Q3. American Health Systems currently has 6,400,000 shares of stock outstanding and will report earnings of $10 million in the current year. The company is considering the issuance of 1,700,000 additional shares that will net $30 per share to the corporation.
What is the immediate dilution potential for this new stock issue?
Shares of stock outstanding = 6,400,000 shares.
Current year earnings = $10,000,000
Net value of additional shares = (1,700,000 × $30) = $51,000,000
Immediate dilution potential = (($10,000,000)/ ($10,000,000 + $51,000,000)) × 100%
Answer = 16.39%
Assume that American Health Systems can earn 9% on the proceeds of the stock issue in time to include them in the current year’s results. Calculate earnings per share. Should the new issue be undertaken based on earnings per share?
Delegate your assignment to our experts and they will do the rest.
Net Profit = 9% × $51,000,000
= $4,590,000
Value in current shares = (($51,000,000 - $4,590,000)/ ($30))
= 1,547,000 shares.
Diluted shares = (1,700,000 – 1,547,000) shares = 153,000 shares.
Diluted earnings per share = (($4,590,000)/ (6,400,000 + 153,000) shares)
Answer = $0.7 per share.
Basic earnings per share = ($4,590,000)/ (6,400,000 shares)
= $0.71 per share.
Hence, the new issue should not be undertaken since the diluted earnings per share is lower than the basic earnings per share.
Q4. Using the information in problem 3, assume that American Health Systems’ additional shares can only be issued at $18 per share.
Assume that American Health Systems can earn 6% on the proceeds. Calculate earnings per share.
Net Profit = 6% × ($18 × 1,700,000) = $1,836,000
Net value of additional shares = (1,700,000 ×$18) = $30,600,000
Value in current shares = (($30,600,000 - $1,836,000)/ ($18)) = 1,598,000 shares.
Diluted shares = (1,700,000 – 1,598,000) shares = 102,000 shares.
Diluted earnings per share = (($1,836,000)/ (6,400,000 + 102,000) shares)
Answer = $0.28 per share .
Should the new issue be undertaken based on earnings per share?
Basic earnings per share = ($1,836,000)/ (6,400,000) shares = $0.28 per share.
Hence the new issue can be undertaken as the diluted earnings per share equals the basic earnings per share.
Q8. Assume Sybase Software is thinking about 3 different size offerings for issuance of additional shares.
| Size of Offer | Public Price | Net to Corporation |
| 1.1 million | $30 | $27.50 |
| 7.0 million | $30 | $28.44 |
| 28.0 million | $30 | $29.15 |
What is the percentage underwriting spread for each size offer?
((($30 - $27.50) ×1.1 million)/ ($30 × 1.1 million)) × 100% = 8.3%
((($30 - $28.44) × 7.0 million)/ ($30 × 7.0 million)) × 100% = 5.2%
((($30 - $29.15) × 28.0 million)/ ($30 ×28.0 million)) × 100% = 2.83%
Q19. The Presley Corporation is about to go public. It currently has after tax earnings of $7,200,000 and 2,100,000 shares owned by the present stockholders (the Presley family). The new public issue will represent 800,000 new shares. The new shares will be priced to the public at $25 per share, with a 5% spread on the offering price. There will be also $260,000 in out of pocket costs to the corporation.
Compute the net proceeds to the Presley Corporation.
Public issue = 800,000 shares.
Public Price = $25 per share.
Net price to the corporation = 95% × $25 = $23.75 per share
Out of pocket costs = $260,000
Net Proceeds = ($23.75 × 800,000) - $260,000 = $18,740,000
Compute earnings per share immediately before stocks issue.
Basic earnings per share = ($7,200,000)/ (2,100,000 shares) = $3.42 per share.
Compute earnings per share immediately after stocks issue.
Net amount paid = $18,740,000
Value in current shares = ($18,740,000)/ ($25 per share) = 749,000 shares.
Diluted shares = (800,000 – 749,000) shares = 50,400 shares.
Diluted earnings per share = (($7,200,000)/ (2,100,000 + 50,400) shares)
Answer = $3.34 per share.
Determine what rate of return must be earned on the net proceeds to the corporation so there will not be a dilution in earnings per share during the year of going public.
Basic earnings per share = Diluted earnings per share = $3.428571429 per share.
New value in current shares = 800,000 shares.
New net amount paid = ($25 × 800,000) = $20,000,000
Rate of return to be earned = (($20,000,000 - $18,740,000)/ ($20,000,000)) × 100% = 6.3%
Determine what rate of return must be earned on the proceeds to the corporation so there will be a 5% increase in earnings per share during the year of going public.
Increased diluted earnings per share = 105% × $3.348214286 per share = $3.515625 per share.
Number of shares = ($7,200,000)/ ($3.515625 per share) = 2,048,000 shares.
Diluted shares = (2,048,000 - 2,100,000) shares = -52,000 shares.
Value in current shares = (800,000 + 52,000) shares = 852,000 shares.
New net amount paid = ($25 × 852,000) = $21,300,000
Rate of return to be earned = (($21,300,000 - $18,740,000)/ ($21,300,000)) × 100%
Answer = 12.01%
Q4. An investor must choose between 2 bonds: Bond A pays $72 annual interest and has a market value of $925. It has 10 years to maturity. Bond B pays $62 annual interest and has a market value of $910. It has 2 years to maturity. Assume the par value of the bonds is $1000.
Compute the current yield on both bonds.
Bond A – (($72 annual interest)/ ($925 for bond)) × 100% = 7.78%
Bond B – (($62 annual interest)/ ($910 for bond)) × 100% = 6.81%
Which bond should be selected based on your answer to part i?
Bond A as it has a higher current yield value.
A drawback of current yield is that it does not consider the total life of the bond. For example, the yield to maturity (YTM) on bond A is 8.33%. What is the yield to maturity on bond B?
Approximate YTM on bond B = ((($62) + (($1000 - $910)/ 2))/ (($1000 + $910)/ 2))
Approximate YTM rate = 11.20418848%.
After getting the approximate rate, I used the trial and error method to get the exact YTM rate.
Assuming YTM rate = 11.25%;
$62 × ((1.1125^2 – 1)/ (0.1125 × 1.1125^2)) + ($1000/ 1.1125^2) = $913.804
Assuming YTM rate = 11.45%;
$62 × ((1.1145^2 – 1)/ (0.1145 × 1.1145^2)) + ($1000/ 1.1145^2) = 910.63
Assuming YTM rate = 11.48%;
$62 × ((1.1148^2 – 1)/ (0.1148 × 1.1148^2)) + ($1000/ 1.1148^2) = $910.15
Thus, taking the YTM rate = 11.485%;
$62 × ((1.11485^2 – 1)/ (0.11485 × 1.11485^2)) + ($1000/ 1.11485^2) = $910.07%
Since the market value of the bond is $910, the yield to maturity on bond B is 11.485%.
Has your answer changed between parts ii and iii of this question in terms of which bond to select?
Yes, because in terms of the yield to maturity rate, Bond B should be selected as it has a higher yield to maturity rate.
Q7. Cox Media Corporation pays an 11% coupon rate on debentures that are due in 10 years. The current yield to maturity on bonds of similar risk is 8%. The bonds are currently callable at $1,110. The theoretical value of the bonds will be equal to the present value of the expected cash flow from the bonds.
Find the market value of the bonds using the semiannual analysis.
Since the interest is paid semi-annually;
Bond interest rate per period = (11%/ 2) = 5.5%
Market interest rate = (8%/ 2) = 4%
Number of periods = (2 × 10) = 20.
Bond market value = 5.5% × $1,110 × ((1 – ((1 + 4%) ^ -20))/ 4%) + (($1000)/ ( (1 + 4%)^20))
Answer = $(829.6894231 + 506.5895103)
Answer = $1336.278933
Do you think the bonds will sell for the price you arrived at in part I? Why?
No. This is because the market value has been calculated as the present value of the expected future cash flows without factoring in the effect of risk.
Q17. The Bowman Corporation has a $18 million bond obligation outstanding, which it is considering refunding. Though the bonds were initially issues at 10%, the interest rates on similar issues have declined to 8.5%. The bonds were originally issued for 20 years and have 10 years remaining. The new issue would be for 10 years. There’s a 9% call premium on the old issue. The underwriting cost on the new $18,000,000 issue is $530,000 and the underwriting cost on the old issue is $380,000. The company is in a 35% tax bracket, and it will use an 8% discount rate (rounded after tax of debt) to analyze the refunding decision.
Calculate the Present Value of total outflows.
Call Premium = 9% × $18,000,000 = $1,620,000
New underwriting cost = $530,000
Present Value of total outflows = $(1,620,000 + 530,000) = $2,150,000
Calculate the Present Value of total inflows.
Old underwriting cost = $380,000
Present Value of the issue = (($18,000,000)/ ((1 + 8.5%) ^ 10)) = $7,961,137.471
Tax effect = (0.65 × $7,961,137.471) = $5,174,739.356
Effect of discount rate = (0.92 × $5,174,739.356) = $4,760,760.207
Present Value of total inflows = $(4,760,760.207 + 380,000 = $5,140,760.207
Calculate the Net Present Value.
Net Present Value = $(5,140,760.207 – 2,150,000) = $ 2,990,760.207
Should the old issue be refunded with the new debt?
Yes, because the net present value is positive.
