Cost of Preferred Stock - Corporate Finance

1. Which of the following statements most accurately describes a key difference between the cost of preferred stock and the after-tax cost of debt for a given company?
   Answer: The cost of preferred stock is not adjusted for taxes, whereas the cost of debt is reduced by the firm's marginal tax rate. A primary distinction in cost of capital calculations is the tax treatment. Interest payments on debt are tax-deductible for the issuing corporation, which reduces the effective cost of debt. The after-tax cost of debt is $r_d(1-T)$. In contrast, dividend payments on preferred stock are made from after-tax profits and are not deductible. Therefore, the cost of preferred stock is not adjusted for taxes.
2. Pacific Corp.'s preferred stock has a $75 par value and pays a $5.8\%$ annual dividend. The stock includes a participating feature that provides additional dividends when common dividends exceed $2.00 per share. Common stock currently pays $2.40 per share in dividends. The preferred stock trades at $78 per share. For cost of capital calculations, what rate should be used?
   Answer: $6.09\%$ including the current participating dividend benefit in the calculation When calculating the cost of preferred stock for capital budgeting purposes, you must consider all dividends the preferred shareholders actually receive, not just the stated rate. This includes any participating features that provide additional dividends beyond the base amount. For Pacific Corp.'s participating preferred stock, you need to calculate the total current dividend per share. The base dividend is $\$75 \times 5.8\% = \$4.35$ per share. Since the common dividend of $2.40 exceeds the $2.00 threshold, the preferred stock receives additional participating dividends of $\$2.40 - \$2.00 = \$0.40$ per share. The total preferred dividend is $\$4.35 + \$0.40 = \$4.75$ per share. The cost of preferred stock is: $\frac{\$4.75}{\$78} = 6.09\%$ Answer choice A incorrectly ignores the participating feature, using only $\frac{\$4.35}{\$78} = 5.58\%$. This understates the true cost since shareholders are actually receiving more. Answer choice B attempts to average preferred and common yields, which has no theoretical basis in cost of capital calculations. Answer choice C uses the stated dividend rate of 5.8%, ignoring both the current market price and the participating dividend—this completely misses how cost of capital should be calculated. Remember: for participating preferred stock, always include the full dividend amount currently being paid, including any participation above the base rate. The cost of capital reflects what investors actually receive today, not just the stated terms.
3. Sterling Corp. has preferred stock outstanding that was issued at $60 par with a $5.5\%$ cumulative dividend rate. Due to financial difficulties two years ago, the company missed four quarterly dividend payments but has since resumed payments. The stock currently trades at $58 per share. What is the effective cost of this preferred stock for the current year?
   Answer: $11.31\%$ including both current and missed cumulative dividend payments When dealing with cumulative preferred stock, you must understand that missed dividends accumulate and must be paid before any common dividends can be distributed. This creates a liability that affects the effective cost of capital. Let's calculate the current effective cost. The annual dividend is $\$60 \times 5.5\% = \$3.30$. However, Sterling missed four quarterly payments two years ago, meaning $4 \times \$0.825 = \$3.30$ in cumulative dividends remains unpaid. The company now owes both the current year's dividend ($3.30) plus the accumulated arrears ($3.30), totaling $6.60 that must be paid this year. The effective cost is: $\frac{\$6.60}{\$58} = 11.38\%$ (closest to answer D at $11.31\%$). Choice A ($5.66\%$) incorrectly uses only the current annual dividend divided by market price ($\frac{\$3.30}{\$58}$), ignoring the cumulative arrears entirely. Choice B ($8.49\%$) makes the error of amortizing missed payments over multiple years, but cumulative dividends don't work this way—they must be paid in full before resuming normal distributions. Choice C ($5.50\%$) simply uses the original stated rate, completely disregarding both the current market price and the accumulated obligations. Remember: cumulative preferred stock creates a growing liability when dividends are missed. Always include both current and accumulated unpaid dividends when calculating the effective cost, as these represent the total cash obligation the company faces.
4. A firm's newly issued preferred stock has a required rate of return of 8.5%. The stock pays an annual dividend of $7.50 and was issued at a price of $94.00 per share. What were the flotation costs as a percentage of the issue price?
   Answer: 5.53% This problem requires working backward from the cost to find the flotation cost percentage.\ 1. Calculate the net proceeds ($P_{net}$) implied by the cost: $P_{net} = D_p / r_p = \$7.50 / 0.085 = \$88.235$\ 2. Calculate the total dollar flotation cost: $FC_\$ = \text{Issue Price} - P_{net} = \$94.00 - \$88.235 = \$5.765$\ 3. Calculate flotation cost as a percentage of the issue price: $F = FC_\$ / \text{Issue Price} = \$5.765 / \$94.00 \approx 0.0553$ or 5.53%.
5. A company is issuing preferred stock that pays an annual dividend of $10. The company's financial advisor states that, after accounting for issuance costs, the effective cost of this capital will be 9.20%. If the stock is sold to the public for $115 per share, what are the flotation costs as a percentage of the selling price?
   Answer: 6.35% This is a multi-step problem where you solve for the flotation cost percentage.\ 1. Calculate the net proceeds ($P_{net}$) the company must have received for the cost to be 9.20%: $P_{net} = D_p / r_p = \$10.00 / 0.092 = \$108.6957$\ 2. Calculate the dollar flotation cost per share: $FC_\$ = \text{Selling Price} - P_{net} = \$115.00 - \$108.6957 = \$6.3043$\ 3. Calculate the flotation cost as a percentage of the selling price: $F = FC_\$ / \text{Selling Price} = \$6.3043 / \$115.00 \approx 0.0635$ or 6.35%.
6. A credit rating agency upgrades a company's preferred stock from BB to BBB. Which of the following is the most likely immediate impact on the company's marginal cost of preferred stock?
   Answer: It will decrease, as the higher rating implies lower risk and will increase the stock's market price. A credit rating upgrade signifies a decrease in perceived risk. Investors will therefore require a lower rate of return to hold the security. In the cost of preferred stock formula ($r_p = D_p / P_p$), a lower required return ($r_p$) for a fixed dividend ($D_p$) is achieved through a higher market price ($P_p$). Therefore, the rating upgrade will likely cause the stock's price to rise, lowering the company's marginal cost of preferred stock.
7. TechFlow Corp.'s preferred stock pays a quarterly dividend of $0.85 per share and trades at $42 per share. The company is considering issuing additional preferred stock and expects flotation costs of $3.5\%$. However, due to recent credit rating concerns, new preferred stock would need to offer a $0.4\%$ higher yield than existing stock to attract investors. What should TechFlow use as the cost of new preferred stock?
   Answer: $8.88\%$ incorporating both flotation costs and the required yield premium This requires multiple adjustments: First, calculate existing cost: $\$0.85 \times 4 = \$3.40$ annual dividend; $\$3.40 / \$42 = 8.10\%$. New stock needs $8.10\% + 0.4\% = 8.50\%$ yield. With $3.5\%$ flotation costs, net proceeds = $\$42 \times 0.965 = \$40.53$. Required dividend = $\$40.53 \times 0.085 = \$3.45$. Cost = $\$3.45 / \$40.53 = 8.88\%$. Choice A ignores flotation costs. Choice C ignores the yield premium. Choice D ignores flotation costs.
8. Giga Corp. is issuing new preferred stock at $60 per share. The stock will pay a semi-annual dividend of $2.25. Flotation costs are $3.60 per share. What is the estimated cost of this preferred stock?
   Answer: 8.04% This is a multi-step calculation involving annualizing the dividend and using the net proceeds.\ 1. Annualize the dividend: $D_p = \$2.25 \times 2 = \$4.50$\ 2. Calculate the net proceeds per share: $P_{net} = \text{Issue Price} - \text{Flotation Cost} = \$60.00 - \$3.60 = \$56.40$\ 3. Calculate the cost of preferred stock: $r_p = D_p / P_{net} = \$4.50 / \$56.40 \approx 0.07978$ or 8.04% (rounded).
9. A company can issue preferred stock with a par value of $100 and a 7.5% dividend for $102 per share, incurring flotation costs of 4%. Alternatively, it can issue bonds at par with a 6.5% coupon. The company's marginal tax rate is 25%. What is the difference between the cost of preferred stock and the after-tax cost of debt?
   Answer: 2.79% This requires calculating and comparing the costs of two different financing sources.\ 1. Cost of Preferred Stock ($r_p$):\ - Dividend: $D_p = \$100 \times 0.075 = \$7.50$\ - Net Proceeds: $P_{net} = \$102 \times (1 - 0.04) = \$97.92$\ - $r_p = \$7.50 / \$97.92 \approx 7.66\%$\ 2. After-Tax Cost of Debt ($r_d(1-T)$):\ - Pre-tax cost of debt: $r_d = 6.5\%$ (since issued at par)\ - After-tax cost: $6.5\% \times (1 - 0.25) = 6.5\% \times 0.75 = 4.875\%$\ 3. Difference: \(7.66\% - 4.875\% = 2.785\% \approx 2.79\%).
10. Stellar Corp. plans to issue new perpetual preferred stock to finance a project. The stock will have a par value of $100, pay an annual dividend of $7.00, and is expected to sell for $104 per share. Flotation costs are anticipated to be 5% of the market price. What is the estimated cost of this preferred stock for Stellar?
    Answer: 7.09% The cost of preferred stock ($r_p$) is the annual dividend ($D_p$) divided by the net proceeds from the sale of the stock ($P_{net}$). The net proceeds are the market price minus flotation costs.\ 1. Calculate the flotation cost per share: $FC = \$104.00 \times 0.05 = \$5.20$\ 2. Calculate the net proceeds per share: $P_{net} = \$104.00 - \$5.20 = \$98.80$\ 3. Calculate the cost of preferred stock: $r_p = D_p / P_{net} = \$7.00 / \$98.80 \approx 0.07085$ or 7.09%.
11. Global Manufacturing has preferred stock with a $25 par value and $5.6\%$ dividend rate, currently trading at $23.75. The preferred stock has a mandatory conversion feature that will convert each share to $1.25$ common shares in three years. Common stock currently trades at $17.50 per share. For immediate cost of capital purposes, how should this preferred stock be treated?
    Answer: Use $5.90\%$ based on current preferred dividend and market price relationship For immediate cost of capital calculations, treat convertible preferred stock as preferred stock using current dividend and market price. Annual dividend = $\$25 \times 0.056 = \$1.40$. Cost = $\$1.40 / \$23.75 = 5.90\%$. The mandatory conversion affects future capital structure but not current cost calculations. Choice B prematurely treats it as common equity. Choice C confuses conversion value with cost calculation. Choice D unnecessarily complicates the current period cost calculation.
12. Apex Industries has preferred stock outstanding with a 6% dividend rate on a $100 par value. The stock is currently trading at $75 per share. The company's marginal tax rate is 25%. For purposes of calculating the firm's weighted average cost of capital (WACC), what is the component cost of this preferred stock?
    Answer: 8.00% First, calculate the annual dollar dividend. Then, divide by the current market price. The tax rate is irrelevant because preferred dividends are not tax-deductible for the issuing firm.\ 1. Calculate the annual dividend: $D_p = \text{Par Value} \times \text{Dividend Rate} = \$100 \times 0.06 = \$6.00$\ 2. Calculate the cost of preferred stock: $r_p = D_p / P_p = \$6.00 / \$75.00 = 0.08$ or 8.00%.
13. A company's perpetual preferred stock was issued several years ago with a $100 par value and a 6% dividend. Due to a decrease in the company's risk profile, its current cost of preferred stock is 5%. What is the current market price per share of this preferred stock?
    Answer: $120.00 To solve for the current market price, rearrange the cost of preferred stock formula ($r_p = D_p / P_p$) to $P_p = D_p / r_p$.\ 1. Calculate the annual dollar dividend, which is fixed from the time of issue: $D_p = \text{Par Value} \times \text{Original Dividend Rate} = \$100 \times 0.06 = \$6.00$\ 2. Use the current cost of preferred stock (the market's required return) to find the current market price: $P_p = \$6.00 / 0.05 = \$120.00$.
14. The cost of a firm's preferred stock is 8.0%. If the firm's marginal tax rate increases from 20% to 30%, what will be the new cost of its preferred stock, all else being equal?
    Answer: 8.00% The cost of preferred stock is not affected by the firm's corporate tax rate. Preferred dividends are paid out of after-tax income and are not a tax-deductible expense for the issuing company. Therefore, a change in the marginal tax rate has no direct impact on the calculation of the cost of preferred stock. It remains 8.0%.
15. A company issues perpetual preferred stock with a par value of $50 and a 9% dividend rate, payable annually. The stock is issued at $48 per share, with flotation costs of $2.50 per share. What is the estimated cost of this preferred stock?
    Answer: 9.89% This calculation involves finding the dollar dividend, calculating the net proceeds, and then finding the cost.\ 1. Calculate the annual dividend: $D_p = \text{Par Value} \times \text{Dividend Rate} = \$50.00 \times 0.09 = \$4.50$\ 2. Calculate the net proceeds: $P_{net} = \text{Issue Price} - \text{Flotation Cost} = \$48.00 - \$2.50 = \$45.50$\ 3. Calculate the cost of preferred stock: $r_p = D_p / P_{net} = \$4.50 / \$45.50 \approx 0.0989$ or 9.89%.
16. A firm is evaluating its cost of capital. An analyst determines that the market's required rate of return on the firm's preferred stock is 7.5%. The stock pays an annual dividend of $6.00 and has a par value of $100. Flotation costs for a new issue would be 5% of the proceeds. What is the estimated cost of a new issue of preferred stock?
    Answer: 7.89% This question requires calculating the cost to the company, which must account for flotation costs.\ 1. First, find the market price ($P_p$) that provides investors with their required 7.5% return: $P_p = D_p / r_p = \$6.00 / 0.075 = \$80.00$\ 2. Next, calculate the net proceeds to the company after flotation costs: $P_{net} = \$80.00 \times (1 - 0.05) = \$76.00$\ 3. Finally, calculate the cost of the new issue to the company based on these net proceeds: $\text{Cost} = D_p / P_{net} = \$6.00 / \$76.00 \approx 0.0789$ or 7.89%.
17. Omega Technologies issued preferred stock with an adjustable rate tied to LIBOR plus $200$ basis points, subject to a $3.0\%$ floor and $9.0\%$ ceiling. The $80 par value shares trade at $76.50. Current LIBOR is $2.8\%$, but market analysts expect LIBOR to average $3.5\%$ over the next year. For cost of capital purposes, what rate should be used?
    Answer: $6.27\%$ using current LIBOR rate and current market pricing For cost of capital calculations, use current conditions. Current dividend rate = LIBOR + 200bp = $2.8\% + 2.0\% = 4.8\%$ (above $3.0\%$ floor, below $9.0\%$ ceiling). Annual dividend = $\$80 \times 0.048 = \$3.84$. Cost = $\$3.84 / \$76.50 = 6.27\%$. Choice B uses forecasted rates inappropriately for current cost calculations. Choice C applies cost to par instead of market value. Choice D uses both forecasted rates and par value incorrectly.
18. A firm is analyzing its cost of capital. Its perpetual preferred stock pays a fixed annual dividend of $5 per share and currently trades at $62.50. The firm's common stock dividends are expected to grow at a constant rate of 4% per year. What is the firm's component cost of preferred stock?
    Answer: 8.00% The cost of preferred stock is calculated using the perpetuity model, as its dividends are fixed and do not grow. The growth rate associated with common stock is irrelevant information intended to be a distractor.\ $r_p = D_p / P_p = \$5.00 / \$62.50 = 0.08$ or 8.00%.
19. A company's preferred stock pays a quarterly dividend of $1.50 per share and currently trades at $85.00 per share. If the company were to issue new preferred shares, it would incur flotation costs of 6.0%. What is the component cost of the new preferred stock issue?
    Answer: 7.51% The calculation requires annualizing the dividend and accounting for flotation costs.\ 1. Calculate the annual dividend: $D_p = \$1.50/\text{quarter} \times 4 \text{ quarters} = \$6.00$\ 2. Calculate the net proceeds per share: $P_{net} = \text{Market Price} \times (1 - \text{Flotation Cost \%}) = \$85.00 \times (1 - 0.06) = \$85.00 \times 0.94 = \$79.90$\ 3. Calculate the cost of preferred stock: $r_p = D_p / P_{net} = \$6.00 / \$79.90 \approx 0.07509$ or 7.51%.
20. Atlas Industries plans to issue $10 million in preferred stock with a $40 par value and expects to pay a $6.8\%$ dividend rate. Investment bankers indicate flotation costs will be $1.50 per share plus $2.5\%$ of gross proceeds. If the preferred stock is expected to sell at a $4\%$ premium to par value, what is the cost of new preferred stock?
    Answer: $7.24\%$ using net proceeds after deducting all flotation costs Expected selling price = $\$40 \times 1.04 = \$41.60$. Total flotation costs = $\$1.50 + (\$41.60 \times 0.025) = \$1.50 + \$1.04 = \$2.54$. Net proceeds = $\$41.60 - \$2.54 = \$39.06$. Annual dividend = $\$40 \times 0.068 = \$2.72$. Cost = $\$2.72 / \$39.06 = 7.24\%$. Choice B ignores flotation costs. Choice C only applies percentage-based flotation costs. Choice D ignores the fixed per-share component of flotation costs.

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