^[46] You purchase a new car. The dealer requires that you put $6,000 down, followed by monthly payments of $999 over four years. (The first payment is made one month after you buy the car.) The interest rate is 9.9% effective.

(a) What is the cash price (selling price) of the car?

(b) What is the cost of financing?

 

^[47] You contribute $2,500 into your RRSP at the end of every quarter for 5 years. If your RRSP earns 8% compounded quarterly, how much interest will you earn in the 5 years?

 

^[48] A computer that sells for $3,999 may be purchased by making a down payment, plus a series of month-end payments of $225 for one and a half years. If the interest rate is 9% compounded monthly, what is the size of the down payment?

 

^[49] You are buying a house for $260,000 with a down payment of 20%. The interest rate is 8.5% compounded semiannually. The mortgage is amortized over 25 years for a 3-year term.

(a) Calculate the size of the monthly payment. The lender’s policy is to round payments up to the next whole dollar.

(b) How many payments would be required?

(c) How much interest will you pay in the first 3 years?

(d) How much interest would you pay in the third year only?

(e) You make an extra lump-sum payment of $40,000 at the end of 3 years. What is the outstanding balance after this lump-sum payment?

(f) When you go to renew your mortgage at the end of 3 years, the rates have fallen to only 5.5% compounded semi-annually for a 3-year term. Find the size of the new payment.

(g) The payment determined in part (f) is much smaller than you thought due to the lower rate and lump sum payment. You have decided to increase the monthly payment so that you pay off the remaining balance in only 12 years instead of 22 years. Find the size of the new payment. Round up to the next dollar.

(h) Find the size of the final payment.

 

^[50] A summer cottage, valued at $120,000, may be purchased by paying a $20,000 down payment and financing the balance with a mortgage at 9% compounded semi-annually and monthly payments for 15 years.

(a) Find the monthly payment. Round up to the next dollar.

(b) How much of the 60th payment pays interest, and how much goes toward the principal?

(c) After the 100th payment, how much of the original mortgage is still left to be paid?

(d) After making 115 payments, what percent of the original debt will have been paid off?

 

^[51] You are contemplating purchasing a business selling computer software over the Internet.

• • You estimate that the purchase price would be $40,000.
  • Your expenses should be $10,000 per year.
  • You expect annual revenues to be $15,000 for the first two years and $20,000 each year after that.
  • You plan to sell the business at the end of six years and estimate you will get $55,000.
  • Your MARR is 15% effective.
  • Assume all expenses are paid at the beginning of the year and revenues are received at the end of the year. Time diagram is required.

(a) What is the IRR? Should you purchase the business? Why or why not?

(b) Calculate the NPV. Should you purchase the business? Why or why not?

(c) What is the highest purchase price you could pay and still be willing to buy the business?

(d) What is the lowest selling price you could tolerate and still be willing to undertake the business? Round to the nearest dollar.

(e) Your accountant advises you that your annual revenue projections are too high. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

 

^[52] A food concession at an airport has a 7-year life and costs $200,000. Renovations will cost you another $50,000. The concession’s operation is expected to produce net incomes of $60,000 a year. The salvage value of the equipment and ending inventory are expected to total $40,000. Your MARR is 20%.

(a) Find the IRR. Would you buy this concession? Why or why not?

(b) Find the NPV. Would you buy this concession? Why or why not?

(c) By how much does the purchase price of the concession have to fall to make the investment worthwhile? What is the new price?

(d) Your accountant tells you your salvage estimate is too low. What is the minimum salvage value you require to make the investment worthwhile?

(e) The Canadian government has decided to offer a one-time subsidy to encourage the creation of concession stands at the airport. The subsidy is received one year later. How large of a subsidy would you require to make the investment worthwhile?

(f) Your accountant advises you that your projected net income is too low. What is the minimum annual increase in revenue you require to make the investment worthwhile?

 

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