Course: Corporate Finance. 25 questions in total. Please answer correctly with the solutions.

Question 1. Which of the following statements is FALSE?

The annual percentage rate indicates the amount of simple interest earned in one year.
Because interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of our cash flows.
The effective annual rate indicates the amount of interest that will be earned at the end of one year.
The annual percentage rate indicates the amount of interest including the effect of compounding.

Question 2. Your bank is offering you an account that will pay 29% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of each of the following (Round to two decimal places):

Six months.
One year.
One month.

Question 3. You have found three investment choices for a one-year deposit: 11 % APR compounded monthly, 10 % APR compounded annually, and 10 % APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.) (Round to three decimal places.

Question 4. Your bank account pays interest with an EAR of 9 %. What is the APR quote for this account based on semi-annual compounding? What is the APR with monthly compounding? (Round to three decimal places)

Question 5. Suppose the interest rate is 8.9 % APR with monthly compounding. What is the present value of an annuity that pays $ 83 every three months for five years?

The three-month effective interest rate is ______%. (Round to three decimal places.)

Question 6. Suppose you invest $ 104 in a bank account, and five years later it has grown to $138.78. (Round to four decimal places).

1. What APR did you receive if the interest was compounded semi-annually?
2. What APR did you receive if the interest was compounded monthly?

Question 7. Suppose the Bank of Montreal is offering a mortgage with an effective annual rate (EAR) of 4.625%. If you plan to borrow $170,000, what will your monthly payment be assuming a 30-year amortization? (Note: Be careful not to round any intermediate steps less than six decimal places.) (Round to nearest cent)

Question 8. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2,918 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.089% (APR with semi-annual compounding). How much do you owe on the mortgage today? (Note: Be careful not to round any intermediate steps less than six decimal places.)

Also, The monthly discount rate is _____%. (Round to five decimal places.)

Question 9. You have just sold your house for $1,100,000 in cash. Your mortgage was originally a 35-year mortgage with monthly payments and an initial balance of $750,000. The mortgage is currently exactly 18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 7.75% (APR with semi-annual compounding), how much cash will you have from the sale once you pay off the mortgage? (Note: Be careful not to round any intermediate steps.)

1. What is the discount rate for the mortgage?

The discount rate for the mortgage is ____%. (Round to six decimal places to answer but carry full precision for remaining calculations.)

What is the monthly mortgage payment? The monthly mortgage payment is $ ______. (Round to the nearest cent, for example, 1234.56 to answer, but carry full precision for remaining calculations.)
What is the remaining balance on the mortgage? The remaining balance is $_____. (Round to the nearest cent.)
How much cash will you have from the sale once you pay off the mortgage? The amount of cash left over from the sale is $_____. (Round to the nearest cent.)

Question 10. Most provinces in Canada have harmonized their cost of credit disclosure requirements so that when the compounding interval for the APR is not stated explicitly, it is equal:

1. 1. to the interval between the payments
  2. to the number of payment intervals in a year
  3. to the effective rate
  4. to the nominal rate

Question 11. Your mortgage has 21 years left and has an APR of 6.965% (with semi-annual compounding) with monthly payments of $1,500. (Round to nearest cent)

1. What is the outstanding balance?
2. Suppose you cannot make the mortgage payment and you are in danger of losing your house to foreclosure. The bank has offered to renegotiate your loan. The bank expects to get $167,000 for the house if it forecloses. They will lower your payment as long as they will receive at least this amount (in present value terms). If current 21-year mortgage interest rates have dropped to 4.527% (APR with semi-annual compounding), what is the lowest monthly payment you could make for the remaining life of your loan that would be attractive to the bank?

Question 12. You have a credit card debt of $25,000 that has an APR (monthly compounding) of 18%. Each month you pay the minimum monthly payment only. You are required to pay only the outstanding interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 12%. After considering all your alternatives, you decide to switch cards, roll over the outstanding balance on the old card into the new card, and borrow additional money as well. How much can be borrowed today on the new card, in total (the rolled-over amount plus additional borrowings), without changing the minimum monthly payment you will be required to pay? Note: Make sure all calculations are held to at least five (5) decimal places.

The original loan payment is $_____. (Round to the nearest cent.)

Question 13. Assume that in Canada in 1974 interest rates were 7.77% and the rate of inflation was 11.77%.

1. What was the real interest rate in 1974? (NOTE: do not approximate). (Answer to round to two decimal places.)
2. How would the purchasing power of your savings have changed over the year?

Question 14. If the rate of inflation is 5.9%, what nominal interest rate is necessary for you to earn a 2.1% real interest rate on your investment? (Round to two decimal places.)

Question 15. Consider a project that requires an initial investment of $96,000 and will produce a single cash flow of $148,000 in six years.

1. What is the NPV of this project if the six-year interest rate is 4.9% (EAR)?
2. What is the NPV of this project if the six-year interest rate is 10.2% (EAR)?
3. What is the highest six-year interest rate such that this project is still profitable?

Question 16. The target range of annual inflation rates established by the Bank of Canada and the federal government currently extends:

from 1 to 3 percent
from 5 to 8 percent
from 0 to 1 percent
from 10 to 12 percent

Question 17. What is the shape of the yield curve given the term structure below? What expectations are investors likely to have about future interest rates?

Term	1 year	2 years	3 years	5 years	7 years	10 years	20 years
Rate (EAR %)	2.01	2.42	2.72	3.31	3.77	4.15	4.93

What is the shape of the yield curve for the term structure? (Select the best choice below.)

The yield curve is an inverted yield curve (decreasing).
The yield curve is a flat yield curve.
It is hard to tell because we are not given an EAR for every year.
The yield curve is a normal yield curve (increasing).

Question 18. The rate of growth of your purchasing power, after adjusting for inflation, is determined by _______.

the periodic interest rate
the risk-free interest rate
the nominal rate of interest
the real interest rate

Question 19. Sherritt's five-year borrowing rate is 43.061% and the Government of Canada's is 1.44%. Both interest rate quotes are effective annual rates (EARs). Which would you prefer? $500 from Sherritt paid today or a promise that the firm will pay you $800 in five years? Which would you choose if the Government of Canada offered you the same alternatives?

You would prefer: (Select the best choice below)

$800 from the Government of Canada in five years and $500 from Sherritt today.
$500 from the Government of Canada today and $800 from Sherritt in five years.
$800 from the Government of Canada in five years and $800 from Sherritt in five years.
$500 from the Government of Canada today and $500 from Sherritt today.

Question 20. Which of the following statements is FALSE?

To compensate for the risk that they will receive less if the firm defaults, investors demand a lower interest rate than the rate on Treasury Bills of the Government of Canada.
The actual cash flow that the investor will get to keep will be reduced by the amount of any tax payments.
The right discount rate for a cash flow is the rate of return available in the market on other investments of comparable risk and term.
The equivalent after-tax interest rate is r(1 - τ).

Question 21. Your best taxable investment opportunity has an EAR of 4.7%. Your best tax-free investment opportunity has an EAR of 2.7%. If your tax rate is 32%, which opportunity provides the higher after-tax interest rate?

The (taxable or tax-free?) ______ investment opportunity has a higher after-tax interest rate with __%.

(round to one decimal place.)

Question 22. The government of Canada pays lower rates of interest than Canadian corporations when each of them borrows from the public because _______.

the government of Canada only pays the nominal rate when it borrows
the government of Canada only pays the real rate when it borrows
the government of Canada only pays the risk-free rate when it borrows
the government of Canada only pays the overnight rate when it borrows

Question 23. Your best friend consults you for investment advice. You learn that his tax rate is 38%, and he has the following current investments and debts:

A car loan with an outstanding balance of $5,000 and a 4.73% APR (monthly compounding)
Credit cards with an outstanding balance of $10,000 and a 14.91% APR (monthly compounding)
A regular savings account with a $30,000 balance, paying a 5.41% effective annual rate (EAR)
A money market savings account with a $100,000 balance, paying a 5.15% APR (daily compounding)

1. Which savings account pays a higher after-tax interest rate? Regular savings pays _____%. (round to two decimal places)
2. Should your friend use his savings to pay off any of his outstanding debts?

Question 24. In the summer of 2008, at Heathrow Airport in London, BB (best of the best), a private company, offered a lottery to win a Ferrari or 81,302 British pounds, equivalent at the time to about $162,604. Both the Ferrari and the money, in 100-pound notes, were on display. If the U.K. interest rate was 6% per year (EAR), how much did it cost the company in pounds each month to keep the cash on display? That is, what was the opportunity cost of keeping it on display rather than in a bank account? (Ignore taxes.) (Hint: Make sure to carry at least six decimal places for all intermediate calculations.)

The opportunity cost of keeping it on display rather than in a bank account is £_____ per month. (Round to two decimal places).

Question 25. Your firm is considering the purchase of a new office phone system. You can either pay $31,500 now, or $1,000 per month for 39 months.

1. Suppose your firm currently borrows at a rate of 6% per year (APR with monthly compounding). Which payment plan is more attractive?
2. Suppose your firm currently borrows at a rate of 16% per year (APR with monthly compounding). Which payment plan would be more attractive in this case?