?(Individual or component costs of? capital)?Compute the cost of capital for the

Question

?(Individual or component costs of? capital)?Compute the cost of capital for the firm for the? following:

a. A bond that has a ?$1,000 par value? (face value) and a contract or coupon interest rate of 10.3 percent. Interest payments are ?$51.50 and are paid semiannually. The bonds have a current market value of ?$1,128 and will mature in 10 years. The? firm's marginal tax rate is 34 percent.

b. A new common stock issue that paid a ?$1.82 dividend last year. The? firm's dividends are expected to continue to grow at 7.4 percent per? year, forever. The price of the? firm's common stock is now ?$27.35.

c. A preferred stock that sells for ?$132?, pays a dividend of 8.5 ?percent, and has a? $100 par value.??

d. A bond selling to yield 11.9 percent where the? firm's tax rate is 34 percent.

Explanation / Answer

Requirement (a)

Yield To Maturity[YTM] = C + [ (Par Value – Bond Price) / Maturity Years ] / [(Par Value + Bond Price) / 2]

= $103 + [ ($1,000 - $1,128) / 10 ) ] / [($1,000 + $1,128) / 2]

= [$103 – 12.80 / 2,128] x 100

= 8.38%

After Tax Cost of Capital = 8.38% x [ 1 - 0.34 ] = 5.53%

Requirement (b)

Po = Do[1 + g ] / [ Ke – g ]

$27.35 = $1.82[ 1.074 ] / [Ke – 0.074]

$27.35 = $1.95468 / [Ke – 0.074]

[Ke – 0.074] = 0.0715

Therefore, Cost of Equity[Ke]

[Ke – 0.074] = 0.0715

Ke = 0.0715 + 0.074

Ke = 0.1455 or

Ke = 14.55%

Cost of Equity [Ke] = 14.55%

Requirement (c)

Cost of Capital = Annual Dividend / Selling price of the preferred stock

Annual Dividend = $100 x 8.50% = $8.50 per share

Cost of capital = [ $8.50 / $132 ] x 100

= 6.44%

Cost of capital = 6.44%

Requirement (d)

Cost of capital = Bond Yield x [ 1 – Tax Rate ]

= 11.90% x [ 1 – 0.34 ]

= 11.90% x 0.66

= 7.85%

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