You are planning to buy a house in Oshawa that has a price of $1,200,000. One of the local financial institutions has offered you a mortgage at a quoted rate of 4.2% per year. Interest will be compounded semi-annually. The bank has indicated that they will require a $300,000 down payment. The bank is prepared to lend you the remainder of the purchase price of the house. The amortization period will be 25 years and the term of the mortgage will be 2 years. You are going to make monthly payments on your mortgage. The payments will be made at the end of each month. a) Answer the following questions: i. What is the amount of your monthly payment? ii. How much will you pay in total on your mortgage over the life of your mortgage? iii. What is the total interest that will be paid over the life of your mortgage? iv. What is the total you will pay during the term of the mortgage? V. What is the balance of the mortgage (the principal outstanding) at the end of the term? vi. How much principal will you have paid off during the initial term of your mortgage? vii. How much interest will you have paid off during the initial term of your mortgage? b) Prepare a mortgage amortization schedule to illustrate how the mortgage will be repaid over the next 25 years and calculate the following: i. Use the amortization table to determine the first payment when the principal portion of the payment is greater than 50% of the total payment. Identify the payment number where this occurs. Amortization Schedule Payment Principal Interest Balance Amount Principal Principal Principal Number Amount Expense Owing of Component Amount Paid / at the incurred Before Beginning during Payment Payment of Payment at the End of Period Amount of the month Payment 1 2 c) You have decided to increase your monthly payments by $500 until the mortgage is paid off. i. How long does it take to pay off your mortgage? (Hint: Create a new amortization schedule with the increased payment and identify the payment number where your mortgage is fully paid off. The last payment will be the principal outstanding in the previous month.) ii. How much interest do you save by making the extra payment of $500 every month? (Hint: Determine the new total paid over the life of your mortgage) You are an analyst in charge of valuing common stocks. You have been asked to value two stocks. The first stock NEWER Inc. just paid a dividend of $6.00. The dividend is expected to increase by 60%, 45%, 30% and 15% per year, respectively, in the next four years. Thereafter, the dividend will increase by 4% per year in perpetuity. a) Calculate NEWER's expected dividend for t = 1, 2, 3, 4 and 5. The required rate of return for NEWER stock is 14% compounded annually. b) What is NEWER's stock price? The second stock is OLDER Inc. OLDER Inc. will pay its first dividend of $10.00 three (3) years from today. The dividend will increase by 30% per year for the following four (4) years after its first dividend payment. Thereafter, the dividend will increase by 3% per year in perpetuity. c) Calculate OLDER's expected dividend for t = 1, 2, 3, 4, 5, 6, 7 and 8. The required rate of return for OLDER stock is 16% compounded annually. d) What is OLDER's stock price? Now assume that both stocks have a required rate of return of 40% per year compounded annually for the first six years, 25% per year compounded annually for the following five years, then 12% per year compounded annually thereafter. e) What is NEWER's stock price? f) What is OLDER's stock price? (Hint: You may need to forecast more dividends than you did in parts a, and c.)
Q1:
Blossom is 30 years old. She plans on retiring in 25 years, at the age of 55. She believes she will live until she is 105.
In order to live comfortably, she needs a substantial retirement income. She wants to receive a weekly income of $5,000 during retirement. The payments will be made at the beginning of each week during her retirement.
Also, Blossom has pledged to make an annual donation to her favorite charity during her retirement. The payments will be made at the end of each year. There will be a total of 50 annual payments to the charity. The first annual payment will be for $20,000. Blossom wants the annual payments to increase by 3% per year. The payments will end when she dies.
In addition, she would like to establish a scholarship at Toronto Metropolitan University. The first payment would be $80,000 and would be made 3 years after she retires. Thereafter, the scholarship payments will be made every year. She wants the payments to continue after her death, therefore the payments will go on forever. To keep pace with inflation, Blossom would like the amount of the scholarship payments to increase by 2.5% each year.
Blossom has a niece, Maddy. Maddy is 15 years old. Blossom plans on giving Maddy $2,000,000 when Maddy turns 45 years old. (Hint: Consider the number of years between this payment and the time Blossom retires).
During retirement, Blossom expects to earn 6.5% per year compounded annually.
Blossom currently has $100,000 in investment account A, that earns 7% interest per year compounded quarterly. Blossom currently contributes $500 every month to investment account B. These contributions are made at the end of each month and will continue until she retires at age 55. Blossom expects to earn 9% per year compounded semi-annually on her monthly contributions to investment account B.
a) How much money does she need when she retires at the age of 55? Be certain to include all of her retirement goals.
b) How much money will she have when she retires?
c) How much is she short? [Hint: The shortfall is the difference between the amounts in parts (a) and (b)]
d )In order to finance any shortfall, Blossom will make monthly contributions into a new retirement account, investment account C, that will earn 8.5% per year compounded annually. The contributions will be made at the beginning of each month until she retires at age 55. How much must she contribute each month to the investment account C?
Q2:
On December 31st, 2004, your grandmother decided to buy a 30-year Government of Canada bond. The bond had a face value of $1,000,000. The annual coupon rate on the bond was 4.40%. Coupons were paid semi-annually. On December 31st, 2004, the yield to maturity on Government of Canada bonds was 3.70% per year. (The term structure of interest rates or yield curve was flat.)
After holding the bond for 20 years, your grandmother decided to sell the bond on December 31st, 2024. Prior to selling the bond, your grandmother received the December 31st, 2024 coupon payment. On December 31st, 2024, the yield to maturity on Government of Canada bonds had increased to 4.10% per year. (The term structure of interest rates or yield curve was flat.)
a) How much did your grandmother pay for the bond on December 31st, 2004?
b) How much did your grandmother sell the bond for on December 31st, 2024?
c) What was the
i)Quote it as an effective periodic rate.
ii)Quote it as an effective annual rate.
d) What would have been your grandmother’s rate of
i)Quote it as an effective periodic rate.
ii)Quote it as an annual percentage rate. What do you notice about this rate?
The questions in the photos will be Q3 and Q4. Please round to nearest 8 decimal places in calculations to ensure correct results. Make sure to get all parts of the question. Use excel/google sheets to make your calculations accurate.
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