aaron's rentals has 45,000 shares of common stock outstanding at a market price of $27 a share. the common stock just paid a $1.10 annual dividend and has a growth rate of 3.2 percent. there are 10,000 shares of 5.5 percent preferred stock outstanding at a market price of $48 a share. the preferred stock has a par value of $100. the outstanding bonds mature in 11 years, have a total face value of $800,000, a face value per bond of $1,000, and a market price of $987.60 each. the bonds pay 7.5 percent interest, semiannually. the tax rate is 35 percent. what is the firm's weighted average cost of capital?

Question

16-12-2022
Business

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aaron's rentals has 45,000 shares of common stock outstanding at a market price of $27 a share. the common stock just paid a $1.10 annual dividend and has a growth rate of 3.2 percent. there are 10,000 shares of 5.5 percent preferred stock outstanding at a market price of $48 a share. the preferred stock has a par value of $100. the outstanding bonds mature in 11 years, have a total face value of $800,000, a face value per bond of $1,000, and a market price of $987.60 each. the bonds pay 7.5 percent interest, semiannually. the tax rate is 35 percent. what is the firm's weighted average cost of capital?

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Qwline Qwline · Answer 1 · 2022-12-20T09:22:40-05:00

The firm's weighted average cost of capital is 7.42% as per the given number of shares and the dividend

Within a business, the firm's weighted average cost of capital is the overall financing cost of the operations. This measure can be treated as the minimum required rate of return on the firm's total assets because the firm's capital is invested in assets.

Equity:

Estimate the market value of equity:

Equity value = Number of shares x Share price = 45,000 x $27 = $1,215,000

Estimate the required rate of return on equity:

[tex]Required\:rate\:of\:return = \displaystyle \frac{Last\:dividend \times (1 + Growth\:rate)}{Price} + Growth\:rateRequired\:rate\:of\:return = \displaystyle \frac{\$1.10\times (1 + 3.2\%)}{\$27} + 3.2\% Required\:rate\:of\:return = 7.40\%[/tex]

Preferred stock:

Estimate the market value of preferred stocks:

Value of preferred stocks = Number of preferred stocks x Price = 10,000 x $48 = $480,000

Estimate the cost of preferred stock:

[tex]Cost\:of\:preferred\:stock = \displaystyle \frac{Par \times Dividend\:rate}{Price}Cost\:of\:preferred\:stock = \displaystyle \frac{\$100 \times 5.5\%}{\$48} Cost\:of\:preferred\:stock = 11.46\%[/tex]

Debt:

Estimate the market value of debt:

[tex]Value\:of\:debt = Number\:of\:bonds \times Price = \dfrac{\$800,000}{\$1,000} \times $987.60 = $790,080[/tex]

Estimate the cost of debt:

Use the financial calculator to solve for I:

PV = -987.60

FV = 1,000

N = 11 x 2 = 22

PMT = 1,000 x 7.5% x 0.5 = 37.50

CPT I = 3.83

YTM = 3.83% x 2 = 7.66%

WACC:

Estimate the total market value of the firm's capital:

Total capital = Equity + Preferred stocks + Debt = $1,215,000 + $480,000 + $790,080 = $2,485,080

Estimate the WACC:

[tex]WACC= Weight_{equity} \times Cost_{equity} + Weight_{preferred\:stocks} \times Cost_{preferred\:stock} + Weight_{debt} \times Cost_{debt}\times (1 - Tax\:rate) WACC= \displaystyle\frac{\$1,215,000}{\$2,485,080} \times 7.40\% + \frac{\$480,000}{\$2,485,080} \times 11.46\% + \frac{\$790,080}{\$2,485,080} \times 7.66\%\times (1 - 35\%) WACC= 7.41\%[/tex]

Learn more about WACC:

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