Lesson-5

Chapter 9: The Cost of Capital

1. Post answers to Questions 9-1 thru 9-5 on p. 370.

2. Answer Problems 9-1 thru 9-8 on p. 371.

Discussion Questions (DQs)

9.1 Answer:

a) A company has several ways it can raise capital, the main ways it can do it is with help of debt, stock and preferred stocks. Companies try to use these options to the fullest to minimize their cost. The way they minimize the cost is by creating an optimal mix of all these options. Since the market is discrete and different methods of raising capital have different cost and also each company has its own mix of capital structure, the weighted average cost of capital is necessary to understand. WACC is simply the market rate of raising capital multiplied to the weightage or contribution in the company's capital structure.

The formula for WACC is

WACC= wd * rd + ws * rs  + wps * rps

Where,

Wd = weight of debt

Ws = weight of stock

Wps = weight of preferred stock

Rd= after tax cost of debt

Rs = cost of raising stock

Rps = cost of raising preferred stock

Investors generally argue between raising capital via debt or equity. Debt and equity both have their advantages and over the years it's been found that a company with higher debt is in trouble as it is required to pay a high amount of interest whereas a company which uses higher equity is to pay a high amount of taxes reducing the shareholders gains, because of which it is necessary for any company to use both debt and equity to raise capital. Also we need to understand the meaning of tax shield, when issuing debt the company has to pay interest which is a tax deductible item, companies can take advantage of issuing debt by reducing its non-productive tax expenses. The after tax cost of debt is actual interest paid by the company after taking into consideration the tax shield created by the debt. The formula to calculate the after tax debt rate is

Debt rate = Debt rate * ( 1 - Tax Rate )

b) Whenever a company issues stock there are lots of costs associated during the issue process.

Cost of preferred stock is the cost to the firm of issuing new preferred stock. For perpetual preferred, it is the preferred dividend divided by the net issuing price. Since stocks don't provide the tax benefit like that of debt and preferred stock don't provide all the feature of the stocks, preferred stocks are not that wall demanded. Also there are additional cost such as floatation cost that the company needs to pay when issuing these stocks which increases its cost.

The formula for calculating cost of preferred stock is

rps = Dividend / price of preferred stock ( 1 - flotation cost)

The cost of common stock is the cost of raising equity for any firm which is denoted by rs. There is a general misconception that the cost of common stock is only the cost of raising capital through new issue to stock but we also need to consider the opportunity cost that is always present in retained earnings. Besides that there are other costs such as flotation costs, brokerage cost that the company needs to pay and which must be included while calculating rs.

The cost of new common equity is the cost to the firm of equity obtained by selling new common stock. It is, essentially, the cost of retained earnings adjusted for flotation costs. Flotation costs are the costs that the firm incurs when it issues new securities. The funds actually available to the firm for capital investment from the sale of new securities is the sales price of the securities less flotation costs.

c) The main sources of raising capital is through debt or equity. Every company has its own ways to determine how much debt and how much equity they want to raise. The target capital structure is the relative amount of debt, preferred stock, and common equity that the firm desires.

d) When issuing common stocks or preferred stocks, the company can't do all the required procedures on their own and they hire external organization who help them to do all the necessary activities. In return for their service provided these external organizations charge a small percentage of capital raised which is known as flotation costs.

The cost of new external common equity is simply when the company raises capital from the market by issuing common stocks. The cost of this type of equity is generally higher than that of raised internally with help of retained earnings as there are flotation costs and brokerage cost which increase the overall cost of the process.

Q 9-2. Answer:

The WACC is an average cost because it is a weighted average of the firm's component costs of capital. However, each component cost is a marginal cost; that is, the cost of new capital. Thus, the WACC is the weighted average marginal cost of capital.

Q 9-3. Answer:

Factors which effect a firm's cost of debt, rd(1-T); its cost of equity, rs; and its weighted average cost of capital, WACC are as follow:

	rd(1-T)	rs	WACC
The corporate tax rate is lowered	+	0	+
Federal reserve tighter credit	+	+	+
Firm doubles the amount of capital it rises during the year	0 or +	0 or +	0 or +
Firm expend into a risky new area	+	+	+
Investors become more risk average	+	+	+

a. When corporate tax rate is lowered cost of debt after tax increase while cost of equity does not have any effect and WACC will increase as cost of debt increase.

b. When federal reserve tightens credit, cost of debt increase as in the economy few funds are available hence increase interest rate as well as cost of debt, equity, and WACC.

c. When the firm uses more debt, firm's capital structure consists of more debt and hence seems riskier. It increases cost of debt, equity, WACC.

d. When the firm doubles the amount of capital raise within a year cost of debt, cost of equity and WACC may increase or remain the same depending on purpose of raising the fund. In most of the case when company doubles its capital WACC, cost of debt and cost of equity tend to increase.

e. When firm expands its business into risky area its cost of capital, cost of equity and WACC increase because of the variability in return.

f. When investors become more risk adverse cost of debt, cost of equity and WACC increase as it increases the interest rates.

Q9.4 Answer:

Difference between beta risk, corporate risk and stand alone risk are:

Beta Risk: This looks at the risk of a project through the eyes of the stockholder. It looks at the project not only from a company's perspective, but from the stockholder's overall portfolio. It is measured by the effect the project may have on the company's beta.

Corporate Risk: This risk assumes the project a company intends to pursue is not a single asset but incorporated with a company's other assets. As such, the risk of a project could be diversified away by the company's other assets. It is measured by the potential impact a project may have on the company's earnings.

Stand alone risk: This risk assumes the project a company intends to pursue is a single asset that is separate from the company's other assets. It is measured by the variability of the single project alone. Stand-alone risk does not take into account how the risk of a single asset will affect the overall corporate risk.

Among the three measures, market risk is theoretically most relevant because market risk has direct effect on stock prices and thus it replicates the changes on economy as a whole.

Q 9.5 Answer:

If firm estimates its cost of capital depending on riskiness of the projects then it is known as risk-adjusted cost of capital. Suppose a firm estimates its cost of capital 10% for coming year then cost of capital for average-risk project would be 10%, cost of capital of high-risk project would be higher than 10%, and cost of capital of low-risk project would be lower than 10%. For example, if cost of capital of firm is 12% then average-risk project will have cost of capital of 12%, high-risk project will have cost of capital of 15%, and low-risk project will have cost of capital of 9%. This approach is better and well manages than no risk adjustment but in real practice it is very hard to specify exact risk as well as exact cost of capital. Therefore is approach is subjective and vary from firm to firm.

References

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Eugene F. Brigham, Michael C. Ehrhardt. (2011). Financial Management: Theory and Practice . Natorp Boulevard Mason, USA: South-Western Cengage Learning.

Manandhar, Dr. K. D.; Thapa, Kiran; Koirala, Narayan; Shah, Manoj; Pyakurel, Santosh. (2065). Corporate Finance (4 ed.). Kathmandu,Nepal: Januka Publication.

Problem 9-1

a)      Solution

Here given,

Before tax component cost of debt (r_d)          = 13%

Marginal tax rate (T)                                       = 0%

After tax cost of debt                                     =?

Now,

After tax cost of debt = r_d (1 -T)

                                   = 13% (1 - 0)

                                   = 13%

Therefore, when interest rate is 13% and tax rate is 0% then the after- tax cost of debt is 13 %

b)     Solution

Here given,

Before tax component cost of debt (r_d)          = 13%

Marginal tax rate (T)                                       = 20%

After tax cost of debt                                     =?

Now,

After tax cost of debt = r_d (1 -T)

                                   = 13% (1 - 0.20)

                                   = 10.40%

Therefore, the after- tax cost of debt is 10.40 % when interest rate is 13% and tax rate is 20%.

      c) Solution

Here given,

Before tax component cost of debt (r_d)          = 13%

Marginal tax rate (T)                                       = 35%

After tax cost of debt                                     =?

Now,

            After tax cost of debt = r_d (1 -T)

                                                = 13% (1 - 0.35)

                                                = 8.45%

Therefore, the after- tax cost of debt is 8.45 % when interest rate is 13% and tax rate is 35%.

Problem 9-2. Solution:

Here given,

Coupon rate (I)                                                                                   = 11%

Before- tax component cost of debt (r_d)                                             = YTM on new issue

= 8%

Marginal tax rate (T)                                                                           = 35%

After -tax cost of debt                                                                                    =?

Now,

After- tax cost of debt = r_d (1- T)

                                     = 8% (1 - 0.35)

                                     = 5.2%

Therefore, LL's after-tax cost of debt is 5.2% when LL's bond has yield to maturity of 8% and marginal tax rate is 35%.

Problem 9-3 Solution:

Here given,

Preferred stock price (P_ps)       = $50

Preferred dividend (D_ps)         = $4.50

Flotation cost (F)                    = 0

Cost of preferred stock (r_ps)    =?

Now,

Cost of preferred stock (r_ps) = D_ps / P_ps (1 - F)

                                             = $4.50 / $50(1 - 0)

                                             = $4.50 / $50

                                             = 9%

Therefore, Duggins Veterinary Supplies cost of preferred stock is 9% when price of preferred stock is $ 50 with annual dividend of $ 4.50 per share.

Problem 9-4 Solution:

Here given,

Par value of Preferred stock   = $60

Rate of Dividend                    = 6%

Preferred Dividend (D_ps)        = 6% of $60

                                                = $3.60

Preferred stock price (P_ps)       = $70

Flotation cost (F)                    = 5%

Cost of preferred stock (r_ps)    =?

Now,

Cost of preferred stock (r_ps) = D_ps / P_ps (1 - F)

                                             = $3.60 / [$70 (1 - 0.05)]

                                             = $3.60 / $66.5

                                             = 5.41%

 Therefore, the cost of preferred stock (r_ps) of Burnwood Tech is 5.41%.

Problem 9-5 Solution:

Here given,

Current stock price (P₀)                       = $36

Dividend at the year-end (D₁)                        = $3

Expected dividend growth rate (g)    = 5%

Cost of common equity (r_s)                 =?

Now,

 Cost of common equity (r_s) = D₁ / P₀ + g

                                             = ($3 / $36) + 0.05

                                             = 0.0833 + 0.05

                                             = 13.33%

 Therefore, Summerdahl Resort's cost of common equity is 13.33%.

Problem 9-6 Solution:

Here given,

Yield on 3- month T-bill         = 4%

Yield on 10- year T-bond       = 6%

Yield on 10-year T-bond        = Risk- free rate (r_RF)

= 6%

 Market risk premium (RP_M)   = 5.5%

Market return (r_M)                   = 15%

Beta (β_i)                                  = 0.8

According to CAPM approach, we have,

Estimated cost of common equity (r_s)  = r_RF + RP_M × β_i

                                                              = 6% + (5.5% × 0.8)

                                                              = 10.40%

 Therefore, the estimated cost of common equity under CAPM approach is 10.40%.

Problem 9-7 Solution:

Here given,

Amount of debt                      = $300 million

Amount of preferred stock     = $50 million

Amount of common equity     = $250 million

Marginal tax rate (T)               = 40%

Cost of debt (r_d)                      = 6%

Cost of preferred stock (r_ps)    = 5.8%

Cost of common equity (r_s)     = 12%

Target capital structure:

Debt (w_d)                                                        = 30%

Preferred stock (w_ps)                                       = 5%

Common equity (w_s)                                      = 65%

Weighted average cost of capital (WACC)    =?

Now,

Weighted average cost of capital (WACC) = w_d r_d (1-T) + w_psr_ps + w_sr_s

 = [0.30× 6% (1 - 0.40)] + (0.05 × 5.8%) + (0.65 × 12%)

= 1.08% + 0.29% + 7.8%

= 9.17%

Therefore, Shi Importer's weighted average cost of capital (WACC) is 9.17%.

Problem 9-8 Solution:

Here given,

Cost of debt (r_d)                                              = 9%

Marginal tax rate (T)                                       = 40%

Weighted average cost of capital (WACC)    = 9.96%

Target capital structure:

Debt (w_d)                                                        = 40%

Equity (w_s)                                                      = 60%

Cost of equity capital (r_s)                                =?

Now,

Weighted average cost of capital (WACC) = w_d r_d (1-T) + w_sr_s

Or, 9.96%= [0.40 × 9% (1 - 0.40)] + (0.60 × r_s)

 Or, 9.96% = 2.16% + (0.60 × r_s)

Or, 7.8% = 0.60 × r_s

Or, r_s = 13%

Therefore, David Ortiz Motors' cost of equity capital is 13%.

References

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Eugene F. Brigham, Michael C. Ehrhardt. (2011). Financial Management: Theory and Practice . Natorp Boulevard Mason, USA: South-Western Cengage Learning.

Manandhar, Dr. K. D.; Thapa, Kiran; Koirala, Narayan; Shah, Manoj; Pyakurel, Santosh. (2065). Corporate Finance (4 ed.). Kathmandu,Nepal: Januka Publication.