Question

(Individual or component costs of capital) Your firm is considering a new investment proposal and would like to calculate its weighted average cost of capital. To help in this, 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 12.4 percent that is paid semiannually. The bond is currently selling for a price of $1,125 and will mature in 10 years. The firm's tax rate is 34 percent. b. If the firm's bonds are not frequently traded, how would you go about determining a cost of debt for this company? c. A new common stock issue that paid a $1.79 dividend last year. The par value of the stock is $16, and the firm's dividends per share have grown at a rate of 8.7 percent per year. This growth rate is expected to continue into the foreseeable future. The price of this stock is now $27.97. d. A preferred stock paving a 9.2 percent dividend on a $121 par value. The preferred shares are currently selling for S150 62 nd selling to vield 13.2 percent for the purchaser of the bond. The borrowing firm faces a tax rate of 34 percent. a. The after-tax cost of debt from the firm is 6.84 %. (Round to two decimal places.) b. If the firm's bonds are not frequently traded, how would you go about determining a cost of debt for this company? (Select the best choice below.) O A. It is standard practice to estimate the cost of debt using the bond's coupon rate and adjust it for inflation. B. It is standard practice to estimate the cost of debt using the yield to maturity on a portfolio of bonds with a similar credit rating and maturity as the firm's outstanding debt. OC. It is standard practice to estimate the cost of debt using the average coupon rate on a portfolio of bonds with a similar credit rating and maturity as the firm's outstanding debt. O D. It is standard practice to estimate the cost of debt using the yield to maturity on a treasuty bond of the same maturity. c. The cost of common equity for the firm is 15.66 %. (Round to two decimal places.) d. The cost of preferred stock for the firm is 7.39%. (Round to two decimal places.) e. The after-tax cost of debt for the firm is 8.71 %. (Round to two decimal places.)

Answer 1

Given,

Par value = $ 1000

Coupon rate = 12.4%

Semi annual coupon rate = 12.4%/2 = 6.2%

Semi annual coupon payment (C) = $ 1000 x 6.2% = $ 62

Maturity = 10 years

Number of compounding periods = 10 years x 2 = 20

Solution :-

ra) Let's Vield assume Semi - annual to maturity is 5% g 0.05 VTm(Y) = 5% of 0.05 No. of compounding periods (n) = 20 Now, PV = [ 1 - 1 tin + playin where, C- - Y - Semi-annual Coupon - Payment Semi-annual Vield to maturity Par value of bond pu - Pvdel 109 9] + valores looo 62 0.05 (1.05) Rot (1.0520

- 40 ਕ ily 320 ) 26S224 | 0X- 632922) ੨.6532972) 1200 ੨, 852242॥ - ੨. 651 + 36 . 88੧੫8 2 $1)੫੧, S46 48 let's assume Semi-annual yield to maturity is Gl. To y) - 6% 0% # 0.06. Now, 200 - 2 ੨ 006) 06) - ਤਤਧ Up (20 ੨੦੧੫ 2,06 3.੨੭73Sਪ2. ਨ

220713547 3.207135un looo 3.20713547 - 711.1351153 +3 11.804727 $ 1072.93984 Thus, YTM - LR +R-Le) (Puot Le - PV where, Le = He = pu= lower Higher Present rate of YTM rate of YTM value Now, 16.06-0.05) (1149.54648 - 1225 149.54648-1022.93984 YIM = 0.05 + 60.06-0.05) (nuq. susu8 - 1125 1 = 0.054(0.01) Charles una - 0.05 t 0.00194 ? 0.05194 of So 194%

Annual YTM = S. 194% X 2 - 10. 388 % This is the cost of debt. Alter-tax cost of debt. = Cost of debt (1 - tax rate) - 10.388% (1 – 0.34) = 10.388% (0.66) = 6.86% So Cost of capital for the from is 6.86% The correct answer is Option 'B. It is standard practice to estimate the cost of debt using the yield to matunity on a portfolio of bonds with a similar credit rating and maturity as

the from's outstanding debt. (0 Price of Stock (Po) = $27.97 Dividend (0) = $1.79 Growth rate (g) = 8.7% or 0.087 Now, Cost of common equity for - Dolltg & g the firm. + 0.087 1.79 (1+0.087) 27.97 1.79 (1.087) 27.97 - & 087 - 1.94573 27.97 & 0.087 - - 0.069565 + 0.087 O. 1566 or 1s. 66%

par Value = $121 Dividend rate = 9.2% Current Selling Price = $ 150.62 Annual dividend eleg - Par Value & Dividend rate $121 X 9.2% – $11.132 Now, Cost of Preferred Stock - Annual dividend Current Selling Price $11.132 $ 150.62 0.0739 or 7.39 %

Cost of debt = 13.2% Tax rate = 34% of 0.34 Now, After dax cost of debt = Cost of debt ( 1- tax rate) - 13.7% (- 0.34) = 13.2% (0.66) = 8,71%