Sample Quiz 2 with Solutions

.pdf

School

University of Rochester *

*We aren’t endorsed by this school

Course

402

Subject

Finance

Date

Jan 9, 2024

Type

pdf

Pages

5

Uploaded by UltraSteel12891

Report
Finance 402 Capital Budgeting and Corporate Objectives Professor Alex Priest Sample Quiz 2 SOLUTIONS 1
1. (a) (30 points) Suppose you expect Tech Inc.’s earnings to grow at 5% per year forever. This firm pays dividends annually, and pays out all of the earnings as dividends. It just paid a dividend of $2 per share. The cost of capital is 15% per year compounded monthly. i. (23 points) What is the value of Tech Inc.’s stock? Next years dividend will be 2(1 + 0 . 05) = 2 . 1 so that the value of the firms stock is The effective annual rate is (1 + . 15 12 ) 12 - 1 = 0 . 160755 . Which implies that the value of the firm’s stock should be 2 . 1 0 . 1608 - 0 . 05 = $18 . 96 ii. (4 points)What would be the value of Tech Inc.’s stock if instead it were able to grow earnings at a rate of 6.5% by reinvesting 25% of earnings into the firm instead of paying dividends? Going forward, the firm would pay 75% of earnings. Earnings in the first year will be unchanged from before. The earnings in the first year will still be $ 2.10 per share. If 75% of earnings are paid out in the first year, then the first dividend payment will be $2 . 10 × 0 . 75 = $1 . 575 . With this reinvestment, the growth rate increases to 6.5%. Thus the value of the stock with reinvestment is 1 . 575 0 . 1608 - 0 . 065 = $16 . 44 iii. (3 points) If you hold shares of Tech Inc, do you want them to reinvest the earnings or continue to pay out 100%? If you are a shareholder, you prefer that they do not reinvest earnings because the stock will be worth less. (b) (10 Points) Suppose you expect XYZ stock’s quarterly dividends to remain constant for the next 10 years and grow at 4% per quarter thereafter. The firm has just paid its quarterly dividend and you expect the next quarterly dividend to be $1 per share. What is the maximum price that you would be willing to pay for XYZ stock if you require an 8% quarterly rate of return? (Hint: Try to break the problem up into pieces.) Solution: We split the evaluation into 2 parts the first is the present value of a ten year annuity, with quarterly dividends. The second is the present value of the stock price at time 10. Step 1: Find the value of the annuity: 2
1 0 . 08 [1 - 1 1 . 08 40 ] = 11 . 92 (1) Step 2: d 41 = 1(1 . 04) = 1 . 04 (2) Then compute the present value 10 years from today of all the future cash flows: P 40 = d 41 r e - g = 1 . 04 0 . 08 - 0 . 04 = 26 (3) Next, find the present value of this figure. PV ( P 40 ) = P 40 (1 . 08) 40 = 1 . 197 (4) The final price is simply the sum of these two components 11 . 92 + 1 . 197 = 13 . 117 3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help