Final Examination, BUS312, Spring 2011

NAME: ______Student #______

Instructions: For qualitative questions, point form is not an acceptable answer. For quantitative questions, show your work. There are a total of 120 marks on this examination composed of 12 questions and 12 pages. Answer all questions on the examination. No other sheets of paper will be marked. The examination period is three hours: there will be no extensions. No cell phones, computers, or other communications devices may be used during the examination period. Remove baseball caps or wear them backwards. No washroom breaks.

Caution — In accordance with the Academic Honesty Policy (T10.02), academic dishonesty in any form will not be tolerated. Prohibited acts include, but are not limited to, the following:

  • making use of any books, papers, electronic devices or memoranda, other than those authorized by the examiners.
  • speaking or communicating with other students who are writing examinations.
  • copying from the work of other candidates or purposely exposing written papers to the view of other candidates.

1.  (10 marks) Consider a bond that offers a fixed per annum coupon rate, paid semi-annually, and has a par value of $10,000. The coupon rate on the bond is 9% per annum compounded and paid semi-annually. When you buy the bond, the yield to maturity is 9% per annum compounded semi-annually. The next coupon on the bond is in 4 months. You sell the bond 5 years and 8 months from today. At that time, the yield to maturity is 9% per annum compounded semi-annually. Between when you buy the bond and when you sell the bond, you reinvest coupons at 8.2% per annum compounded monthly.

Required: What is the annualized holding period rate of return compounded semi-annually on your bond investment between your purchase and your sale including reinvested coupons with interest?

2. (10 marks) Today, ABC Company is planning a business investment. ABC is a start-up firm and, therefore, it has no previous investments. Also, ABC has no other investments planned or contemplated other than the one described in this problem. For an investment (expenditure) of $I today, the expected cash flow to ABC is $C per annum at the end of the upcoming year which then grows at the rate 6% per year indefinitely (that is, each cash flow after the first is expected to be 6% greater than the previous). This cash flow is profit on the investment, net of taxes and commissions, etc. Currently, ABC has no debt in its financial structure and its book equity is zero. Book equity is the sum of share-capital and retained earnings. In order to undertake its investment, ABC needs to do some financing. They plan to sell new shares to new shareholders in the amount of $I to finance their business investment. ABC’s market to book ratio for equity immediately after the share issue and the business investment is 3.0. The IRR on ABC’s business investment is 20% per annum.

Required: What is the opportunity cost for ABC’s new business investment (stated as a per annum rate of return)? Hint: you cannot determine “C” and “I” separately in this question.

3.  (10 marks) Consider a bond that offers a fixed per annum coupon rate, paid semi-annually, and has a par value of $10,000. The coupon rate on the bond is 9% per annum compounded and paid semi-annually. When you buy the bond, the quoted price is $8,630.32 and you have to wait for 4 months before you get the first coupon. You sell the bond 5 years and 8 months from today. At that time, the quoted price of the bond is $8,431.48. Between when you buy the bond and when you sell the bond, you reinvest coupons at 8.2% per annum compounded monthly.

Required: What is the annualized holding period rate of return compounded continuously on your bond investment between your purchase and your sale including reinvested coupons with interest?

4.  (10 marks) Today, you are planning a business investment. You have a start-up business and therefore, it has no previous investments. Also, your business has no other investments planned or contemplated other than the one described in this problem. Currently, your business has no debt in its financial structure and its book equity is zero. Book equity is the sum of share-capital and retained earnings. For an investment (expenditure) of $I today, the expected cash flow to the investment is $200,000 at the end of the upcoming year. Afterwards, each cash flow is 1+g greater than the previous year indefinitely. This cash flow is profit on the investment, net of taxes and commissions, etc. The IRR on the business investment is 20% per year. In order to undertake this investment, you need to do some financing. The opportunity cost on the business investment (the cost of capital) is 15% per year. You have found a possible common equity investor who is willing to finance the new business venture in exchange for a fractional common equity ownership. You plan to sell new shares to this investor in the amount of $I to finance the business investment. After financing, the investor will own 40% of common shares and you will own 60%.

Required: Jointly determine “I” and “g” described in the question.

5.  (10 marks) You believe that the constant growth version of the discounted dividend model is a reasonable representation of ABC common share value. ABC pays dividends once per year and it has just made a dividend payment (i.e., the ex-dividend date is today). The next and upcoming dividend is in one year. You belong to a dividend reinvestment plan that purchases additional ABC shares for you with your dividends (at the ex-dividend price at that time). Fractional shares are possible. ABC’s share price today is $20. The expected ex-dividend share price in one year is $21.6. Expected share price one trading day before the ex-date in one year is $23.

Required: If you purchase 100 shares today, how many shares will you have in 10 years immediately after the dividend and your reinvestment of that dividend at that time?

6.  (10 marks) On Dec 31, 2009 you borrow $X from the Royal Bank of Canada (RBC) in a mortgage agreement. Since your mortgage requires monthly payments, your first payment is at the end of January 2010. Your monthly payments are $1,500. The interest portion of your 45th payment (exactly 45 months from today) is $1,154.35. The outstanding balance on your mortgage immediately after this payment is $200,409.52.

Required: How much did you originally borrow?

7.  (10 marks) ABC has 1,250,000 outstanding shares. These common shares trade on the Toronto Stock Exchange. The value of ABC’s existing operations is $2,000,000. ABC has no debt in its financial structure and its book equity is $1,000,000. Book equity is the sum of share-capital and retained earnings. In addition to existing operations, ABC is planning a business expansion. For an investment (expenditure) of $I today, the expected cash flow to ABC’s business expansion is $525,000 at the end of the upcoming year and then 5% per year greater indefinitely. This cash flow is profit on the investment, net of taxes and commissions, etc. The internal rate of return for this new investment is 20% per annum. In order to undertake its investment, ABC needs to do some financing. They plan to sell new shares in a general cash offer to new shareholders in the amount of $I to finance their business investment. You own 20% of the outstanding shares of ABC Company before the new issue. Because you do not plan to buy new shares, your fractional ownership in ABC falls to 12.5% as the result of the issue. In solving this question, presume capital market efficiency, which, in this problem means that the stock market recognizes the value of ABC’s new venture in share price before the new share offering.

Required: Find the cost of capital on ABC’s business investment.

8.  (10 marks) ABC’s forward earnings per share for the upcoming year is $2.0. Their market to book ratio is 3.0, their forward dividend yield is 5% per annum, and their book value of equity per share is $10.

Required: What is the expected return on the purchase of an ABC common share? What major assumption are you making in determining this expected return?

9.  (10 marks) ABC share price is $25 (the price of old shares before a rights issue). ABC has just announced that they are planning a rights issue of new common shares (ABC gives existing shareholders one right per outstanding share). Ignore commissions and other transaction costs. If you subscribe in the rights offer (exercise your rights), the number of ABC shares that you own increases by 25%. The ex-rights share price, that is, ABC’s secondary market share price after the rights issue (new and old shares) is $24 per share.

Required: Find the percentage increase in your dollar investment in ABC common shares.

10.  (10 marks) Today, you purchase a financial asset that makes semi-annual payments with the first payment exactly 15 months from today and the last 12 years and 3 months from today. After the first, each semi-annual payment is 3% less than the previous. There are no other cash flows or payments on this financial asset. When you purchase the financial asset it offers a rate of return of 5.8% per annum compounded monthly. Three months after you receive the 8’th payment, you sell the financial asset. At this time, the financial assets offers a rate of return of 5.8% per annum compounded monthly. Between your purchase and your sale of the financial asset you reinvest payments in interest bearing financial assets that offer a rate of return of 5.8% per annum compounded monthly.

Required: What is the annualized holding period rate of return compounded continuously on your investment between purchase and sale including reinvested payments with interest?

11.  (10 marks) ABC Company Ltd., is considering two possible business investments that are of approximately the same risk. These investments are mutually exclusive. In both cases, their incremental free cash-flow begins one year from today. Investment A requires an expenditure today of $1,000,000. Investment A has an IRR of 15% per annum and incremental non-growing free cash flow of $A per annum indefinitely. Investment B requires an expenditure today of $1,500,000. Investment B has an IRR of 12% per annum and incremental non-growing free cash flow of $B per annum indefinitely. Ignore capital cost allowance and depreciation in this problem.

Required: ABC has asked for your advice on which project they should choose. How do you respond? Describe the circumstances that would lead you to recommend one of these investments and which one. Full marks require a complete explanation.

12.  (10 marks) ABC Co. Limited of Coquitlam, British Columbia has just started their business. Nonetheless, their shares trade on the Toronto stock exchange. Their investment into business activity is comprised of $1,100,000 of depreciable assets and $200,000 of trade capital assets. The capital cost allowance rate on depreciable assets is 4% per annum. Ignore the half-year rule in this problem. ABC anticipates that economic depreciation on depreciable assets is also 4% per annum. Because economic depreciation is 4% per annum, ABC uses a depreciation charge for financial statement purposes equal to 4% of the book value of net fixed assets. Also, in order to offset the adverse effect of economic depreciation, ABC makes per-annum “maintenance” capital expenditures equal to 4% of the book value of net fixed assets. Maintenance capital expenditures are depreciable and belong to the same capital cost allowance asset class as the original depreciable asset investment. Because accounting depreciation, economic depreciation, and maintenance capital expenditure are all 4% per annum, (and ignoring the half year rule), the book value of ABC’s fixed assets for financial statement purposes is always (year after year into the future) equal to the undepreciated capital cost for tax purposes. Both net fixed assets and the undepreciated capital cost (book value of assets for tax purposes) are expected to be $1,100,000 indefinitely.

Based on their best estimates, ABC predicts per annum revenues of $S per annum. Their contribution margin is 20% and fixed operating costs are $50,000 per annum. They expect no business growth. ABC’s corporate tax rate is 40%. The payback period on ABC’s business investment is 10.5178 years.

ABC is a non-growing firm, and therefore, they have no retention for the purpose of reinvestment. Dividends, year after year indefinitely, are expected to be equal to ABC’s net income. ABC has financed their investment of $1,300,000 with long term bonds and with common equity. The bonds are of sufficiently long term that they can be represented as a perpetuity of coupons (i.e., par value repayment can be ignored for the purpose of valuation). Coupons are paid annually and the next and upcoming coupon is in exactly one year. The par value on the bonds is $950,000 and the coupon rate is 6% per annum (compounded once per year). The average rate of return, for shares of approximately the same risk as those of ABC, is about 10%. ABC has 100,000 shares outstanding.

Required:

(i)  What is the forecast for ABC’s per annum revenues?

(ii) What is your best estimate of the value of a share in ABC?

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