## Grandma Essay

This paper seeks to analyze and discuss a case of a person who has inherited some money and how he will manage his money to accomplish a financial objective in the future of having the amount of needed down payment to acquire a house.  To be specific about the person, case facts provided that he has recently inherited \$25000 from his Grandmother and he has decided to invest it in order to have a big enough down payment to buy a house later on.  How does he plan to invest it?  Why?  How much does he need to accumulate for down payment?

Given the above case facts without other information as to what is the age of the person and when is  the time to have house and other important fact will leave use nowhere. Hence we need to make further assumptions.  Let us therefore assume further that the heir is 21 years old and that he plans to have a house in Canada at age of 31, or after 10 years from now. There is also a needed to assume the value of a house that will be acquired ten years from now. As of now present bungalow type in Canada cost about \$300,000 and it is assumed that after every five years price will increase by 100% so that after 10 years the typical value of the house from now the \$300,000 would have increase to \$1,200,000, because five years before that the value was already \$600,000.

Since the problems calls for the amount of down payment to be made after ten years, it must be further assumed that a minimum 25% down-payment is needed in order to acquire the house with the balance in loans that will be  payable over the next ten years.  Hence 25% of the \$1,200,000 is \$300,000 to be out target amount for the downpayment.

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We needed the additional assumptions are needed to supply the deficiency of the facts.  To illustrate the justification of the need to make assumption, one cannot determine the amount of down payment for the house if the value of the house cannot be estimated and the age of the person who just inherited must be assumed because we cannot say if he is already too old to plan to own a house.

We will  now to proceed to analyze the options  available.   First option: he can invest the \$ 25,000 at the safest and secured investment at the highest rate possible and said future value of investment must be made available after ten years.

While the \$ 25,000 money is not needed for now, since we need it after 10 years it must first be invested at the maximum rate but be made secure and available at the time the money will be required for down-payment after ten years.  In our additional assumption, we determined that the target amount is 25% of the \$1,200,000 or \$300,000 as down payment.  To reach the target amount, it must be made clear that investment is a function of time and available rates of return on investments.  To get a \$300,000 after ten years with the amount of \$25,000 invested today what is the expected rate of return to be used as guide in planning our investment?  Knowing the rate of return of the investment will more or less guide us what type of investment is suited to take.  Using the formula of compound interest the rate needed is 28.20%.  Please see Appendix A to verify the computation.  Is there a bank that offers a rate of 28.20% per annum compounded annually?  Is there a bond investment or stock investment that would promise such rate?  It would seem there is none in both questions.  It would therefore mean that to set a target amount of \$300,000 at the rate of 28.20% for ten years is virtually impossible. Since the target is not attainable, let us try the next option.

Our next option for that heir to save \$500 monthly from his salary  and deposit in a bank that would give 5% interest per year compounded monthly. The future value of the monthly investment after 10 years will complement the amount of deficiency that could be generated from the future amount of the \$25,000 invested at a realistic and attainable rate.   This option assumes that after inheriting the money, the heir is employed and he will  be able to make a savings of \$ 500 per month from his salary and make an investment monthly at the bank with an interest of 5%  per annum compounded monthly.  The question then that will be answered is what is the future value (Brigham and Houston, 2002) of a 500 US dollar invested to day at 5% compounded monthly in ten years?  This question requires the use of annuity formula which when applied will give g us the amount of \$77,641.66.  Please see appendix B.  Given therefore the  \$77,642 (rounded off), the needed targeted amount for the \$ 25,000-investment is \$ 222,358,which is difference of \$ 300,000 and \$77,642.   After applying the same formula where earlier got 28.20% (See Appendix A), given the future amount targeted of \$222,358 (rounded off) with \$ 25,000 invested now compound annually in ten year, the rate is 24.2%. It is now lower than the 28.20%.  If we look at the stock market, it is difficult to get 24.20 as rate of return to guarantee the amount of \$ 222,358 after ten years.  So, what is the next option?

Let us examine our next option which to save and invest \$1,000 per month at a bank at 5% monthly for 10 years to  supplement the deficiency of the value generated by the \$ 25,000 ten year investment.

This option is simple, since using now the principle derived in number 2, the amount that could be derived by the investing \$1,000 at 5% for ten years compounded annually is \$155,284 or just double the amount generated by \$500 under the same condition at the amount of \$77,642.  By getting the future amount of savings from salary of \$155,284 after ten years, what is now the rate at which we should invest the \$25,000 inherited money.  Applying the formulas, the needed amount is \$ 144,716 the rate needed would now be 19.19%, which still is quite high.  If there are stock investments that could generate 19.19% then go for it.

We can now conclude that investing the 25,000 to have the desired future amount of \$300,000 after 10 years, we needed to have at least have a saving of \$1,000 dollars per month to be invested at the banks at the rate of 5% compounded monthly for 10 years to generate \$ 155,284 to complement the deficiency of \$ 300,000 which allow the investment of \$25,000 at 19.19%. However, the rate is still high to find a stock investment that could give such rate.

Investing the \$25,000 is stock will simply not allow us to have the targeted amount of \$ because of the low rates of return from said type of investment. As a rule stock investments may be possible within the range of 6 to 12%.  Higher than those rates, the investment would be considered too risky.  It should be understood that prices of real estate was assumed to double in every five years, which means that the minimum effective rate of return on investing in real estate is 20% per year as compare to stock investment at the rate of 6 to 12%.  This means that investing in real estate generates higher than stock investment because real estate investment is normally long-term, hence the risk is higher in terms of convertibility to cash as compared to other investment.  The lesson then here is that an investment in ordinary stocks could not surpass the rates generated by real estate investment.  The best option for the heir is not wait for ten years to make an investment in the house.  He must make the down payment to acquire house now with the down payment of only \$75,000. Since he has inherited \$25,000 he needs \$50,000 from friends more but as to how he will get the money is assumed again to be available at the rate that would allow him to pay assuming he has a salary. In addition to amortization of the \$ 50,000 loan from friends, he still have to pay for the amortization of \$225,000 balance of the price of the house. That is the only best possible option he could pay for the house. In short, the heir needs not to wait for ten years to make the down payment, he must make it now.

Appendices

Appendix A –   Computation of implicit interest rate, See excel file
Appendix B-  Computation future value of ordinary annuity. See excel fie

Reference:

1. Brigham and Houston (2002) Fundamentals of Financial Management, Thomson South-Western, London, UK