The Series 7 doesn’t have many math questions, but they’re the easiest points to lose to a slip. These 124 practice questions cover every calculation the exam tests: current yield and yield to maturity, taxable-equivalent yield, convertible parity, rights, accrued interest, margin and SMA, mutual fund sales charges, cost basis, ratios and options breakevens.
Write your numbers in the scratch pad under each question, then read Ken’s take: it shows the setup and why each wrong answer is wrong. Work at your own pace, or click Exam mode for a 2-hour timer. Your results break down by topic so you know exactly which formulas to fix.
A customer buys 500 shares at $40 and later receives a 10% stock dividend. She sells 200 shares at $50. What is her gain?
Ken’s take
Total cost $20,000 ÷ 550 shares = $36.36 per share; 200 × ($50 − $36.36).
Why the others are wrong
- $2,000 gain: Leaves the basis per share at the original price despite the extra shares.
- $2,800 gain: Reduces the price by 10% instead of spreading the cost over 110% of the shares.
- $10,000 gain: Treats the sale as all gain, as if the shares had no basis.
A customer buys 1,000 shares at $50 on margin, paying the Regulation T (Reg T) minimum. The stock falls to $32. What is the minimum amount needed to satisfy the maintenance requirement?
Ken’s take
Debit $25,000; equity = $32,000 − $25,000 = $7,000; maintenance = 25% × $32,000 = $8,000; call = $8,000 − $7,000.
Why the others are wrong
- $2,600: Uses the 30% short-account percentage.
- $8,000: Reports the maintenance requirement itself, not the shortfall.
- $9,000: Restores the account to 50% Reg T equity instead of 25% maintenance.
A $1,000 par debenture is convertible at $50 per share. The common stock trades at $57 and the debenture trades at 108.5. A trader buys 8 debentures and simultaneously sells short the number of shares they convert into, then converts and delivers. Ignoring commissions, what is the locked-in result?
Ken’s take
Parity $1,140 exceeds the $1,085 paid, so buying the bond and shorting the stock locks in $55 per bond × 8.
Why the others are wrong
- $440 loss: Reverses the trade: selling bonds and buying stock when the bond is the cheaper side.
- $55 gain: Per-bond result, never multiplied by the eight bonds.
- $680 gain: Measures the premium over par, which has nothing to do with the stock leg.
In one year a customer has a $8,000 short-term gain, a $3,000 short-term loss, a $1,000 long-term gain and a $6,000 long-term loss. What is her net result, if any?
Ken’s take
Short-term net +$5,000 and long-term net −$5,000 offset exactly.
Why the others are wrong
- $5,000 loss: Reports the long-term net loss alone.
- $5,000 gain: Taxes the short-term net and ignores the long-term loss.
- $9,000 gain: Counts gains only.
A customer buys 1,000 shares at $40 in a new margin account, depositing only the Regulation T (Reg T) minimum. The stock rises to $52. What is the special memorandum account (SMA) balance?
Ken’s take
Gain = $12,000; SMA is 50% of the gain.
Why the others are wrong
- $12,000: Counts the entire price gain instead of 50% of it.
- $26,000: Reports the Reg T requirement on the new market value.
- $32,000: Reports total equity.
A customer in the 24% federal bracket compares a taxable corporate bond yielding 5.20% with a federally exempt municipal bond yielding 4.10%. What is the after-tax yield of the corporate bond?
Ken’s take
After-tax yield = 5.2 × (1 − 0.24) = 5.2 × 0.76. The 4.1% municipal yield needs no adjustment, so the municipal bond is ahead.
Why the others are wrong
- -18.80%: Subtracts the bracket from the yield as if both were points.
- 1.25%: Reports the tax paid rather than what is left after it.
- 3.12%: Applies the haircut to the exempt bond, which owes no federal tax.
A $1,000 par debenture is convertible at $40 per share and trades at 115. The common stock trades at $41.60. The debenture's premium over parity is what percentage of parity?
Ken’s take
Parity = 25 × $41.60 = $1,040; premium = $1,150 − $1,040 = $110; $110 ÷ $1,040.
Why the others are wrong
- 11.00%: Divides the premium by par.
- 15.00%: Measures the premium over par instead of over parity.
- 90.43%: Reports parity as a share of the price, the complement of the premium.
A fund charges a sales charge of 5.5% of the public offering price (POP) on purchases below $50,000 and 4.5% of the POP on purchases from $50,000 to $99,999. The net asset value (NAV) is $20.00. A customer who holds $40,000 in the fund adds $20,000 and has a right of accumulation. How many shares does the new $20,000 buy?
Ken’s take
$40,000 + $20,000 = $60,000 reaches the 4.5% level; shares = $20,000 × 0.955 ÷ $20.00.
Why the others are wrong
- 945 shares: Prices the new money alone, ignoring the existing holding.
- 957 shares: Adds the 4.5% to the NAV instead of taking it out of the POP.
- 1,000 shares: Ignores the sales charge and divides by the NAV.
A customer buys 1 put at a $55 strike for 5.60 and sells 1 put at a $45 strike for 1.80, same expiration. What is the maximum loss?
Ken’s take
Net debit = $5.60 − $1.80 = $3.80, × 100.
Why the others are wrong
- $560: Counts only the premium paid for the long put.
- $620: Reports the maximum gain.
- $1,000: Reports the width of the strikes.
A customer bought a stock at $25 several years ago. It now trades at $50 and pays $1.50 per share annually. What is the stock's current yield?
Ken’s take
Current yield uses today's market price: $1.50 ÷ $50.
Why the others are wrong
- 1.50%: Reports the dividend dollars as the percentage.
- 4.00%: Divides by the average of cost and market price.
- 6.00%: Yield on original cost, which current yield never uses.
A customer is fed up with a stock and sells 300 shares at $20 that had cost her $30 a share. Ten days later she changes her mind and buys 300 shares of the same stock at $24. What is the cost basis of the new shares?
Ken’s take
Numbers to write down: sold 300 at $20; cost $30; repurchased 300 at $24 after 10 days.
Disallowed loss $3,000 is added to the new cost: $7,200 + $3,000.
Why the others are wrong
- $3,000: Reports the disallowed loss alone.
- $7,200: Uses the purchase price and drops the disallowed loss.
- $9,000: Carries over the old basis.
A company has current assets of $300M and current liabilities of $200M. It uses $50M of cash to pay down accounts payable. What happens?
Ken’s take
Current ratio goes from 1.50 to 1.67; working capital stays at $100M because both sides fall by the same amount.
Why the others are wrong
- The current ratio falls; working capital falls: Believes spending cash drains working capital.
- The current ratio falls; working capital is unchanged: Applies the ratio-below-1 outcome to a ratio above 1 (or reverses it).
- The current ratio rises; working capital rises: Believes paying a debt must increase working capital.
A customer buys 5 bonds at 103 and amortizes the premium each year until the bonds are redeemed at par at maturity. What is her capital gain or loss at maturity, if any?
Ken’s take
Amortization reduces basis to par by maturity, so redemption at par produces no capital gain or loss.
Why the others are wrong
- $1,500 loss: Treats the 3-point premium as $300 per bond instead of $30.
- $150 loss: Treats the premium as an unamortized loss.
- $150 gain: Treats the premium as a gain.
An affiliate wants to sell restricted stock. The issuer has 10,000,000 shares outstanding, the average weekly volume for the last four weeks is 130,000, and the affiliate sold 45,000 shares under the rule in the past 90 days. How many shares may she sell now?
Ken’s take
Greater of 1% (100,000 shares) or volume (130,000) = 130,000; less 45,000 already sold.
Why the others are wrong
- 55,000 shares: Uses the 1% figure when the volume figure is larger.
- 100,000 shares: Uses the 1% figure and ignores prior sales.
- 130,000 shares: Ignores shares already sold.
A customer sells short 150 shares at $20 in a new margin account. What is the minimum initial deposit required?
Ken’s take
50% of $3,000 is $1,500, below the $2,000 minimum equity, so $2,000 governs.
Why the others are wrong
- $750: Takes half of the Reg T amount.
- $1,500: Applies the 50% requirement and ignores the $2,000 minimum.
- $4,500: Reports total account value (150%) as the deposit.
A stock trading at $80 pays $0.50 per share each quarter. The company declares a 2-for-1 split and keeps its total dividend payout unchanged. What is the annual dividend yield after the split?
Ken’s take
The dividend per share halves along with the price, so the yield does not change: $2.00 ÷ $80 = 2.50%.
Why the others are wrong
- 0.50%: Reads the $0.50 quarterly dividend as a percentage.
- 0.62%: Uses the post-split quarterly dividend without annualizing it.
- 1.25%: Halves the dividend but forgets that the price halves too.
A company's balance sheet shows cash of $45M, receivables of $120M, inventory of $160M, prepaid expenses of $15M and fixed assets of $400M. Current liabilities are $140M and long-term debt is $200M. What is the company's working capital?
Ken’s take
Numbers to write down: cash $45M; receivables $120M; inventory $160M; prepaid $15M; current liabilities $140M (fixed assets and long-term debt are not working capital).
Current assets = $45M + $120M + $160M + $15M = $340M; working capital = $340M − $140M.
Why the others are wrong
- $340M: Reports current assets without subtracting current liabilities.
- $400M: Reports net worth (total assets less total liabilities) instead of working capital.
- $600M: Adds fixed assets, which are not current.
A rights offering gives each shareholder one right per share. Every 5 rights plus $42 buy one new share, which trades in the market at $55. How much must a holder of 1,000 shares pay to exercise all of her rights?
Ken’s take
1,000 rights ÷ 5 = 200 new shares × $42.
Why the others are wrong
- $11,000: Uses the market price instead of the subscription price.
- $42,000: Treats each right as buying one share.
- $210,000: Multiplies by the rights ratio instead of dividing by it.
A company has total assets of $900M, total liabilities of $540M and preferred stock with a $60M liquidation value. It has 20M common shares. What is the book value per common share?
Ken’s take
($900M − $540M − $60M) ÷ 20M.
Why the others are wrong
- $12.00: Deducts the preferred claim twice.
- $18.00: Leaves the preferred claim in common equity.
- $45.00: Divides gross assets by shares.
A customer is short 1 put at a $70 strike for $6.30 while the stock trades at $64. What is the put's intrinsic value per contract, if any?
Ken’s take
Intrinsic value = ($70 − $64) × 100; the other $30 of the premium is time value.
Why the others are wrong
- $0: Null answer: believes a short position carries no intrinsic value.
- $30: Reports the time value instead.
- $6,400: Reports the value of the shares.
A customer calls her broker-dealer (BD) to buy shares of a stock the firm trades out of its own inventory. The BD fills the order at $31.50, and the prevailing market price at that moment is $30.00. What is the markup as a percentage?
Ken’s take
($31.50 − $30.00) ÷ $30.00, measured against the prevailing market price.
Why the others are wrong
- 0.05%: Leaves the result as a decimal.
- 1.50%: Reads the dollar markup as a percentage.
- 4.76%: Divides by the customer's price.
A customer pays a $3 premium for a call at $40, exercises it, and later sells the stock at $52. What is her gain on one contract?
Ken’s take
Basis = $40 + $3 = $43; ($52 − $43) × 100.
Why the others are wrong
- $300 gain: Reports the premium paid.
- $1,200 gain: Ignores the premium in basis.
- $1,500 gain: Adds the premium instead of folding it into basis.
A customer buys 1 XYZ Jan 50 call at 6.20 and sells 1 XYZ Jan 60 call at 2.70. What is the breakeven point at expiration?
Ken’s take
Net debit = $6.20 − $2.70 = $3.50; breakeven = $50 + $3.50.
Why the others are wrong
- $52.70: Uses the premium received instead of the net debit.
- $56.20: Uses the long call's premium alone.
- $56.50: Subtracts the net debit from the short strike.
A customer in the 28% federal bracket owns a municipal bond yielding 4.2% that is exempt from federal tax. What is the taxable equivalent yield?
Ken’s take
TEY = tax-exempt yield ÷ (1 − bracket) = 4.2 ÷ 0.72.
Why the others are wrong
- 3.02%: Multiplies by (1 minus rate), which computes an after-tax yield on a taxable bond, the reverse direction.
- 4.20%: Reports the tax-exempt yield itself, forgetting to gross it up.
- 5.38%: Grosses the yield up by multiplying by (1 + rate).
A retired schoolteacher asks her broker to buy 8 corporate bonds with a 6.0% coupon. The order fills at 103.5. When the trade settles, the broker explains that the last interest payment was 47 days earlier under the 30/360 convention. What is the total amount due at settlement, excluding commission?
Ken’s take
Numbers to write down: 8 bonds; 103.5; 6.0%; 47 days; 30/360.
Principal $8,280 (8 × 1,035) plus accrued $62.67 (8 × $60 × 47 ÷ 360).
Why the others are wrong
- $8,062.67: Uses par instead of the quoted price.
- $8,217.33: Subtracts accrued interest: that is what a seller does to their own proceeds in reverse; a buyer pays it.
- $8,280.00: Omits accrued interest.
A customer's long margin account carries a debit balance of $24,000. At what long market value does the account first fall to the minimum maintenance requirement?
Ken’s take
Equity must be 25% of LMV, so the debit is 75% of LMV: $24,000 ÷ 0.75.
Why the others are wrong
- $18,000: Takes 75% of the debit.
- $30,000: Adds 25% to the debit instead of treating the debit as 75% of market value.
- $48,000: Uses the 50% Reg T percentage.
A customer sold 4 long-dated puts 14 months ago at 2.50 each. The puts expire worthless. How is the result treated?
Ken’s take
A writer's gain on expiration is always short-term, and one contract covers 100 shares.
Why the others are wrong
- $1,000 long-term gain: Applies the more-than-one-year rule that belongs to purchased positions.
- $10 long-term gain: Wrong on both axes.
- $10 short-term gain: Drops the 100-share multiplier.
A margin account has a long market value of $50,000 and a debit balance of $30,000, and no SMA. The customer asks to withdraw $3,000 in cash without selling anything. How much, if any, may she withdraw?
Ken’s take
Equity is $20,000, or 40% of market value, below the 50% Reg T level. With no SMA, a restricted account cannot release cash without a sale.
Why the others are wrong
- $1,500: Assumes half of the request is allowed.
- $3,000: Treats the account as unrestricted because it is above the 25% maintenance level.
- $7,500: Reports the excess over the 25% maintenance requirement; true for the maintenance test but not for cash withdrawals.
A company declares a cash dividend with a record date of Tuesday, November 17, 2026. Regular-way settlement is one business day. On which date does the stock first trade without the dividend?
Ken’s take
Under T+1 the ex-date equals the record date.
Why the others are wrong
- Wednesday, November 18: Confuses the ex-date with the day after the record date.
- Monday, November 16: Superseded (pre-May 2024): ex-date one business day before the record date under T+2.
- Friday, November 13: Superseded (pre-September 2017): ex-date two business days before the record date under T+3.
A stock trades at $60 with a price-earnings (P/E) ratio of 15. Earnings per share are expected to rise 10% while the P/E ratio stays the same. What is the expected price?
Ken’s take
EPS rises to $4.40; $4.40 × 15.
Why the others are wrong
- $60.00: Null answer: believes a constant P/E means a constant price.
- $60.40: Adds the dollar rise in earnings to the price.
- $69.00: Reads the P/E of 15 as a 15% increase.
A company earns $12M and pays $1M in preferred dividends. It has 5M common shares, plus convertible bonds that convert into 1M shares and cost $0.6M a year in after-tax interest. What is the diluted earnings per share?
Ken’s take
($12M − $1M + $0.6M) ÷ (5M + 1M).
Why the others are wrong
- $1.83: Adds the shares but not the interest saved.
- $2.10: Forgets the preferred dividends.
- $2.20: Basic EPS, ignoring the convertible.
A fund holds $450M in securities and $20M in cash and owes $14M in liabilities. It has 20M shares outstanding. What is the net asset value (NAV) per share?
Ken’s take
($450M + $20M − $14M) ÷ 20M.
Why the others are wrong
- $20.80: Subtracts cash as if it were a liability.
- $21.80: Subtracts liabilities but ignores cash.
- $22.50: Counts securities only.
A customer's fund account holds shares bought as 300 at $20, 200 at $30 and 100 at $35. She sells 150 shares at $32 using the average cost method. What is her gain or loss?
Ken’s take
Average cost = $15,500 ÷ 600 = $25.83; 150 × ($32 − $25.83).
Why the others are wrong
- $200 loss: Uses last-in, first-out (100 at $35 and 50 at $30).
- $550 gain: Averages the three prices instead of weighting by shares.
- $1,800 gain: Uses first-in, first-out.
A customer sells 2 puts at a $48 strike for $3.20 each and is assigned. What is the cost basis of the stock she acquires?
Ken’s take
($48 − $3.20) × 100 × 2.
Why the others are wrong
- $4,480: Covers only one contract.
- $9,600: Ignores the premium.
- $10,240: Adds the premium instead of subtracting it.
A customer's short margin account already has a special memorandum account (SMA) of $2,000. The 500 shares sold short fall from $60 to $54. What is the SMA now?
Ken’s take
Decline = 500 × ($60 − $54) = $3,000; new SMA = $2,000 + 1.5 × $3,000.
Why the others are wrong
- $3,000: Reports the decline and drops the existing SMA.
- $3,500: Adds 50% of the decline, the long-account percentage.
- $4,500: Reports the new SMA only and drops the existing balance.
A customer sells 1 ABC Mar 70 call at 4.50 and 1 ABC Mar 70 put at 3.00. What are the breakeven points?
Ken’s take
Combined premium $7.50 is added to and subtracted from the $70 strike.
Why the others are wrong
- $66.25 and $73.75: Splits the combined premium between the two sides.
- $67.00 and $73.00: Uses the put premium alone on both sides.
- $65.50 and $74.50: Uses the call premium alone on both sides.
A customer opens her first margin account to buy shares in a company she has followed for a while. She buys 1,500 shares at $44, putting up only the Regulation T (Reg T) minimum. The stock later climbs to $52. What is the equity in the account?
Ken’s take
Numbers to write down: 1,500 shares; buy $44; Reg T minimum; now $52.
Debit = 50% × $66,000 = $33,000; equity = LMV $78,000 − debit $33,000.
Why the others are wrong
- $12,000: Reports the gain only, forgetting the customer's original deposit.
- $33,000: Reports the original equity and ignores the gain.
- $39,000: Applies the 50% Reg T percentage to the current market value.
A company earns $18M after tax, pays $2M in preferred dividends, and has 4M common shares outstanding trading at $60. What is the price-earnings ratio?
Ken’s take
EPS = ($18M − $2M) ÷ 4M = $4.00; $60 ÷ $4.00.
Why the others are wrong
- 6.67: Inverts the ratio into an earnings yield.
- 12.00: Adds the preferred dividends to earnings instead of subtracting them.
- 13.33: Ignores the preferred dividends.
A customer is considering a 6.25% corporate bond that matures in 10 years and currently quotes at 94.5. What is the bond's current yield?
Ken’s take
Current yield = annual interest ÷ market price = $62.50 ÷ $945.
Why the others are wrong
- 5.92%: Adds the discount to par instead of subtracting it, so the denominator is too large.
- 6.25%: Nominal yield: reads the coupon rate as the yield and ignores the discounted price.
- 6.99%: Approximate yield to maturity: spreads the discount over the ten years, which current yield never does.
A company earns $20M a year with 10M shares outstanding, and its stock trades at $50. It repurchases 1M shares. Assume earnings and the stock price do not change. What is the price-earnings (P/E) ratio afterward?
Ken’s take
EPS rises from $2.00 to $2.22; $50 ÷ $2.22. Fewer shares raise EPS and lower the P/E at an unchanged price.
Why the others are wrong
- 25.00: Null answer: believes a buyback leaves the P/E untouched.
- 27.50: Adds the repurchased shares instead of removing them.
- 27.78: Scales the P/E up by the share reduction instead of down.
A customer buys 1,000 shares at $40 in a new margin account, depositing only the Regulation T (Reg T) minimum. The stock rises to $52 and then falls back to $44. What is the special memorandum account (SMA) balance, if any?
Ken’s take
SMA built at $52 ($6,000) stays on the books when the price falls; excess equity at $44 is only $2,000.
Why the others are wrong
- $0: Null answer: believes the gain disappears when the price falls.
- $2,000: Recomputes excess equity at the lower price; SMA is not reduced by a price decline.
- $4,000: Reports 50% of the price decline as the SMA.
A customer paid $10,000 for fund shares and reinvested $1,200 of distributions over the years. She redeems everything for $14,500. What is her gain?
Ken’s take
Basis = $10,000 + $1,200 = $11,200; $14,500 − $11,200.
Why the others are wrong
- $2,100 gain: Subtracts the reinvested amount twice.
- $4,500 gain: Ignores the basis added by reinvested distributions.
- $5,700 gain: Adds the reinvested amount to the gain.
A fund charges 5.5% on purchases below $50,000, 4.5% from $50,000 to $99,999 and 3.5% at $100,000 and above, applied to the dollars invested. A customer signs a letter of intent (LOI) for $100,000 and pays 3.5% on each purchase. The LOI expires after she has invested only $75,000. What additional sales charge does she owe, if any?
Ken’s take
She earned the 4.5% level: 4.5% × $75,000 = $3,375, less $2,625 paid at 3.5%.
Why the others are wrong
- $1,500: Adjusts to the 5.5% rate, ignoring the breakpoint she did reach.
- $2,625: Reports the charge already paid.
- $3,375: Reports the full 4.5% charge instead of the shortfall against what she paid.
A customer buys 3 index calls at a 4,500 strike for 22.00 each. At expiration the index closes at 4,520. What is her result?
Ken’s take
Intrinsic value 20 is below the 22 premium: (20 − 22) × 100 × 3.
Why the others are wrong
- $6,600 loss: Reports the full premium as the loss, ignoring cash settlement.
- $600 gain: Reverses the sign.
- $6,000 gain: Ignores the premium paid.
A company with 12,000,000 shares outstanding announces a rights offering to sell 800,000 new shares, issuing one right per outstanding share. A customer owns 6,000 shares. How many new shares can she buy by exercising all of her rights?
Ken’s take
15 rights are needed per new share (12,000,000 ÷ 800,000); 6,000 rights ÷ 15 = 400 shares.
Why the others are wrong
- 6,000 shares: Treats each right as buying one share.
- 6,400 shares: Reports total holdings after exercise instead of the new shares purchased.
- 90,000 shares: Multiplies by the number of rights needed per share instead of dividing by it.
A stock trades at $96 with earnings of $6 per share. The company completes a 3-for-2 split. What is the price-earnings ratio afterward?
Ken’s take
Price falls to $64 and EPS to $4; the ratio stays 16.
Why the others are wrong
- 8.00: Halves the ratio, as if a 2-for-1 split.
- 10.67: Adjusts the price but not the earnings.
- 12.00: Treats a 3-for-2 split as a 25% price cut with no change in earnings.
A customer sells $25,000 par of a 7.0% corporate bond at 96. The bond pays interest each April 1 and October 1, and the sale settles June 15. What are the seller's proceeds, before commission?
Ken’s take
The seller is owed 74 days (April 1 to June 15, 30/360) of interest on top of principal: $24,000 + $1,750 × 74 ÷ 360 = $359.72.
Why the others are wrong
- $23,640.28: Subtracts accrued interest, treating the seller as the payer.
- $24,000.00: Omits the accrued interest the seller is owed.
- $25,359.72: Uses par instead of the sale price.
A customer buys $10,000 par of a corporate bond at 98 and pays $60 of accrued interest at settlement. Later she sells at 101 and receives $120 of accrued interest. What is her capital gain on the bond?
Ken’s take
Accrued interest is taxed as interest income, not capital gain; basis is the price, not the price plus accrued: $10,100 − $9,800.
Why the others are wrong
- $60: Reports only the difference between the accrued interest amounts.
- $240: Treats the accrued interest paid on purchase as part of the basis.
- $420: Includes the accrued interest received on sale but not the accrued paid on purchase.
A customer's margin account holds securities with a market value of $60,000 and carries a debit balance of $20,000. What is the most the broker-dealer may rehypothecate?
Ken’s take
Rehypothecation is limited to 140% of the debit: 1.40 × $20,000.
Why the others are wrong
- $40,000: Reports the customer's equity.
- $60,000: Treats every security in the account as available.
- $84,000: Applies 140% to market value instead of the debit.
A shareholder owns 40,000 of a company's 2,000,000 outstanding shares. The company sells 500,000 new shares through a rights offering, and she lets all of her rights expire. What is her percentage ownership afterward?
Ken’s take
The rights offer the opportunity to keep her share; unexercised, her 40,000 shares are spread over 2,500,000: 1.60%.
Why the others are wrong
- 2.00%: Null answer: believes preemptive protection preserves her percentage even if she does nothing.
- 8.00%: Divides by the new shares only.
- 25.00%: Reports the size of the offering as a percentage of the old shares.
A customer buys $50,000 par of a 3.2% Treasury note that pays interest each May 15 and November 15. The order executes on Tuesday, August 4, and settles regular way. Use a 365-day year. How much accrued interest does the customer pay?
Ken’s take
Treasuries accrue on actual days to settlement. T+1 settlement is Wednesday, August 5: 82 actual days; $1,600 × 82 ÷ 365.
Why the others are wrong
- $355.07: Counts actual days to the trade date rather than the settlement date.
- $355.56: 30/360 day count, the corporate and municipal method.
- $363.84: Counts through August 6, the superseded T+2 settlement date (pre-May 2024).
A company's charter grants preemptive rights. It has 3,000,000 shares outstanding and will sell 600,000 more. A shareholder owns 45,000 shares. How many of the new shares must she buy to keep her percentage ownership unchanged?
Ken’s take
She owns 1.5% of the company; 1.5% of the 600,000 new shares is 9,000.
Why the others are wrong
- 45,000 shares: Reports her existing shares.
- 54,000 shares: Reports total holdings after the offering rather than the shares purchased.
- 600,000 shares: Assumes she must buy the entire offering.
A fund charges a sales charge of 5.5% of the public offering price (POP) on purchases below $50,000 and 4.5% of the POP on purchases from $50,000 to $99,999. The net asset value (NAV) is $20.00. A customer invests $60,000 in a single purchase. How many shares does she receive?
Ken’s take
$60,000 qualifies for 4.5%; shares = $60,000 × 0.955 ÷ $20.00.
Why the others are wrong
- 2,835 shares: Uses the 5.5% rate, ignoring the breakpoint.
- 2,871 shares: Adds the 4.5% to the NAV instead of taking it out of the POP.
- 3,000 shares: Ignores the sales charge and divides by the NAV.
A customer buys 20 Treasury notes quoted at 99-24. What is the total principal amount?
Ken’s take
99 + 24/32 = 99.75, times $10 per point, times 20.
Why the others are wrong
- $19,800: Drops the fraction.
- $19,848: Reads 24 as a decimal instead of 32nds.
- $19,875: Uses 64ths.
A customer sells short 800 shares at $45 in a new margin account, depositing the Regulation T (Reg T) minimum. The stock falls to $38. What is the special memorandum account (SMA) balance?
Ken’s take
Credit balance = 150% × $36,000 = $54,000; equity = $54,000 − $30,400 = $23,600; Reg T requirement = 50% × $30,400; SMA = excess = $8,400, which is 150% of the $5,600 decline.
Why the others are wrong
- $2,800: Uses 50%, the long-account percentage.
- $5,600: Counts the decline in short market value as SMA, without the Reg T effect.
- $23,600: Reports total equity.
A stock earns $4.00 per share and trades at 15 times earnings. Earnings per share rise 10%, but investors now pay only 13 times earnings. What is the new price?
Ken’s take
EPS = $4.40; $4.40 × 13: price falls despite higher earnings.
Why the others are wrong
- $52.00: Applies the new P/E to the old earnings.
- $60.00: Null answer: assumes the earnings gain and the lower multiple cancel.
- $66.00: Applies the old P/E to the higher earnings.
A stock trades at $36 with a price-earnings ratio of 12 and pays $1.20 per share in annual dividends. What is the payout ratio?
Ken’s take
EPS = $36 ÷ 12 = $3.00; $1.20 ÷ $3.00.
Why the others are wrong
- 3.33%: Dividend yield.
- 10.00%: Divides the dividend by the P/E ratio.
- 33.33%: Divides the P/E by the price.
A margin account holds long securities with a market value of $40,000 and a debit balance of $12,000. Ignoring any prior special memorandum account (SMA), how much additional stock can the customer purchase using only the excess equity?
Ken’s take
Equity = $28,000; Reg T on the current holdings = $20,000; excess = $8,000; buying power = $8,000 ÷ 0.50.
Why the others are wrong
- $4,000: Multiplies by 50% instead of dividing.
- $8,000: Treats the excess equity as buying power rather than dividing by the 50% requirement.
- $56,000: Divides the entire equity by 50%, ignoring the requirement on existing holdings.
Which statement about preemptive rights is true?
Ken’s take
Preemptive rights protect existing holders against dilution of their percentage ownership by giving them first call on new shares.
Why the others are wrong
- They let holders cast all their votes for a single director: True of cumulative voting, a separate feature of the stock.
- They usually last several years, giving holders ample time to exercise: True of warrants, whose long lives distinguish them from rights.
- They allow holders to buy new shares at a price above the current market: True of warrants issued out of the money; a rights subscription price is set below market.
A customer buys 5 zero-coupon bonds ($1,000 par, 10 years) at $600 each and holds them 4 years. She sells them at $820 each. What is her gain or loss?
Ken’s take
Accretion $40/yr; basis $760; ($820 − $760) × 5.
Why the others are wrong
- $500 loss: Accretes twice.
- $1,100 gain: Ignores accreted basis.
- $2,000 gain: Treats the discount to par as the gain.
A portfolio has 60% in a stock with a beta of 1.4 and 40% in a stock with a beta of 0.8. If the market falls 10%, what is the portfolio's expected change?
Ken’s take
Portfolio beta = 1.16; 1.16 × -10%.
Why the others are wrong
- -11.00%: Averages the betas without weighting.
- -10.40%: Swaps the weights.
- -10.00%: Assumes a beta of 1.
A fund charges 5% on purchases below $25,000 and 4% on purchases from $25,000 to $49,999, applied to the dollars invested. A customer holding $21,000 in the fund adds $6,000 and has a right of accumulation. What sales charge does she pay on the new purchase?
Ken’s take
Combined value $27,000 crosses the $25,000 breakpoint, so the new $6,000 is charged 4%.
Why the others are wrong
- $300: Prices the new purchase alone, ignoring the existing holding.
- $1,080: Applies the lower rate to the whole account, including shares already bought.
- $1,350: Applies the higher rate to the whole account.
A customer in the 32% federal bracket buys a new-issue municipal bond with a 4.0% coupon at an original-issue discount price that produces a 4.5% yield to maturity. What is the taxable equivalent yield of this investment if she holds it to maturity?
Ken’s take
The coupon is irrelevant to the return actually earned; the yield to maturity (4.5%) is grossed up: 4.5 ÷ 0.68.
Why the others are wrong
- 3.06%: Multiplies the basis by (1 − rate), computing an after-tax figure in the wrong direction.
- 5.88%: Grosses up the coupon even though the return she actually earns is the yield to maturity.
- 5.94%: Multiplies by (1 + rate) instead of dividing by (1 − rate).
A $1,000 par debenture is convertible at $20 per share and has been called at 104.5. The common stock trades at $26. What is the most the holder of 5 debentures can realize?
Ken’s take
Each bond converts into 50 shares worth $1,300, versus $1,045 from the call; the holder takes the larger: $1,300 per bond.
Why the others are wrong
- $2,600: Multiplies the stock price by the conversion price instead of by the shares received.
- $5,000: Par, the amount that is repaid at maturity, not on a call.
- $5,225: Takes the other of the two choices the holder has (tender at the call price vs. convert and sell the shares), the one with the lower value.
A customer buys 200 shares at $60 and buys 2 puts at a $55 strike for $3.10. What is the maximum loss?
Ken’s take
($60 − $55 + $3.10) × 200.
Why the others are wrong
- $620: Counts the premium only.
- $1,000: Ignores the premium.
- $12,620: Treats the stock as falling to zero, ignoring the put.
A woman bought stock years ago at $30 per share. When it has slipped to $22, she gives 400 shares to her son for his birthday. A few months later he sells all of them at $26. What is his gain or loss, if any?
Ken’s take
When the sale price falls between the donor's basis and the value at gift, there is neither gain nor loss.
Why the others are wrong
- $3,200 loss: Reports the gap between donor basis and the value at gift.
- $1,600 loss: Measures against the donor's $30 basis alone.
- $1,600 gain: Measures against the $22 value alone.
A $100 par preferred stock pays a dividend of $1.375 each quarter and currently trades at $88. What is its current yield?
Ken’s take
Current yield = annual dividend ÷ market price = $5.50 ÷ $88.
Why the others are wrong
- 1.56%: Quarterly dividend over price: never annualized.
- 4.84%: Multiplies the par-based yield by the price ratio instead of dividing by it.
- 5.50%: Par-based yield: divides the annual dividend by par and ignores the market price.
A customer buys 1,000 shares at $40 paying the Regulation T (Reg T) minimum, borrows the rest at 6% a year, and sells 6 months later at $46. What is her return on her own money?
Ken’s take
Gain $6,000; interest $600; net $5,400 ÷ equity $20,000.
Why the others are wrong
- 13.50%: Divides by the full purchase price instead of her equity.
- 24.00%: Charges a full year of interest.
- 30.00%: Ignores margin interest.
A put at a $60 strike trades at $4.10 while the stock trades at $58. How much of the premium is time value?
Ken’s take
Intrinsic = $60 − $58 = $2; time value = $4.10 − $2.00.
Why the others are wrong
- $2.00: Reports intrinsic value instead.
- $4.10: Reports the entire premium.
- $6.10: Adds intrinsic value instead of subtracting it.
A customer has been following a 5.4% corporate bond issued by a regional utility, which pays interest every March 1 and September 1. On Thursday, June 11 she places an order for $20,000 par, and it executes at the going market price. The trade settles regular way. How much accrued interest does she pay?
Ken’s take
Numbers to write down: $20,000 par; 5.4%; Mar 1 / Sep 1; trade Thu Jun 11; regular-way settlement.
Corporate bonds accrue on a 30/360 basis to the settlement date. Settlement is T+1 (Friday, June 12): March 1 to June 12 is 101 days; $1,080 × 101 ÷ 360.
Why the others are wrong
- $304.77: Actual days over 365: the Treasury method applied to a corporate bond.
- $312.00: Uses the superseded T+2 cycle (pre-May 2024): settlement Monday, June 15, which adds three days across the weekend.
- $540.00: Pays a full semiannual coupon, ignoring the partial period.
A company has 4,000 shares of $100 par 6% cumulative preferred. It skipped the dividend for 2 years and now declares $100,000 in total dividends for the current year. How much is left for common holders?
Ken’s take
Preferred is owed $24,000 × 3 = $72,000; $100,000 − $72,000.
Why the others are wrong
- $52,000: Pays the arrears but not the current year.
- $76,000: Pays only the current year to preferred.
- $100,000: Treats the preferred as non-cumulative and ignores its claim.
A 6% convertible debenture converts into 25 shares of common. The common has fallen 15% this week to $22, so the shares received are worth $550 while the debenture trades at 91. Which factor will now most strongly influence the debenture's price?
Ken’s take
At parity of $550 against a price of $910, the conversion feature is deeply out of the money, so the bond trades on its straight-debt value, which interest rates and credit quality drive.
Why the others are wrong
- The size of the common stock dividend: Dividends affect the income give-up on conversion but do not set the bond's value when conversion is far out of reach.
- The conversion ratio, which sets the price: The ratio fixes parity, but a fixed ratio cannot move a price whose value now rests on the bond's own debt features.
- Changes in the common stock price: The standard 'convertibles follow the stock' heuristic; true when parity is near or above the bond price, not when the bond trades far above parity.
A company reports cash of $60M, marketable securities of $40M, receivables of $140M and inventory of $200M against current liabilities of $220M. What is its quick ratio?
Ken’s take
($440M − $200M) ÷ $220M.
Why the others are wrong
- 0.27: Counts cash alone.
- 0.45: Cash ratio, which leaves out receivables.
- 0.64: Counts receivables alone.
A customer in the 28% federal bracket compares a 3.6% tax-exempt municipal bond with taxable bonds. If her bracket falls to 24%, what taxable yield is now needed to match the municipal bond?
Ken’s take
A lower bracket makes tax exemption less valuable, so the required taxable yield falls from 5.00% to 3.6÷0.76.
Why the others are wrong
- 4.46%: Multiplies by (1 + rate) instead of dividing by (1 − rate).
- 5.00%: Null answer: assumes no change, using the old bracket.
- 15.00%: Divides by the tax rate itself.
A customer's uncle dies and leaves her 500 shares of stock. He had paid $12 per share years earlier, and the shares were worth $38 on the day he died. Five months after his death she sells them at $41. Which describes the result?
Ken’s take
Inherited shares take the date-of-death value as basis ($3 × 500) and are automatically long-term.
Why the others are wrong
- $1,500 short-term gain: Right basis, but treats the holding period as starting at inheritance (gift and purchase rules).
- $14,500 short-term gain: Wrong on both axes: carryover basis and a new holding period.
- $14,500 long-term gain: Right holding period, but carries the uncle's $12 basis (the gift rule).
A customer sells short 150 shares at $30 in a new margin account. What is the minimum initial deposit required?
Ken’s take
50% of $4,500 is $2,250.00, above the $2,000 minimum, so Reg T governs.
Why the others are wrong
- $1,125: Takes half of the Reg T amount.
- $2,000: Applies the $2,000 minimum even though 50% of the proceeds is larger.
- $4,500: Treats the short sale like a cash purchase at 100% of proceeds.
A company has current assets of $150M and current liabilities of $200M. It uses $50M of cash to pay down accounts payable. What happens?
Ken’s take
Current ratio goes from 0.75 to 0.67; working capital stays at $-50M because both sides fall by the same amount.
Why the others are wrong
- The current ratio rises; working capital is unchanged: Applies the ratio-above-1 outcome to a ratio below 1.
- The current ratio falls; working capital falls: Believes spending cash drains working capital.
- The current ratio rises; working capital rises: Believes paying a debt must increase working capital.
A customer buys 1,000 shares at $60 on margin, paying the Regulation T (Reg T) minimum. The stock then falls to $48. What percentage of market value is now equity?
Ken’s take
Debit stays $30,000; equity = $48,000 − $30,000 = $18,000; $18,000 ÷ $48,000. A 20% price drop erodes equity far more than 20%.
Why the others are wrong
- 20.00%: Reports the price decline instead of the equity percentage.
- 30.00%: Divides equity by the original purchase price.
- 50.00%: Assumes the account stays at 50% since no call has been made.
In one year a customer realizes a $14,000 short-term loss, a $6,000 long-term gain and a $1,000 long-term loss. Assuming no other gains, how much loss carries forward to next year?
Ken’s take
Net = −$14,000 + $6,000 − $1,000 = −$9,000; $3,000 is deducted; $6,000 carries forward.
Why the others are wrong
- $3,000: Reports the amount deducted, not the amount carried.
- $5,000: Skips the $1,000 long-term loss.
- $9,000: Forgets the $3,000 annual deduction.
A $1,000 par debenture is convertible at $40 per share and trades at 106. The common stock trades at $42.40. What is the debenture's premium over parity, if any?
Ken’s take
Parity = 25 × $42.40 = $1,060, the same as the $1,060 price, so the premium is zero.
Why the others are wrong
- $25: Reports the number of shares received.
- $60: Measures the premium over par instead of over parity.
- $1,060: Reports the bond's price as the premium.
A customer buys $30,000 par of a new municipal issue with a 4.8% coupon. The bonds are dated June 1, the first coupon is payable December 1, and the trade settles June 24. How much accrued interest, if any, does the customer pay at settlement?
Ken’s take
Interest accrues from the dated date to settlement on a 30/360 basis: 23 days; $1,440 × 23 ÷ 360. The buyer is then repaid in full at the first coupon.
Why the others are wrong
- $0: Null answer: assumes a new issue carries no accrued interest because no coupon has yet been paid.
- $96: Counts both the dated date and the settlement date, adding a day.
- $628: Counts from settlement to the first coupon: the time the buyer will own the bonds, not the time interest has built.
A stock trades at $72. The company declares a 20% stock dividend. All else equal, what is the approximate market price after the distribution?
Ken’s take
Each 100 shares become 120 with the same total value: $72 ÷ 1.20.
Why the others are wrong
- $57.60: Takes 20% off the price instead of dividing by 1.20.
- $72.00: Null answer: believes a stock dividend leaves the price alone.
- $86.40: Raises the price by 20%.
A customer bought 100 shares at $30 fourteen months ago, 100 shares at $38 five months ago, and 100 shares at $44 two months ago. Today she sells 150 shares at $50 without identifying which shares. What is her gain?
Ken’s take
With no identification, shares are sold first-in, first-out: 100 × ($50 − $30) + 50 × ($50 − $38).
Why the others are wrong
- $1,200 gain: Last-in, first-out.
- $1,900 gain: Average cost, which is not the default for stock.
- $3,000 gain: Takes all 150 shares from the oldest lot.
A warrant to buy common stock at $18 sells for $6.50 while the stock trades at $23. What portion of the warrant's price is time value?
Ken’s take
Intrinsic value = $23 − $18 = $5; time value = $6.50 − $5.00.
Why the others are wrong
- $5.00: Reports the intrinsic value rather than the time value.
- $6.50: Reports the entire premium.
- $11.50: Adds intrinsic value to the price instead of subtracting it.
A $1,000 par debenture is convertible at $50 per share. The common stock trades at $57 and the debenture trades at 108.5. At what dollar price would the debenture be trading at parity with the shares it converts into?
Ken’s take
Shares per bond = $1,000 ÷ $50 = 20; 20 × $57 = $1,140.
Why the others are wrong
- $1,000: Par value, the amount repaid at maturity.
- $1,085: The bond's current market price, which is what is being compared with parity.
- $2,850: Multiplies the stock price by the conversion price instead of by the number of shares received.
A company earns $24M, pays $4M in preferred dividends, and reports stockholders' equity of $250M that includes $50M of preferred stock. What is its return on common equity?
Ken’s take
($24M − $4M) ÷ ($250M − $50M).
Why the others are wrong
- 6.67%: Adds preferred stock to equity instead of removing it.
- 8.00%: Deducts preferred dividends but keeps preferred stock in equity.
- 9.60%: Uses total return on total equity.
A Treasury bond with a 3.0% coupon and six years to maturity is quoted at 88-16. What is its current yield?
Ken’s take
Treasury quotes after the dash are 32nds, so 88-16 is 88.50% of par = $885.00; $30 ÷ $885.00.
Why the others are wrong
- 2.69%: Adds the discount to par instead of subtracting it.
- 3.00%: Nominal yield: ignores the discount.
- 3.40%: Reads the 32nds as hundredths (88.16 instead of 88.50), a small but real misread of the quote.
A customer sells 500 shares at a $5,000 loss. Within 30 days she buys back 200 shares of the same stock. What loss may she deduct now, if any?
Ken’s take
200 of 500 shares were replaced, so 40% ($2,000) is disallowed; $3,000 is deductible.
Why the others are wrong
- $0: Null answer: assumes any repurchase disallows the entire loss.
- $2,000: Reports the disallowed portion.
- $5,000: Ignores the wash sale rule.
A customer's long margin account has a market value of $36,000 and a debit balance of $22,000. How much, if any, must be deposited to meet the minimum maintenance requirement?
Ken’s take
Equity is $14,000 (39%), below Reg T's 50% but above the 25% maintenance level of $9,000: the account is restricted, not under a maintenance call.
Why the others are wrong
- $4,000: Restores equity to the 50% Reg T level, which a maintenance call does not require.
- $9,000: Reports the maintenance requirement instead of the shortfall.
- $18,000: Reports the Reg T requirement.
A retired customer owns a 4.5% convertible debenture ($1,000 par) issued by a regional manufacturer. The interest check covers her property taxes, and the company's stock has climbed all year. Each bond converts into 32 shares of common, and the common pays $0.80 per share annually. Which describes her best course?
Ken’s take
Interest is $45.00; dividends on 32 shares are $25.60; converting costs her $19.40 a year of the income she depends on.
Why the others are wrong
- Convert; her income would rise by $19.40 a year: Reverses the sign: the dividends on 32 shares ($25.60) are below the $45.00 interest.
- Convert; her income would rise by $25.60 a year: Counts the dividends and ignores the interest given up.
- Do not convert; her income would fall by $45.00 a year: Right conclusion, wrong number: counts the interest lost and forgets the dividends gained.
A customer owns 100 shares bought 18 months ago at $25 and 100 shares bought 5 months ago at $40. She sells 100 shares at $36 and identifies the lot in writing at the time of the trade. What realized result produces the lowest tax on this sale?
Ken’s take
Identifying the $40 lot realizes a $400 short-term loss, which creates no tax; the older lot's gain would be taxed. A long-term gain's lower rate does not beat no gain.
Why the others are wrong
- $350 gain: Uses the $32.50 average cost, which is not available for individual stock.
- $400 gain: Sells the right lot but reverses the sign of the result.
- $1,100 gain: First-in, first-out: sells the older lot for a long-term gain.
A fund with a net asset value (NAV) of $18.40 goes ex-dividend on a $0.40 per share income distribution. By how much does NAV change on the ex-date, if any?
Ken’s take
The fund's assets shrink by the amount paid out, so NAV falls $0.40 to $18.00.
Why the others are wrong
- NAV falls by $4.00: Slips a decimal place.
- NAV falls by $0.80: Counts the distribution twice.
- No change: Null answer: believes a distribution only moves cash between pockets and leaves NAV unchanged.
A customer is choosing between a corporate bond yielding 5.20% and a municipal bond yielding 3.64%, both rated the same and maturing together. At what federal tax bracket would the two investments produce the same after-tax return?
Ken’s take
Indifference when 3.64 = 5.2 × (1 − bracket), so bracket = 1 − 3.64 ÷ 5.2.
Why the others are wrong
- 1.56%: Reports the yield gap in percentage points as if it were a tax rate.
- 17.65%: Divides the yield gap by the sum of the two yields.
- 42.86%: Divides the yield gap by the municipal yield instead of building the bracket from the ratio.
A customer bought 500 shares of a steady dividend payer at $38. Later she sells 5 calls at a $45 strike, collecting $2.40 each. The stock rallies and the calls are assigned. What is her total gain?
Ken’s take
Numbers to write down: 500 shares; cost $38; 5 calls; strike $45; premium $2.40.
($45 − $38 + $2.40) × 500.
Why the others are wrong
- $1,200 gain: Counts the premium only.
- $2,300 gain: Subtracts the premium instead of adding it.
- $3,500 gain: Leaves out the premium she collected.
A customer owns 900 shares of a company that announces a 2-for-3 reverse split and a 20% cash dividend. How many shares does she own after both?
Ken’s take
900 × 2/3 = 600; a cash dividend adds no shares.
Why the others are wrong
- 720 shares: Treats the cash dividend as a stock dividend.
- 1,080 shares: Ignores the split and treats the cash dividend as a stock dividend.
- 1,350 shares: Treats the reverse split as a forward 3-for-2 split.
A $1,000 par debenture is convertible at $20 per share and has been called at 104.5. The common stock trades at $20.5. What is the most the holder of 5 debentures can realize?
Ken’s take
Converting yields only $1,025 per bond, below the $1,045 call price, so the holder tenders the bonds.
Why the others are wrong
- $2,050: Multiplies the stock price by the conversion price instead of by the shares received.
- $5,000: Par, the amount that is repaid at maturity, not on a call.
- $5,125: Takes the other of the two choices the holder has (tender at the call price vs. convert and sell the shares), the one with the lower value.
A customer buys 1 XYZ Jan 50 call at 6.20 and sells 1 XYZ Jan 60 call at 2.70. What is the maximum gain?
Ken’s take
Width $10 − debit $3.50 = $6.50, × 100.
Why the others are wrong
- $350: Reports the net debit, which is the maximum loss.
- $1,000: Ignores the net debit.
- $1,350: Adds the debit to the width.
A customer decides to invest a year-end bonus in an open-end fund that carries a front-end sales charge. The quote sheet shows a $11.70 net asset value (NAV) and a $12.50 public offering price (POP). She puts in $10,000. How many shares does she receive?
Ken’s take
Numbers to write down: $10,000; NAV $11.70; POP $12.50.
Purchases are at POP: $10,000 ÷ $12.50.
Why the others are wrong
- 748.80 shares: Deducts the sales charge and then divides by POP, charging it twice.
- 854.70 shares: Divides by NAV, ignoring the sales charge.
- 9,360.00 shares: Multiplies by NAV before dividing.
A $1,000 par debenture is convertible at $40 per share. The issuer announces a 2-for-1 split of its common stock. After the split, how many shares does each debenture convert into?
Ken’s take
Anti-dilution provisions adjust the conversion price to $20, so each bond converts into 50 shares: the holder's claim is unchanged.
Why the others are wrong
- 12.5 shares: Halves the ratio, adjusting in the wrong direction.
- 25 shares: No adjustment: assumes the original conversion ratio survives a split.
- 100 shares: Applies the split twice.
A customer owns $10,000 par of a Treasury Inflation-Protected Security (TIPS) with a 2% coupon. After the latest inflation adjustment, the principal on the bond is $10,300. How much interest does the bond pay for the year?
Ken’s take
Coupon applies to adjusted principal: 2% × $10,300.
Why the others are wrong
- $200: Applies the coupon to original par.
- $300: Reports the inflation adjustment as interest.
- $500: Adds the adjustment to the interest.
An open-end fund has a net asset value (NAV) of $14.50 and a sales charge of 6% of the public offering price. What is the public offering price (POP)?
Ken’s take
Sales charge is a percentage of POP, so POP = $14.50 ÷ 0.94.
Why the others are wrong
- $13.63: Subtracts the charge from NAV.
- $14.50: Reports NAV, which is the redemption price.
- $15.37: Adds the charge to NAV instead of dividing by 94%.
A customer redeems all of her Class B shares, bought for $10,000 and now worth $12,500. The contingent deferred sales charge is 4% in the year of redemption. What charge applies, if any?
Ken’s take
The charge is the lesser of original cost or current value: 4% × $10,000.
Why the others are wrong
- $0: Null answer: assumes a profit removes the charge.
- $100: Applies the charge to the gain only.
- $500: Applies the charge to the current value instead of the lesser of cost or value.
A customer sells short 1,000 shares at $40 and meets Regulation T (Reg T). At what price per share does the account first reach the minimum maintenance requirement?
Ken’s take
Credit balance = 150% × $40,000 = $60,000; equity must be 30% of SMV, so SMV = $60,000 ÷ 1.30 = $46,154, or $46.15 per share.
Why the others are wrong
- $40.00: Divides by 150%, which returns the original sale price.
- $48.00: Uses the 25% long-account percentage on the short side.
- $50.00: Applies 25% to the sale price instead of to the credit balance.
A customer is short 1 ABC call at a 60 strike and short 1 ABC put at a 55 strike. ABC trades at 57. Which of the positions, if any, is in the money?
Ken’s take
A call is in the money above its strike (57 is below 60); a put is in the money below its strike (57 is above 55). Neither is.
Why the others are wrong
- The call only: Reverses the call rule: treats a stock below the strike as in the money.
- Both: Reverses both rules.
- The put only: Reverses the put rule: treats a stock above the strike as in the money.
A fund share is purchased at a net asset value (NAV) of $20.00. A year later NAV is $21.50, and the shareholder has received $0.60 in dividends and $0.90 in capital gains distributions in cash. What is the total return?
Ken’s take
($1.50 + $0.60 + $0.90) ÷ $20.00.
Why the others are wrong
- 7.50%: Counts appreciation only.
- 10.50%: Counts dividends but omits the capital gains distribution.
- 12.00%: Counts the capital gains distribution but omits dividends.
An investor places $500 into a fund at the end of each of four months, when the price per share is $20, $25, $16 and $20. What is her average cost per share?
Ken’s take
Shares bought = 101.250; $2,000 ÷ 101.250 = $19.75, below the $20.25 average price because more shares are bought when the price is low.
Why the others are wrong
- $16.00: Reports the lowest price.
- $20.25: Averages the four prices instead of dividing total dollars by total shares.
- $20.50: Takes the midpoint of the price range.
A $100 par convertible preferred is convertible at $40 per common share. The common trades at $38 and the preferred trades at $99.50. By how much does the preferred's price exceed its parity value?
Ken’s take
Shares received = $100 ÷ $40 = 2.5; parity = 2.5 × $38 = $95.00; premium = $99.50 − $95.00.
Why the others are wrong
- $5.00: Reports par minus parity, the shortfall in conversion value, not the premium.
- $61.50: Subtracts the common's price directly, ignoring the 2.5 shares received.
- $95.00: Reports parity itself rather than the premium over it.
A 7% convertible debenture ($1,000 par) converts into 40 shares and trades at 115. The common trades at $26.50 and pays $0.50 per share annually. How many years of income advantage does the debenture holder need to recover the premium over parity?
Ken’s take
Parity = 40 × $26.50 = $1,060; premium = $90; income advantage = $70 interest − $20 dividends = $50; $90 ÷ $50.
Why the others are wrong
- 3.0 years: Measures the premium over par instead of over parity.
- 4.5 years: Uses only the dividends as the income advantage.
- 21.2 years: Divides parity itself by the income advantage.
A stock has gone ex-rights and trades at $58. A holder needs 4 rights plus $52 to buy one new share. What is the theoretical value of one right?
Ken’s take
Once ex-rights: ($58 − $52) ÷ 4 = $1.50.
Why the others are wrong
- $1.20: Cum-rights formula (divide by N + 1), which applies only while the rights are still attached.
- $6.00: Reports the full gap between market and subscription price.
- $24.00: Multiplies by the rights needed instead of dividing.
A customer buys 2,000 shares at $38 in a margin account and deposits $30,000. How much additional money must she deposit to meet the Regulation T (Reg T) requirement?
Ken’s take
Reg T requirement = 50% × $76,000 = $38,000; shortfall = $38,000 − $30,000.
Why the others are wrong
- $4,000: Applies 50% a second time to the shortfall.
- $38,000: Reports the whole Reg T requirement without crediting her deposit.
- $46,000: Subtracts the deposit from the full purchase price instead of from the 50% requirement.
A fund seeks twice the daily return of an index. The index rises 10% on day one and falls 10% on day two. What is the fund's net two-day change in value, if any?
Ken’s take
Daily resetting compounds: 1.20 × 0.80 = 0.96, a 4% loss, against the index's 1% loss.
Why the others are wrong
- -2.00%: Doubles the index's two-day return.
- -1.00%: Uses the index's own two-day return.
- 0.00%: Null answer: assumes equal up and down moves cancel.
A customer opens a taxable account and buys $40,000 par of a 10-year zero-coupon corporate bond at its original offering price of 61.25. The bond pays nothing until maturity, and she holds it that long. For the first year, how much interest income must she report, if any?
Ken’s take
Numbers to write down: $40,000 par, price 61.25, 10 years.
Cost = 61.25% × $40,000 = $24,500; discount $15,500 ÷ 10 years = $1,550 per year, taxable although no cash is paid.
Why the others are wrong
- $0: Null answer: believes no income exists until cash is received.
- $2,450: Divides the purchase price by the years instead of the discount.
- $15,500: Reports the entire discount in the first year.
A margin account is long securities with a market value of $60,000 against a debit balance of $28,000, and short securities with a market value of $24,000 against a credit balance of $36,000. What is the combined equity?
Ken’s take
Long equity $32,000 + short equity $12,000.
Why the others are wrong
- $12,000: Counts the short side only.
- $20,000: Subtracts the short-side equity.
- $32,000: Counts the long side only.
A customer owns 1,500 shares and receives one right per share; 5 rights are needed to buy one new share. She sells all of her rights at $2.40 each. What are her proceeds?
Ken’s take
She holds 1,500 rights; 1,500 × $2.40.
Why the others are wrong
- $600: Divides by six, mixing in the rights-value formula.
- $720: Counts only the new shares she could have bought.
- $18,000: Multiplies by the rights ratio.
A company holds cash of $30M, marketable securities of $50M, receivables of $90M and inventory of $120M, with current liabilities of $160M. What is its cash ratio?
Ken’s take
($30M + $50M) ÷ $160M.
Why the others are wrong
- 0.19: Excludes marketable securities.
- 1.06: Quick ratio, which adds receivables.
- 1.81: Current ratio, which adds inventory too.
A customer bought 100 shares at $30 fourteen months ago, 100 shares at $38 five months ago, and 100 shares at $44 two months ago. Today she sells 150 shares at $50 without identifying which shares. How is the result reported?
Ken’s take
The 100 shares from the $30 lot are long-term (14 months): $2,000; the 50 from the $38 lot are short-term (5 months): $600.
Why the others are wrong
- $2,600 short-term gain: Treats the whole sale as short-term because the latest purchase was recent.
- $2,000 short-term gain and $600 long-term gain: Reverses the two lots' holding periods.
- $2,600 long-term gain: Treats every share sold as part of the oldest lot.
A customer in the 37% federal bracket is offered a federally exempt municipal bond yielding 3.80% or a taxable bond yielding 5.50%. By how many percentage points does the municipal bond's taxable equivalent yield exceed the taxable bond's yield?
Ken’s take
TEY = 3.8 ÷ 0.63 = 6.03%; 6.03 − 5.50.
Why the others are wrong
- 1.70 points: Compares the two stated yields and never adjusts for tax.
- 3.11 points: Reduces the exempt yield by the bracket, the after-tax direction used on the wrong bond.
- 4.77 points: Divides by the tax rate instead of by (1 − rate), which overstates the equivalent yield.
A customer is short 800 shares of a stock trading at $30 in a margin account. What is the minimum maintenance requirement on the short position?
Ken’s take
30% × (800 shares × $30) = 30% × $24,000.
Why the others are wrong
- $6,000: Uses the 25% long-account percentage.
- $12,000: Uses the 50% Reg T percentage.
- $36,000: Reports the total credit balance after the short sale.
A $1,000 par debenture is convertible at $40 per share and trades at 112. The common stock trades at $46. At what stock price would the common be at parity with the debenture?
Ken’s take
Shares per bond = $1,000 ÷ $40 = 25; stock parity = $1,120 ÷ 25.
Why the others are wrong
- $28.00: Divides the dollar price by the conversion price instead of by the number of shares.
- $40.00: Divides par rather than the bond's market price by the shares received.
- $112.00: Uses the bond's quoted points as if they were a stock price.
Which bond is most sensitive to a change in interest rates?
Ken’s take
A zero's duration equals its maturity, 30 years, and every coupon bond's duration is shorter than its maturity, so the zero is the most sensitive.
Why the others are wrong
- A 20-year bond with a 9% coupon: The highest coupon and shortest maturity make it the least sensitive of the four.
- A 25-year bond with an 8% coupon: Shorter maturity and a higher coupon than the 30-year bonds.
- A 30-year bond with a 7% coupon: Same maturity as the zero, but the coupons paid along the way shorten its duration.
A stock trades at $64 with rights attached. A holder needs 3 rights plus $56 to buy one new share. What is the theoretical value of one right?
Ken’s take
With rights attached: ($64 − $56) ÷ (3 + 1) = $2.00; the extra 1 reflects the value in the stock itself.
Why the others are wrong
- $2.67: Ex-rights formula (divide by N), which applies after the stock goes ex-rights.
- $8.00: Reports the full gap between market and subscription price.
- $24.00: Multiplies by the rights needed instead of dividing.
A customer buys a 6.8% corporate bond at 106 with eight years to maturity and holds it to maturity. Which ranking of the bond's yields, highest to lowest, is correct?
Ken’s take
At a premium the coupon rate is highest; current yield (coupon ÷ price) is lower; YTM is lowest because the premium is lost by maturity.
Why the others are wrong
- Nominal yield, yield to maturity, current yield: Right about the coupon being highest, but swaps the order of the other two: the premium amortizes away, pulling YTM below current yield.
- Yield to maturity, current yield, nominal yield: The discount-bond ranking, true of a bond bought below par and wrong here.
- Current yield, nominal yield, yield to maturity: Treats current yield as highest because the price paid sits in the denominator; but the price is above par, so the ratio is below the coupon.
A warrant to buy common stock at $30 sells for $2.50 while the stock trades at $26. What is the warrant's intrinsic value, if any?
Ken’s take
The stock ($26) is below the exercise price ($30), so there is no intrinsic value; the $2.50 is all time value.
Why the others are wrong
- $2.50: Treats the whole premium as intrinsic value.
- $4.00: Reverses the subtraction and reports the strike less the stock price.
- $6.50: Adds the shortfall to the premium.
A customer buys a 7.5% corporate bond at 107 that matures in 15 years but is callable in 3 years at 102. Which measure shows the customer's lowest potential return?
Ken’s take
Computed: nominal 7.50% > current 7.01% > YTM 6.75% > YTC 5.56%. Losing 5 points over only three years drags yield below the 15-year result.
Why the others are wrong
- Nominal yield: The coupon rate is the highest measure on a premium bond, never the lowest.
- Current yield: Current yield sits below the coupon but above both redemption-based yields.
- Yield to maturity: The textbook 'premium bond means lowest YTM' heuristic; true against current yield, but the early call at 102 pulls the yield lower still.