Compute the cost for the following sources of financing: a. A $1,000 par value b
ID: 2713187 • Letter: C
Question
Compute the cost for the following sources of financing:
a. A $1,000 par value bond with a market price of $970 and a coupon interest rate of 10 percent. Flotation costs for a new issue would be approximately 5 percent. The bonds mature in 10 years and the corporate tax rate is 34 percent. b. A preferred stock selling for $100 with an annual dividend payment of $8. The flotation cost will be $9 per share. The company’s marginal tax rate is 30 percent.
c. Retained earnings totaling $4.8 million. The price of the common stock $75 per share, and dividend per share was $9.80 last year. The dividend is not expected to change in the future.
d. New common stock when the most recent dividend was $2.80. The company’s dividends per share should continue to increase at an a8 percent growth rate into the indefinite future. The market price of the stock is currently $53; however, flotation costs of $6b per share are expected if the new stock is issued.
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Explanation / Answer
After tax cost of debt = 7.51%
Cost of preferred stock = 8.79%
Cost of retained earnings = 13.07%
Cost of new common stock = 14.43%
Calculation of Cost of Debt
Par Value F = $1000
Market Price P = $970
Coupon Interest = 10%
Coupon Amount A = 1000 * 10% = 100
Floatation Cost = 5%
Time to maturity n = 10 years
Corporate Tax rate = 34%
Floatation Cost C = 1000 * 5% = 50
Net Proceeds from new issue = 970 – 1000*5% = 920
Let r be the pre-tax cost of debt
920 = 100 * (1-(1/(1+r)^10))/r) + 1000/(1+r)^10
920 - 100 * (1-(1/(1+r)^10))/r) - 1000/(1+r)^10 = 0
At r =11%, LHS will be
= 920 – 100 * (1-(1/(1.11)^10))/0.11) - 1000/(1.11)^10
= 920 – 100 * (1-(1/(2.839421)/0.11) - 1000/2.839421
= 920 – 100 * (1-0.352184)/0.11 – 1000 * 0.352184
= 920 – 100 * (0.647816/0.11) – 352.1845
= 920 – 100 * 5.889232 – 352.1845
= 920 – 588.9232 – 352.1845
= -21.1077
Let r = 11.5%, LHS will be
= 920 – 100 * (1-(1/(1.115)^10))/0.11) - 1000/(1.115)^10
= 920 – 100 * (1-(1/(2.969947)/0.11) - 1000/2.969947
= 920 – 100 * (1-0.336706)/0.11 – 1000 * 0.336706
= 920 – 100 * (0.663294/0.11) – 336.7064
=920 – 100 * 5.767771 – 336.7064
= 920 – 576.7771 – 336.7064
= 6.516561
r = 0.11 + (-21.1077 * (0.11-0.115) / (6.516561-(-21.1077)
r = 0.11 + (0.1055385/27.624261)
r = 0.11 +0.00382
r = 0.11382 or 11.38%
After tax cost of debt rd =11.38% * (1-tax rate) = 11.38% * (1-0.34) = 11.38% * 0.66
= 7.5108 or 7.51% (rounded off)
Calculation of cost of preferred stock
Dividend Payment = $ 8
Sale Price = $ 100
Floatation Cost = $ 9 per share
Cost of Preferred stock = Dividend / Net Price = Dividend / (Price - Floatation cost)
= $ 8 / ($100 - $9) = $ 8 / $ 91 = 0.087912 or 8.79% (rounded off)
(There is no need to adjust for taxes as the dividends are paid after tax)
Calculation of cost of retained earnings
Current Market Price = $ 75
Dividend Last year = $9.80
Dividend is not expected to change in future, that is dividend growth rate = 0
Price of a stock when dividend growth rate = 0 is Price = Dividend / rate of return
Rate of return = Dividend / Price = 9.80/75 = 0.1306667 or 13.07% (rounded off)
Calculation of Cost of New Equity
Most recent Dividend = $ 2.80
Constant dividend growth rate = 8% or 0.08
Market Price = $ 53
Floatation Cost = $ 6 per share
Net Price after floatation cost = $ 53 - $ 6 = $ 47
Expected Dividend next year D1 = Current Dividend * (1+growth rate) = $ 2.80 * (1.08)
= $ 3.024 or $ 3.02 (rounded off)
Net Price = D1 / (required rate of return – growth rate)
47 = 3.02 / (required rate of return - 0.08)
required rate of return - 0.08 =3.02/47
Required rate of return = (3.02 / 47) + 0.08
Required rate of return = 0.064255 + 0.08 = 0.144255 or 14.43% (rounded off)
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