Question

Question 1. (Total: 25 marks) You want to buy a car valued at $48,000. You wi ll make an upfront down -payment of $5,000 on the car , and borrow the rest of the money from your bank. Your bank will give you a 5- year loan at 2.5% APR compounded semi -annually . You plan to make biweek ly payments (i.e., one payment every two weeks) on the loan . The bank requires that you make the first payment two weeks after you signed the loan contract. Find the answer to the following questions . a. What is the effective annual rate? b. What is the effective biweekly rate? (3 marks ) c. What will be your biweekly loan payment? d. What is the balance on your loan in 3 years’ time, after 78 payments? e. Show the amortization schedule (table) for the fi rst 5 payments. If you are doing this on an Excel spreadsheet, copy and paste the first 5 rows from the amortization schedule into a Microsoft Word (or an y other word- processing software) document file . f. You want to put enough money into your bank account to pay for the loan payments for the next six months. If your bank account yields a n APR of 2% (compounded bi -weekly) , how much money should you put in your bank account now?

Question 2. (Total: 25 marks) XYZ Inc. is cons idering a project to manufacture 2 million boxe s of surgical face masks annually for five years, for selling price of $20 per box. To get the project started, XYZ must invest $1 5 million in new plant and equipment. Annual fixed costs are estimated to be $6 million and variable costs are estimated to be $12 per box. The CCA rate for the plant and equipment is 30%, and the firm's marginal tax rate is 35%. After five years, the plant and equipment can be sold for an estimated $2 million. XYZ estimates that net working capital will increase by $ 900,000 at the initiation of the project , and 90% of this amount will be recovered at the end of the project. What is the project's net present value if the required rate of return on projects of similar risk is 16 %? Should XYZ run this project? Assume all cash flows, except CCA tax shields, occur at the end of the year.

Question 3. (Total: 25 marks) Based on your research, the following states of economy, probabilities of states, and returns are forecasted for Stock A and Stock B: Return if State Occurs State of Economy Probability of state Stock A Stock B Recession 0. 65 - 0.15 - 0.2 Normal 0.3 0.13 0.14 Irrational exuberance 0. 05 0.2 0.29 a. What is the expected return on Stock A? b. What is the expected return on Stock B? c. Your research also indicates that s tock A’s beta is greater than stock B’s beta by 0.5. calculate the expected market risk premium based on the Capital Asset Pricing Model (CAPM) ? d. Given that t he risk -free rate is 0.5%, what is the expected return on the market based on the CAPM? (1 mark) e. Given that the risk -free rate is 0.5% , c alculate the expected return on a portfolio that has 20% invested in Stock A, 2 0% invested in Stock B, and the rest invested in the risk- free asset. f. Calculate the standard deviation of returns for the portfolio in part (e).

Question 4. (Total: 25 marks) DEF Company expects an EBIT of $19,750 every year forever. DEF currently has no debt, and its cost of equity is 15 percent. The firm can borrow at 10 percent. T he corporate tax rate is 35 percent . Assume no financial distress risk. a. W hat is the value of the firm with its existing capital structure ? b. What will the value be if the company converts to 50 percent debt? c. What are the cost of equity and WACC if the company converts to 50 perce nt debt? d. What will the value be if the company converts t o 100 percent debt? e. What is the WACC if the company converts to 100 percent debt? f. Compare the firm values and WACCs at 0%, 50%, and 100% debt. What can we conclude regarding the relationship between leverage level, firm value, and WACC?

Answer 1

1.

a) The effective annual rate =(1+semiannual rate/2)^2- 1 = (1+0.025/2)^2-1 =0.025156 or 2.5156%

b) Effective Bi-weekly rate (26 bi-weeks in a year) = 26* ((1+annual rate)^(1/26) - 1)

=26* ((1.025156)^(1/26)-1) = 0.024857 or 2.4857%

c) Loan amount = $48000- $5000 = $43000

No of payments = 26*5 = 130

Interest rate per bi-week = 2.4857%/26 = 0.000956

So, present value of payments(A) = loan amount

=> A/0.000956*(1-1/1.000956^130) = 43000

=> 122.1913 *A = 43000

=> A =$351.91

So, the bi-weekly payment = $351.91

d) Balance on loan after 3 years (78 payments)

= Future value of loan - Future value of payments

=43000*(1.000956)^78 - 351.91/0.000956*(1-1/1.000956^78)

=$19889.30 which is the balance on the loan outstanding after 3 years