a financial calculator for the compound interest, annuities, bonds, sinking funds, and net present value calculations make sure on assignments and exams you show the calculator inputs that you made to solve the questions.i.e P/Y; C/Y;N; 1/Y; PV; PMT; FV and remember to mention if you used the BGN; AMORT; BOND; CF calculator functions and if you used them, make sure you show your inputs for the AMORT, BOND, CF components. This allows the marker to assess part marks. Compound Interest 1 stated or nominal rate of interest number of times interest is added per year j= nominal interest rate; m= the number of compoundings per m year n=the number of compoundings per year times the number of years in the financial obligation n= mx (Number of years in the term) FV PV(1+1) moves a lump sum of money PV ahead in time moves a lump sum of money FV back in time, PV = FV (1+1) maturity value compounding at a variable rate FV = PV(1+iX1 + 1)(1+1,)... (1+1) FV PV -1 In (FV/PV) In (1 + i) Effective Interest rate f (Equivalent Interest Rate per year) f = (1+i)= -1 m=the number of compound periods per year Equivalent Interest Rate (Equivalent Interest Rate per interest period) iz = (1+1), (m. - 1 m C= m2 Number of compoundings per year Number of payments per year 2 = (1+i)= -1 10 Business Mathematics Annuities: FV =PMT (1 + i)"-1 moves a group of equal payments PMT ahead in time to immediately after the last payment is made (1-(1+1) PV=PMT moves a group of equal payments PMT back in time to one interest period before the first payment is made. ix PV In + In ix FV PMT In (1+i) 71- In(1+i) given FV, PMT, and i given PV, PMT, and i The balance of an annuity at any point in time is the present value of the remaining payments Annuities Due (1+i)" - 1 FV (due)=PMT X (1+1) 1-(1+i)n PV(due) = PMT (1+i) In 1- In 1+ PMT(1+i) 1 = In(1+i) [_ix PV(due) PMT(1+i) In(1+i) n Business Mathematics 11 Deferred Annuities Deferred Annuities are annuities where payments start at a later time after the annuity begins. They require the use of annuity formulas and lump sum formulas to solve. Perpetuities Perpetuities are annuities that have no end date PMT PV = Mortgages Mortgages are an application of annuities. Mortgages rates are usually stated as compounded semi-annually, but payments on mortgages are usually made monthly. So the semi-annual mortgage rate has to be converted to an equivalent monthly rate using the Equivalent Interest Rate formula above. before the annuity formulas can be used in mortgage calculations. Bonds: Purchase price of a bond Bond Price = (FV) [1-(1+i) i + FV(1+1)" FV = Face value of the bond b= Coupon rate per interest payment interval (normally six months) i = The bond market's required rate of return per payment interval n = Number of interest payments remaining until the maturity date To find the bond price on an interest date (coupon date) use the above Bond Price formula (15-1) To find the bond price on any other date, find the bond price on the last interest date (coupon date) before the bond purchase date (using the above Bond Price formula) and move that value forward to the purchase date. Business Mathematics 12 Yield to maturity of a bond Use the above Bond Price formula to solve for the interest rate If you are using the Bond Price formula then you must use a trial and error approach to solve for the yield rate. If you are using a financial calculator, the calculator is set up to accept the inputs to do the calculation of solving for the yield rate. Sinking Funds The sinking fund method of debt repayment consists of two parts. The payment required to the sinking fund each period plus the interest that has to be paid on the debt each period, together they are the total cost each period. Book Value of the debt = The Face value of the Debt less the balance in the sinking fund Net Present Valug The Net Present Value approach is used to evaluate Investment opportunities. The Present Value is used because the investment decision is being made at the beginning of the terms of the investments. Calculate the Net Present Value of each investment alternative and choose the appropriate investment. If you are using the formulas to solve for IRR (Internal Rate Of Return) then you must use a trial and error approach to solve for the internal rate of return. NPV = Net present value (of an investment) IRR = Internal rate of return (on an investment) NPV = (Present value of cash inflows)-(Present value of cash outflows) NPV Investment Decision Criterion: Accept the investment if NPV 0. Reject the investment if NPV