A is financed by 60 million equity and 40 million debt. The cost of debt before tax is 0.1 while the dividends just paid 4.1 gwe per share, if divident has grown steadily from 2 gwe years ago. The current share price is 97.5 gwe per share, company tax is 0.3. Calculate the cost of equity and determine the weighted average cost of capital.

Question

GPT-4o mini · Answer

To calculate the cost of equity and the weighted average cost of capital (WACC), we'll follow these steps:

Step 1: Calculate the Cost of Equity

The cost of equity can be estimated using the Gordon Growth Model (Dividend Discount Model), which is given by the formula:

$Cost of Equity = \frac{D_{1}}{P_{0}} + g$

Where:

$D_{1}$ = next year's expected dividend
$P_{0}$ = current share price
$g$ = growth rate of dividends

Given:

Last dividend paid ( $D_{0}$ ) = 4.1 gwe
Current share price ( $P_{0}$ ) = 97.5 gwe
Dividend has grown from 2 gwe (2 years ago) to 4.1 gwe over 2 years.

Calculate the Growth Rate $g$

To find the growth rate, we can calculate the annual growth rate over the last 2 years:

Using the formula for compound annual growth rate (CAGR): $g = {(\frac{D_{0}}{D_{- 2}})}^{\frac{1}{n}} - 1$ Where:

$D_{0}$ = 4.1 gwe
$D_{- 2}$ = 2 gwe
$n$ = number of years = 2

$g = {(\frac{4.1}{2})}^{\frac{1}{2}} - 1$

Calculating this value: $g = {(2.05)}^{0.5} - 1 = 1.43 - 1 = 0.43 (or 43$

Calculate $D_{1}$ , the expected dividend next year:

$D_{1} = D_{0} \times (1 + g) = 4.1 \times (1 + 0.43) = 4.1 \times 1.43 \approx 5.87 gwe$

Now substitute back into the cost of equity formula:

$Cost of Equity = \frac{5.87}{97.5} + 0.43$ Calculating: $Cost of Equity = 0.0601 + 0.43 \approx 0.4901 (or 49.01$

Step 2: Calculate the After-Tax Cost of Debt

The after-tax cost of debt is calculated using the formula: $After-Tax Cost of Debt = r_{d} \times (1 - T)$ Where:

$r_{d}$ = cost of debt before tax = 0.10
$T$ = tax rate = 0.3

Calculating: $After-Tax Cost of Debt = 0.10 \times (1 - 0.3) = 0.10 \times 0.7 = 0.07 (or 7$

Step 3: Calculate the Weighted Average Cost of Capital (WACC)

WACC is given by the formula: $WACC = (\frac{E}{V} \times r_{e}) + (\frac{D}{V} \times r_{d} \times (1 - T))$ Where:

$E$ = Market value of equity = 60 million
$D$ = Market value of debt = 40 million
$V = E + D$ = Total value = 100 million
$r_{e}$ = Cost of equity = 49.01% (or 0.4901)
$r_{d}$ = Cost of debt = 10% (or 0.10)

Calculate the Proportions of Equity and Debt:

$\frac{E}{V} = \frac{60}{100} = 0.6$ $\frac{D}{V} = \frac{40}{100} = 0.4$

Substitute values into the WACC formula:

$WACC = (0.6 \times 0.4901) + (0.4 \times 0.10 \times (1 - 0.3))$

Calculating: $WACC = (0.6 \times 0.4901) + (0.4 \times 0.07)$ $WACC = 0.29406 + 0.028 = 0.32206 (or 32.21$

Summary

Cost of Equity: 49.01%
WACC: 32.21%