# FNCE 300 Assignment 3 –Athabasca

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Assignment 3

Assignment 3 is due after you complete Lessons 9 to 11. It is worth 20% of your final grade.Prepare your responses to these assignment problems in a word processing file; put financial data in a spreadsheet file. As you complete the assignment problems for each lesson, add your responses to these files.

Do not submit your answers for grading until you have completed all parts of Assignment 3. Note: In assignments, show all calculations to 4 decimal places.

Lesson 9: Assignment Problems

1. The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247, says that: P0 = D1 / (k – g)
2. rearrange the terms to solve for:

1. ii.  D1. As an example, to solve for k, we would do the following: 1.  Multiply both sides by (k – g) to get: P0 (k – g) = D1 2.  Divide both sides by P0 by to get: (k – g) = D1 / P0 3.  Add g to both sides: k = D1 / P0 + g

(8 marks)

1. Notation: Let

Pn = Price at time n

Dn = Dividend at time n

Yn = Earnings in period n r = retention ratio = (Yn– Dn) / Yn = 1 – Dn/ Yn = 1 - dividend payout ratio En = Equity at the end of year n k = discount rate

g = dividend growth rate = r x ROE

ROE = Yn / En-1 for all n>0. We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid.

1. Using the Discounted Dividend Model, calculate the price P0 if

D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share

1. What, then, will P5 be if: D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12?

C.   If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2?

D.   Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result.

E.     If k = ROE, we can show that the price P0 doesn’t depend on r. To see this, let

g = r x ROE, and ROE = Yn / En-1, and since r = (Yn – Dn) / Yn , then D1 = (1 – r) x Y1 and

 P0 P0 = [(1 – r) x Y1] / (k – g) P0 = [(1 – r) x Y1] / (k – g), but, since k = ROE = Y1 / E0 P0 = [(1 – r) x Y1] / (ROE – r x ROE) P0 = [(1 – r) x Y1] / (Y1 / E0 – r x Y1 / E0) P0 = [(1 – r) x Y1] / (1 – r) x Y1 / E0), and cancelling (1 – r) P0 = Y1   The firm buys back 10,000 shares for \$10 cash each, and you choose not to sell your share back to the company.

D.   The firm declares a 2-for-1 stock split.

E.    The firm declares a 10% stock dividend.

F.   The firm buys new equipment for \$100,000, which will be used to earn a return equal to the firm's discount rate.

(12 marks)

DoYou are starting a new business, and you want to open an office in a local mall. You have been offered two

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