Solved on Jan 30, 2024

Find the weighted average cost of capital (WACC) for Robin Corp, given a debt-equity ratio of 0.65, tax rate of 35%, cost of equity of 14.4%, and after-tax cost of debt of 5%.

STEP 1

Assumptions
1. Debt-equity ratio (D/E) is 0.65
2. Tax rate is 35%
3. The firm does not issue preferred stock
4. Cost of equity (E) is 0.144%
5. After-tax cost of debt (D) is 0.05%

STEP 2

Understand the formula for the Weighted Average Cost of Capital (WACC). The WACC is calculated using the following formula:
$WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1 - Tc)$
Where: - $E$ is the market value of the equity - $D$ is the market value of the debt - $V$ is the total market value of the firm's financing (Equity + Debt) - $Re$ is the cost of equity - $Rd$ is the cost of debt - $Tc$ is the corporate tax rate

STEP 3

Calculate the total market value of the firm's financing ( $V$ ) using the debt-equity ratio. The debt-equity ratio is given by:
$D/E = 0.65$
This means that for every $1 of equity, there is$ 0.65 of debt.

STEP 4

Express the market value of debt ( $D$ ) in terms of the market value of equity ( $E$ ) using the debt-equity ratio.
$D = 0.65E$

STEP 5

Express the total market value of the firm's financing ( $V$ ) in terms of $E$ .
$V = E + D$ $V = E + 0.65E$ $V = 1.65E$

STEP 6

Now we will express the weights of equity and debt as fractions of the total market value ( $V$ ).
For equity:
$\frac{E}{V} = \frac{E}{1.65E} = \frac{1}{1.65}$
For debt:
$\frac{D}{V} = \frac{0.65E}{1.65E} = \frac{0.65}{1.65}$

STEP 7

Convert the cost of equity and the after-tax cost of debt to decimal form.
For cost of equity ( $Re$ ):
$Re = 0.144\% = 0.00144$
For after-tax cost of debt ( $Rd$ ):
$Rd = 0.05\% = 0.0005$

STEP 8

Calculate the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{E}{V} \times Re$ $Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144$

STEP 9

Calculate the weighted cost of debt, taking into account the tax shield.
$Weighted\, cost\, of\, debt = \frac{D}{V} \times Rd \times (1 - Tc)$ $Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35)$

STEP 10

Now we can calculate the WACC by adding the weighted cost of equity and the weighted cost of debt.
$WACC = Weighted\, cost\, of\, equity + Weighted\, cost\, of\, debt$

STEP 11

Perform the calculations for the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144 \approx 0.00087273$

STEP 12

Perform the calculations for the weighted cost of debt.
$Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35) \approx 0.00021212$

STEP 13

Add the weighted cost of equity and the weighted cost of debt to find the WACC.
$WACC = 0.00087273 + 0.00021212 \approx 0.00108485$

STEP 14

Convert the WACC to a percentage by multiplying by 100.
$WACC = 0.00108485 \times 100 \approx 0.108485\%$
The weighted average cost of capital (WACC) for Robin Corp is approximately 0.108485%.

Was this helpful?

Find the weighted average cost of capital (WACC) for Robin Corp, given a debt-equity ratio of 0.65, tax rate of 35%, cost of equity of 14.4%, and after-tax cost of debt of 5%.

STEP 1

Assumptions
1. Debt-equity ratio (D/E) is 0.65
2. Tax rate is 35%
3. The firm does not issue preferred stock
4. Cost of equity (E) is 0.144%
5. After-tax cost of debt (D) is 0.05%

STEP 2

STEP 3

Calculate the total market value of the firm's financing ( $V$ ) using the debt-equity ratio. The debt-equity ratio is given by:
$D/E = 0.65$
This means that for every $1 of equity, there is$ 0.65 of debt.

STEP 4

Express the market value of debt ( $D$ ) in terms of the market value of equity ( $E$ ) using the debt-equity ratio.
$D = 0.65E$

STEP 5

Express the total market value of the firm's financing ( $V$ ) in terms of $E$ .
$V = E + D$ $V = E + 0.65E$ $V = 1.65E$

STEP 6

Now we will express the weights of equity and debt as fractions of the total market value ( $V$ ).
For equity:
$\frac{E}{V} = \frac{E}{1.65E} = \frac{1}{1.65}$
For debt:
$\frac{D}{V} = \frac{0.65E}{1.65E} = \frac{0.65}{1.65}$

STEP 7

Convert the cost of equity and the after-tax cost of debt to decimal form.
For cost of equity ( $Re$ ):
$Re = 0.144\% = 0.00144$
For after-tax cost of debt ( $Rd$ ):
$Rd = 0.05\% = 0.0005$

STEP 8

Calculate the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{E}{V} \times Re$ $Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144$

STEP 9

Calculate the weighted cost of debt, taking into account the tax shield.
$Weighted\, cost\, of\, debt = \frac{D}{V} \times Rd \times (1 - Tc)$ $Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35)$

STEP 10

Now we can calculate the WACC by adding the weighted cost of equity and the weighted cost of debt.
$WACC = Weighted\, cost\, of\, equity + Weighted\, cost\, of\, debt$

STEP 11

Perform the calculations for the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144 \approx 0.00087273$

STEP 12

Perform the calculations for the weighted cost of debt.
$Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35) \approx 0.00021212$

STEP 13

Add the weighted cost of equity and the weighted cost of debt to find the WACC.
$WACC = 0.00087273 + 0.00021212 \approx 0.00108485$

STEP 14

Convert the WACC to a percentage by multiplying by 100.
$WACC = 0.00108485 \times 100 \approx 0.108485\%$
The weighted average cost of capital (WACC) for Robin Corp is approximately 0.108485%.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the weighted average cost of capital (WACC) for Robin Corp, given a debt-equity ratio of 0.65, tax rate of 35%, cost of equity of 14.4%, and after-tax cost of debt of 5%.

STEP 1

Assumptions1. Debt-equity ratio (D/E) is 0.652. Tax rate is 35%3. The firm does not issue preferred stock4. Cost of equity (E) is 0.144%5. After-tax cost of debt (D) is 0.05%

STEP 2

STEP 3

Calculate the total market value of the firm's financing (VVV) using the debt-equity ratio. The debt-equity ratio is given by:D/E=0.65D/E = 0.65D/E=0.65This means that for every 1ofequity,thereis1 of equity, there is 1ofequity,thereis0.65 of debt.

STEP 4

Express the market value of debt (DDD) in terms of the market value of equity (EEE) using the debt-equity ratio.D=0.65ED = 0.65ED=0.65E

STEP 5

Express the total market value of the firm's financing (VVV) in terms of EEE.V=E+DV = E + DV=E+D V=E+0.65EV = E + 0.65EV=E+0.65E V=1.65EV = 1.65EV=1.65E

STEP 6

STEP 7

Convert the cost of equity and the after-tax cost of debt to decimal form.For cost of equity (ReReRe):Re=0.144%=0.00144Re = 0.144\% = 0.00144Re=0.144%=0.00144For after-tax cost of debt (RdRdRd):Rd=0.05%=0.0005Rd = 0.05\% = 0.0005Rd=0.05%=0.0005

STEP 8

Calculate the weighted cost of equity.Weighted cost of equity=EV×ReWeighted\, cost\, of\, equity = \frac{E}{V} \times ReWeightedcostofequity=VE​×Re Weighted cost of equity=11.65×0.00144Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144Weightedcostofequity=1.651​×0.00144

STEP 9

STEP 10

Now we can calculate the WACC by adding the weighted cost of equity and the weighted cost of debt.WACC=Weighted cost of equity+Weighted cost of debtWACC = Weighted\, cost\, of\, equity + Weighted\, cost\, of\, debtWACC=Weightedcostofequity+Weightedcostofdebt

STEP 11

Perform the calculations for the weighted cost of equity.Weighted cost of equity=11.65×0.00144≈0.00087273Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144 \approx 0.00087273Weightedcostofequity=1.651​×0.00144≈0.00087273

STEP 12

Perform the calculations for the weighted cost of debt.Weighted cost of debt=0.651.65×0.0005×(1−0.35)≈0.00021212Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35) \approx 0.00021212Weightedcostofdebt=1.650.65​×0.0005×(1−0.35)≈0.00021212

STEP 13

Add the weighted cost of equity and the weighted cost of debt to find the WACC.WACC=0.00087273+0.00021212≈0.00108485WACC = 0.00087273 + 0.00021212 \approx 0.00108485WACC=0.00087273+0.00021212≈0.00108485

STEP 14

Convert the WACC to a percentage by multiplying by 100.WACC=0.00108485×100≈0.108485%WACC = 0.00108485 \times 100 \approx 0.108485\%WACC=0.00108485×100≈0.108485%The weighted average cost of capital (WACC) for Robin Corp is approximately 0.108485%.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. Debt-equity ratio (D/E) is 0.65
2. Tax rate is 35%
3. The firm does not issue preferred stock
4. Cost of equity (E) is 0.144%
5. After-tax cost of debt (D) is 0.05%

Calculate the total market value of the firm's financing ( $V$ ) using the debt-equity ratio. The debt-equity ratio is given by:
$D/E = 0.65$
This means that for every $1 of equity, there is$ 0.65 of debt.

Express the market value of debt ( $D$ ) in terms of the market value of equity ( $E$ ) using the debt-equity ratio.
$D = 0.65E$

Express the total market value of the firm's financing ( $V$ ) in terms of $E$ .
$V = E + D$ $V = E + 0.65E$ $V = 1.65E$

Convert the cost of equity and the after-tax cost of debt to decimal form.
For cost of equity ( $Re$ ):
$Re = 0.144\% = 0.00144$
For after-tax cost of debt ( $Rd$ ):
$Rd = 0.05\% = 0.0005$

Calculate the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{E}{V} \times Re$ $Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144$

Now we can calculate the WACC by adding the weighted cost of equity and the weighted cost of debt.
$WACC = Weighted\, cost\, of\, equity + Weighted\, cost\, of\, debt$

Perform the calculations for the weighted cost of equity.
$Weighted\, cost\, of\, equity = \frac{1}{1.65} \times 0.00144 \approx 0.00087273$

Perform the calculations for the weighted cost of debt.
$Weighted\, cost\, of\, debt = \frac{0.65}{1.65} \times 0.0005 \times (1 - 0.35) \approx 0.00021212$

Add the weighted cost of equity and the weighted cost of debt to find the WACC.
$WACC = 0.00087273 + 0.00021212 \approx 0.00108485$

Convert the WACC to a percentage by multiplying by 100.
$WACC = 0.00108485 \times 100 \approx 0.108485\%$
The weighted average cost of capital (WACC) for Robin Corp is approximately 0.108485%.