Sollutions To Cost Of Capital.docx 235j2t

1.

Calculate the after-tax cost of debt under each of the following conditions: a)

Interest rate, 13% ; tax rate, 0%

b)

Interest rate, 13% ; tax rate, 20%

c)

Interest rate, 13% ; tax rate, 34%

Solution a)

Given, Interest rate (Kd) = 13%; Tax rate (t) = 0% After tax cost of debt (Kdt) = Kd(1-t) = 13% ( 1- .0) = 13%

b)

Given, Interest rate (Kd) = 13%; Tax rate (t) = 20% After tax cost of debt (Kdt) = Kd(1-t) = 13% ( 1- .20) = 10.40%

c)

Given, Interest rate (Kd) = 13%; Tax rate (t) = 34% After tax cost of debt (Kdt) = Kd(1-t) = 13% ( 1- .34) = 8.58%

2.

The Kathmandu company’s financing plans for the next year include the sale of long-term bonds with a 10 percent coupon. The company believes it can sell the bonds at a price that will produce a yield to maturity of 12 percent. If the marginal tax rate is 30 percent, what is Kathmandu’s after tax cost of debt? Solution Given, Coupon interest rate = 10% Yield to maturity (YTM) = 12% Tax rate (T) = 30% We have, After tax cost of debt (Kdt) = Kd(1-t) = 12% ( 1- .30) = 8.40%

3.

Calculate the after-tax cost of debt under each of the following conditions assuming 30 percent tax rate: a.

A 12% bond of Rs.1000 is selling at par.

b.

A 12% bond of Rs.1000 is selling at 5% discount.

c.

A 12% bond of Rs.1000 is selling at 10% .

Solution

4. A 5 years, 12% bond of Rs 1,000 is selling at par. It incurs a flotation cost of 5 percent of the face value. Compute after tax cost of debt assuming 40 percent tax rate. 5. A 5 years, 9% bond of Rs 1,000 is selling at 7 percent discount. Further, it incurs a flotation cost of 2 percent of the face value. Compute after tax cost of debt assuming 40 percent tax rate. 6. Morang Company issued 10 years, 11 % bonds of Rs60,000 at 9 percent . Further, it incurs a flotation cost of 5 percent of the face value. Compute after tax cost of debt assuming 40 percent tax rate. 7.

A Company issued 10 years, 10 % redeemable bond of Rs 1,000 each at Rs 1,200 less underwriting fee of Rs40. These bonds are callable in 5 years at a call price of Rs 1080. Compute the after tax cost of bonds assuming 30 percent tax rate and bonds will be called in 5 years.

1. Anharath Farm issued a 22 year, 9% bond 8 years ago. The bond currently sells for 105%of its face value.

The company's tax rate is 35%. a) What is the pre-tax cost of debt?

b)

What is the after-tax cost of debt?

Given, Life of bond Interest rate Current selling price of bond (Vo) Tax rate (T)

= 22 years = 9% semiannual payment = 105% of face value i.e. Rs.1,000 × 1.05 = Rs.1,050 = 35%

Now, a)

b)

Approximate before-tax cost of debt (Kd) M – Vo (Rs.1,000 – Rs.1,050) I+ n Rs.90 + 22 = M + 2V × 100 = (Rs.1,000 + 2 × Rs.1,050) × 100 = 8.5% o 3 3 After-tax cost of debt (Kdt) = Kd(1 – T) = 8.51% (1 – 0.35) = 5.53%

2. The earnings, dividends, and stock price of JK Tie Butwal are expected to grow at 7% per year in the future. JK common stock sells for Rs.23 per share, its last dividend was Rs.2.00, and the company will pay a dividend of Rs.2.14 at the end of the current year. Using the discounted cash flow approach, what is its cost of common equity? Given, Expected growth rate (g) Current selling price (P0) Expected dividend per share (D1)

= 7% = Rs.23 = Rs.2.14

Now, D1 Rs.2.14 Cost of equity (Ke) = P – F + g = Rs.23 – 0 + 0.07 = 0.1630 i.e., 16.30%. 0 3. The Durga Company’s EPS was Rs.6.50 in 1995 and Rs.4.42 in 1990. The Company pays out 40% of its earnings as dividends, and the stock sells for Rs.36. a)

Calculate the past growth rate in earnings.

b)

Calculate the next expected dividend per share.

c)

What is the cost of retained earnings, Ke, for Durga Company?

Given, Earning per share in the year 1995 = Rs.6.50 Earning per share in 1990 Dividend payout ratio (DPR) = 40% Current selling price of stock (P0) = Rs.36 Now, a) Earning in 1995 = Earning in 1990 (1 + g)5 or, Rs.6.50 = Rs.4.42 (1 + g)5 Rs.6.50 or, (1 + g)5 = Rs.4.42 Taking the 5th root on both sides or, 1 + g = (1.4706)1/5  g = 1.08 – 1 = 0.08 i.e. 8%.  The growth rate on earnings is 8%. b)

Current dividend per share (D0) = Earning in the year 1995 × DPR = Rs.6.50 × 0.40 = Rs.2.60 

c)

= Rs.4.42

Expected dividend per share (D1) = D0 (1 + g) = Rs.2.60 (1 + 0.08) = Rs.2.81.

Cost of retained earnings (Kr)

D1 Rs.2.81 = P + g = Rs.36 + 0.08 = 0.1581 i.e., 15.81%. 0



Cost of retained earnings is 15.81%.

4. The Anugya Company's next expected dividend, D1, Rs.3.18, its growth rate is 6%, and the stock now sells for Rs.36. New stock (external equity) can be sold to net the firm Rs.32.40 per share. a)

What is Anugya's flotation cost, F?

b)

What is Anugya's cost of new common stock, ke?

Given, Expected dividend per share (D1) Growth rate (g) Selling price of stock (Po) Net proceed per share (NP)

= Rs.3.18

a)

Percentage of flotation cost (F)

=

b)

Cost of new common stock (Ke)

D1 Rs.3.18 = NP + g = Rs.32.40 + 0.06 = .1581 i.e. 15.81%

= 6% = Rs.36 = Rs.32.40

Now, Po – NP Rs.36 – Rs.32.40 × 100 = 10% Po × 100 = Rs.36

5. Ram & Sons' common stock is currently trading at Rs.30 a share. The stock is expected to pay a dividend of Rs.3.00 a share at the end of the year (D1 = Rs.3.00), and the dividend is expected to grow at a constant rate of 5% a year. If the company were to issue external equity, it would incur a 10% flotation cost. What are the costs of internal and external equity? Given, Current selling price of stock (P0)

= Rs.30

Expected dividend per share (D1)

= Rs.3

Constant growth rate (g)

= 5%

Flotation cost (F)

= 10%

Now, i)

D1 Rs.3 Cost of internal equity (Kr) = P + g = Rs.30 + 0.05 = 0.15 i.e., 15%. 0

ii)

D1 D1 Cost of external equity (Ke) = NP + g = P – F + g 0 Rs.3 = Rs.30 – Rs.30 × 0.10 + 0.05 = 0.1611 i.e., 16.11%.



The cost of internal and external equities are 15% and 16.11% respectively.

6. The Ashwet Company's next expected dividend, D1, is Rs.3.18, its growth rate is 6%, and the stock now sells for Rs.36. New stock (external equity) can be sold to net the firm Rs.32.40 per share. a)

What is Ashwet's cost of retained earnings, kr?

b)

What is Ashwet's flotation cost, F?

c)

What is Ashwet's cost of new common stock, ke?

Given, Expected dividend per share (D1)

= Rs.3.18

Growth rate (g)

= 6%

Selling price of stock (P0) Net proceed per share (NP)

= Rs.36 = Rs.32.40

Now, a)

D1 Rs.3.18 Cost retained earning (Kr) = P + g = Rs.36 + 0.06 = 0.148 i.e. 14.8% 0

b)

Percentage of flotation cost (F)

=

P0 – NP Rs.36 – Rs.32.40 × 100 = 10% P0 × 100 = Rs.36

c)

Cost of new common stock (Ke)

D1 Rs.3.18 = NP + g = Rs.32.40 + 0.06 = 0.1581 i.e. 15.81%

7. The Arju Co. just issued a dividend of Rs.2.10 per share on its common stock. The Company is expected to maintain a constant 7% growth rate in its dividends indefinitely. If the stock sells for Rs.40 a share, what is the Company's cost of equity? Given, Current dividend per share (D0)

= Rs.2.10

Constant growth rate (g)

= 7%

Selling price of stock (P0)

= Rs.40

Now, Cost of equity (Ke) =

D0 (1 + g) P0 – F + g =

Rs.2.10 (1 + 0.07) + 0.07 = 0.1262 i.e., 12.62% Rs.40 – 0

8. Binu & Sons' common stock is currently trading at Rs.300 a share. The stock is expected to pay a dividend of Rs.30 a share at the end of the year (D1 = Rs.30), and the dividend is expected to grow at a constant rate of 5% a year. If the company were to issue external equity, it would incur a 10% flotation cost. What are the costs of internal and external equities? Given, Current selling price per share (P0) Expected dividend per share (D1) Constant growth rate on dividend (g)

= Rs.300 = Rs.30 = 5%

Now, D1 Rs.30 Cost of internal equity (Kr) = P + g = Rs.300 + 0.05 = 0.15 i.e. 15% 0 D1 D1 Cost of external equity (Ke) = NP + g= P – F + g 0 Rs.30 = Rs.300 – Rs.300 × 0.10 + 0.05 = 0.1611 i.e. 16.11%. 9. Ankit Industries can issue perpetual preferred stock at a price of Rs.47.50 a share. The issue is expected to pay a constant annual dividend of Rs.3.80 a share. What is the company's cost of preferred stock, Kp? Give, Selling price of preferred stock (P0)

= Rs.47.50

Expected dividend per share (DPS)

= Rs.3.80

Now, DPS DPS Rs.3.80 Cost of preferred stock (KP) = NP = P – F = Rs.47.50 – 0 = 0.08 i.e., 8%. 0 The cost of preferred stock is 8%.

1.

Anish Tool Company was recently formed to manufacture a new product. The Company has the following capital structure in market value : 13% debentures of 2005 12% preferred stock Common stock (320,000 shares) Total

Rs.6,000,000 2,000,000 8,000,000 Rs.16,000,000

The common stock sells for Rs.25 a share, and the Company has a marginal tax rate of 40%. A study of publicly held companies in this line of business suggests that the required return on equity is about 17% for a company of this sort. a) Compute the firm's present weighted average cost of capital. Given, Interest on debenture (Kd)

= 13%

Dividend on preferred stock

= 12%

Selling price of common stock

= Rs.25

Tax rate (T)

= 40%

Required rate of return on equity (Ke) = 17% Now, After-tax cost of debt (Kdt)

= Kd (1 – T) = 13%(1 = .40) = 7.8%

After-tax cost of preferred stock (Kp) = 12% After-tax cost of equity (Ke)

= 17%

Then, a)

Weighted average cost of capital WACC

= WdKdt + WpKp + WeKe Rs.6,000,000 Rs.2,000,000 Rs.8,000,000 = Rs.16,000,000 × 7.8% + Rs.16,000,000 × 12% + Rs.16,000,000 × 17% (

(

2.

)

(

)

(

)

(

)

(

)

)

Goma Motors has a target capital structure of 40% debt and 60% equity. The yield to maturity on the company's outstanding bonds is 9%, and the company's tax rate is 40%. Goma's CFO has calculated the company's WACC as 9.96%. What is the company's cost of common equity? Given, Proportion of debt (Wd) Proportion of equity (We) Yield to maturity of bond (YTM) Tax rate (T) Weighted average cost of capital (WACC) Now, WACC

= Wd Kdt + WeKe

or,

9.96 = 0.40 × 9% (1 – 0.40) + 0.60 × Ke

or,

9.96 – 2.16 = 0.6 Ke



Ke

= 13%

Hence, the cost of equity capital is 13%.

= 40% = 60% = 9% = 40% = 9.96%