Series 7 TO Math computations practice
If a municipal bond maturing in 10 years is bought for 110, its cost basis at the end of the sixth year is:
104 $100 premium is amortized over 10 years: $100 ÷ 10 = $10. Then, multiply the annual amortization amount by the number of years the bond is held ($10 × 6 = $60). Finally, subtract the amount of the amortized premium from the original cost of the bond ($1,100 − $60 = $1,040, or 104).
If a customer buys 100 XYZ at 49 and writes 1 XYZ Nov 50 call, receiving $350 in premiums, the breakeven point is:
45.5. Explanation This is a covered call, so the investor is protected against declining stock prices to the extent of the premium received, and the breakeven is 45.50 (49 − 3.50).
A customer purchases a 6% municipal bond in the secondary market on a 7% basis. The effective after-tax yield is
6 to 7% In every case but one, the yield to maturity is the effective after-tax yield to a municipal-bond buyer. The one exception is a bond bought at a discount in the secondary market. In this case, the annual accretion is taxed as ordinary income. The discount, which is included in the stated yield to maturity, is taxable, reducing the effective after-tax yield to somewhere between the coupon of 6% and the yield to maturity of 7%.
The current yield on a bond with a coupon rate of 7.5% currently selling at 105-½ is approximately
A bond with a coupon rate of 7.5% pays $75 of interest annually. Current yield equals annual interest amount divided by bond market price, or $75 / $1,055 = 7.109%, or approximately 7.1%. Reference: 2.2.7.2
A customer purchased 100 shares of SNP at $38. At the time of purchase, the PE ratio was 12. Approximately what are the earnings per share of SNP?
Answer: C The PE ratio is a comparison of the current market price at the close to the earnings of the company; $38 (CMV) ÷ 12 (PE ratio) = $3.16 (approximate EPS)
A customer bought a bond that yields 6-½% with a 5% coupon. If the bond matures at this point, the customer will receive
B. Upon redemption of a bond, whatever current interest rates may be, the investor receives par ($1,000) plus the final semiannual interest payment ($25 in this case), for a total of $1,025.
A new client takes the following options position: Sells 1 MNO July 40 put @ 6 The client has no other open positions and MNO's current market price is $46 per share. The breakeven price per share for this customer would be what price at expiration of the options contract?
When you are given one individual option position by itself you always want to remembeR: CALL UP PUT DOWN to get to Breakeven - This is a put so we will take the strike price of the put minus the premium of 6 40 less 6 = 34 Breakeven
A convertible bond callable at 101 is trading at 105. The bond is a 4% bond convertible at $25. The common stock is trading at $27. If an investor bought the bond and converted, his profit would be:
First, calculate the number of shares each bond will convert to: $1,000 (par) / $25 per share = 40 shares per bond. With market value at 105, each bond costs $1,050. What is the stock parity price? $1,050 / 40 shares = $26.25 per share stock parity price. CMV of the stock minus stock parity price equals profit (or loss). $27.00 − $26.25 = $.75 per share × 40 shares = $30.
A trader writes 10 uncovered ABC June 50 calls at 4.75 when ABC stock is trading at 45. If the trader closes out their option position at 2.15 what is her gain?
Premiums S + 4,750 B - 2,150 writes 10 uncovered ABC June 50 calls at 4.75 closes (buys) 10 ABC June 50 calls at 2.15 What is her gain? + 2,600
A corporation in the 35% tax bracket reports operating income of $4 million for the year. The firm also received $200,000 in preferred dividends. Assuming no other items of income or expense, what is the company's tax liability?
The corporation's $4 million operating income is taxed at a rate of 35%. For tax purposes, corporations can exclude 70% of all dividends received from domestic common and preferred stocks. Thus, 30% of the $200,000 received from preferred dividends is taxed at the 35% tax rate ($200,000 times 30% equals $60,000). The $4 million in income plus the $60,000 in taxable dividends equals $4,060,000 ($4,060,000 multiplied by a 35% tax rate equals taxes of $1,421,000).
Paying a premium of $10 per bond, Ms. Tracey Pringle bought 10 municipal bonds with 20 years to maturity. Ten years later, she sold the bonds for 103. For tax purposes, she has a:
The cost per bond is $1,010. The amortization amount each year is 10/20 years, which equals $.50 per year. $.50 per year × 10 years = $5 per bond. After 10 years, the adjusted cost basis is $1,005 per bond. She sells the bonds for $1,030 per bond. $1,030 − $1,005 = $25 per bond 25 × 10 = $250 gain.
What is the current yield on a corporate bond trading at 103 with a 7% coupon?
The current yield on a corporate bond equals the annual interest income divided by the market price of the bond ($70 / 1,030 = 0.06786 or 6.8%). In this case, the annual interest income is $70 ($1,000 par value x 7% coupon = $70) and the market price of the bond is $1,030. (103 points x $10 per point = $1,030).
When XYZ stock is at 72 1/2, an investor buys 10 XYZ June 60 calls @ 23 1/2 and sells 10 XYZ June 90 calls @10. What is the investor's maximum profit potential?
The maximum profit on a debit spread is the difference between the strike prices adjusted by the premiums. Premiums buys 10 XYZ June 60 calls at 23.5 B - 23,500 sells 10 XYZ June 90 calls at 10 S + 10,000 Premium Debit - 13,500 difference between strikes 30 times shares per contract x 100 profit per contract 3,000 times 10 contracts x 10 Maximum Profit 30,000 minus Premium Debit - 13,500 Net Max Profit Potential $ 16,500
An investor in the 28% income tax bracket is considering purchasing either a 4% municipal bond or a 5% corporate bond. Which of the following statements regarding the two bonds' after-tax yields is TRUE?
The municipal bond's yield is higher than the corporate bond's yield. To compare the two bonds, use the tax-free equivalent yield formula: (taxable yield) × (100% − tax bracket) = (tax-free equivalent yield). In this case, 5% × (100% − 28%) = 5% × .72 = 3.6%. Because the municipal bond yields 4% tax free, the investor should buy it; after taxes have been paid, the corporate bond yields only 3.6%.
When calculating the tax-equivalent yield on municipal bonds, what represents the formula used? Example: John is currently in the 28% tax bracket and is considering a 5% municipal bond. What would a fully-taxable corporate bond have to yield in order to equate to the tax-free municipal?
The tax-exempt yield divided by (100% - the investor's income tax rate). The tax-equivalent yield is found by dividing the tax-exempt yield of the municipal bond by 100% minus the investor's income tax rate. 5% / (100% - 28%) = Taxable Equivalent 0.05 / 0.72 = 0.0694 or 6.94% Because it is fully taxable, the corporate would have to be yielding 6.94% in order to equate to the 5% municipal bond.
On February 7, a customer buys 100 shares of LMN at $39 per share and simultaneously writes an LMN Oct 35 call option at 6. If the call is exercised on July 19, what will he report for tax purposes?
$200 gain The premium received for writing a call becomes part of the stock sales proceeds for a total of $4,100. Because the investor bought the stock 5 months earlier for $3,900, he incurred a $200 capital gain (short-term).
An investor buys 2 LMN 40 calls and pays a premium of 4 each, and also buys two LMN 40 puts and pays a premium of 2.50 each. At the time of purchase, LMN is trading at $40.75. On the expiration date, LMN is trading at $32.50. If the investor closes his position for its intrinsic value. Excluding commissions, the investor realizes a:
$200 profit. Closing out a position is the opposite of the opening transaction. In this situation, the investor opened by buying 2 calls for a total of $800, and closed them out by selling for their intrinsic value (calls have intrinsic value when the market value is above the strike price; in this situation there is no intrinsic value). The investor also bought 2 puts for a total of $500 and closed them out by selling for their intrinsic value of $1,500 (puts have intrinsic value when the market value is below the strike price; in this situation the intrinsic value is $7.50 per contract) or 40 − 32.50 = 7.5 × 2 = 15 × 100 shares = $1,500). The resulting profit on the position is $200 ($1,500 − $1,300), the total of the premiums paid for all of the options. Reference: 4.4.2.1
A customer buys 5 municipal bonds maturing in 20 years for 104. If he sells the bonds after 10 years at 103, the customer has a: A) $100 capital gain. B) $100 capital loss. C) $50 capital gain. D) $50 capital loss.
$50 capital gain. The premium on the municipal bonds must be amortized. The bonds were bought at 104 and therefore each bond has $40 in premiums (5 bonds X $40 = $200 premium to be amortized over 20 years). This means the cost basis of the bonds ($5,200) decreases by $10 a year ($200 / 20 years = $10). After 10 years amortization, $100 has been amortized (10 years × $10 per year), and the customer has an adjusted cost basis of $5,100. If the bonds are sold for 103 ($5,150), the customer has a $50 taxable capital gain
An investor sells 10 5% bonds at a profit and buys another 10 bonds with a 5-1/4% coupon rate. The investor's yearly return will increase by:
C. Explanation The first bonds are 5% and pay $50 per year per bond. The new bonds are 5-1/4% and pay $52.50 per year per bond, for a difference of $2.50 per bond. Reference: 2.1.5
XYZ Corporation has outstanding a 7% convertible bond currently trading at 102. The bond, which has a conversion price of $50, was issued with an antidilution covenant. If XYZ declares a 10% stock dividend, the new conversion price, as of the ex-date, will be:
To compute a new conversion price, divide the current conversion price by 100% plus the percent increase in shares. $50 / 110% = $45.45.
ABC Corporation has outstanding a 7-¾% convertible debenture currently trading at 102. The bond is convertible into common stock at $40. ABC stock is trading $45 per share. solve
To profit in this situation, the investor should buy the bonds and short the stock. With a conversion price of $40, the bond is convertible into 25 shares of ABC common stock ($1,000 / $40 = 25 shares). As the common stock is currently trading at $45 per share, the value of the stock as converted would be $1,125 (25 shares × $45 = $1,125), which is greater than the current price of the bond ($1,020). Therefore, the bond and the stock are not at parity. An investor could profit in this situation by shorting the stock and buying an equivalent number of bonds. A bond could be purchased for $1,020 and immediately converted into stock worth $1,125, a risk-free profit opportunity.
An investor is long 100 shares of ABC common stock trading at $60 per share. ABC announces a 5 for 1 split. After the split, this investor would
When calculating a stock split you would multiply the ratio of the stock split (5/1) by the number of shares owned (100/1) to arrive at the new number of shares: 5/1 X 100/1 = 500/1 = 500 shares after the split Next, you would take the former total value ($60/share x 100 shares = $6000) and divide this by the new number of shares (500 shares after the split) to find the new market value: $6000 divided by 500 shares = $12 new market value per share after the split
Mr. Smith decides to enter a spread order and buys 1 ABC August 40 call and sells 1 ABC August 45 call when the current quotes are: ABC August 40 calls - 3.23 - 3.38 ABC August 45 calls - 1.25 - 1.38. Which of the following would be the result of Mr. Smiths trades per share?
When trading options, investors buy at the quoted ask (higher price) and sell at the bid (lower price) of the quote. Therefore, this investor would: buy the Aug 40 call @ 3.38 (Ask) (B - 338); and sell the Aug 45 call @ 1.25 (Bid) (S + 125) buys 1 ABC Aug 40 call at the ask (3.38) B - 3.38 sells 1 ABC Aug 45 call at the bid (1.25) S + 1.25 = - 2.13 Net Debit -2.13
A customer purchases an XYZ municipal bond at 108. It is scheduled to mature in 16 years. After owning the bond for 10 years, he sells the bond at 102. What capital gain or loss must he report for tax purposes at the time of the sale?
Your answer, $60 loss., was incorrect. The correct answer was: $10 loss. If a municipal bond is purchased at a premium, the premium must be amortized over the time until maturity. An $80 premium on a 16-year municipal bond indicates that $5 will be amortized each year ($80 divided by 16 = $5). After 10 years, the tax basis would be 103 ($1,030). Since the sale was for 102 ($1,020), the customer has a $10 loss on one bond. Reference: 15.5.7.1 in the License Exam Manual.
If a customer buys 1 OEX Feb 350 call at 5, then sells 1 OEX Feb 335 call at 16 when the underlying index is at 344, the breakeven point is:
Your answer, 342., was incorrect. The correct answer was: 346. To determine a call spread, add the net premium to the lower strike price to find the breakeven point. The net premium is the difference between the premium paid (5) and the premium received (16), or 11 (335 + 11 = a breakeven point of 346).
Gargantuan Computers, Inc. (GCI) conducts a rights offering to its current shareholders at $50 per share, plus 1 right. If the current market price of GCI is $70, what is the value of one right before the stock trades ex-rights?
Your answer, 5, was incorrect. The correct answer was: 10 The stock is trading cum rights (before the ex-date). The formula to calculate the value of one right before the ex-date is follows: CMV − subscription price / Number of rights to purchase 1 share + 1. Therefore one right is valued at $10, computed as ($70 − $50) / 2 = $10. Reference: 1.7.1.3 in the License Exam Manual.
PDQ Corporation has a 6-1/4% convertible preferred stock (conversion ratio of 4) outstanding. The stock has an antidilution covenant. If PDQ declares a 10% stock dividend, the antidilution covenant will adjust:
the conversion price to $22.72. The stock is convertible at $25 ($100 par / 4 shares). To determine the new conversion price, $100 / 4.4 shares = $22.72, or divide $25 by 110%.
