This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ompany’s stock you need is: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1 / (7 + 1) Percent of stock needed = .1250 or 12.50% 332 So, the number of shares you need to purchase is: Number of shares to purchase = (600,000 × .1250) + 1 Number of shares to purchase = 75,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 75,001 × $39 Total cost = $2,925,039 2. If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats up for election. So, the percentage of the company’s stock you need is: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% So, the number of shares you need is: Number of shares to purchase = (5,800 × .25) + 1 Number of shares to purchase = 1,451 So, the number of additional shares you need to purchase is: New shares to purchase = 1,451 – 300 New shares to purchase = 1,151 3. If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats up for election. So, the percentage of the company’s stock you need is: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% So, the number of shares you need to purchase is: Number of shares to purchase = (1,200,000 × .20) + 1 Number of shares to purchase = 300,001 And the total cost will be the shares needed times the price per share, or: Total cost = 300,001 × $9 Total cost = $2,700,009 333 4. Under cumulative voting, she will need 1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats up for election. So, the percentage of the company’s stock she needs is: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1 / (6 + 1) Percent of stock needed = .1429 or 14.29% Her nominee is guaranteed election. If the elections are staggered, the percentage of the company’s stock needed is: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% Her nominee is no longer guaranteed election. 5. Zero coupon bonds are priced with semiannual compounding to correspond with coupon bonds. The price of the bond when purchased was: P0 = $1,000 / (1 + .035)50 P0 = $179.05 And the price at the end of one year is: P0 = $1,000 / (1 + .035)48 P0 = $191.81 So, the implied interest, which will be taxable as interest income, is: Implied interest = $191.81 – 179.05 Implied interest = $12.75 6. a. The price of the bond today is the present value of the expected price in one year. So, the price of the bond in one year if interest rates increase will be: P1 = $60(PVIFA7%,58) + $1,000(PVIF7%,58) P1 = $859.97 If interest rates fall, the price if the bond in one year will be: P1 = $60(PVIFA3.5%,58) + $1,000(PVIF3.5%,58) P1 = $1,617.16 Now we can find the price of the bond today, which will be: P0 = [.50($859.97) + .50($1,617.16)] / 1.0552 P0 = $1,112.79 For students who have studied term structure, the assumption of riskneutrality implies that the forward rate is equal to the expected future spot rate. 334 b. If the bond is callable, then the bond value will be less than the amount computed in part a. If the bond price rises above the call price, the company will call it. Therefore, bondholders will not pay as much for a callable bond. 7. The price of the bond today is the present value of the expected price in one year. The bond will be called whenever the price of the bond is greater than the call price of $1,150. First, we need to find the expected price in one year. If interest rates increase next year, the price of the bond will be the present value of the perpetual interest payments, plus the interest payment made in one year, so: P1 = ($100 / .12) + $100 P1 = $933.33 This is lower than the call price, so the bond will not be called. If the interest rates fall next year, the price of the bond will be: P1 = ($100 / .07) + $100 P1 = $1,528.57 This is greater than the call price, so the bond will be called. The present value of the expected value of the bond price in one year is: P0 = [.40($933.33) + .60($1,150)] / 1.10 P0 = $966.67 Intermediate 8. If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the company will not call them. The firm would be foolish to pay the call price for something worth less than the call price. In this case, the bondholders will receive the coupon payment, C, plus the present value of the remaining payments. So, if interest rates rise, the price of the bonds in one year will be: P1 = C + C / 0.13 If interest rates fall, the assumption is that the bonds will be called. In this case, the bondholders will receive the call price, plus the coupon...
View
Full
Document
This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

Click to edit the document details