Question

EMR Limited has an EBIT of $450,000 that it expects it will earn forever, and it pays all of its earnings as dividends to shareholders (i.e. no growth). The firm has a corporate tax rate of 40% and has an un-levered beta of .90. The firm has 92,656 common shares issued and outstanding. In the market, you observe that Government T-bills are being sold to yield 4% and the S\&P/TSX Composite Index is expected to yield 10%. Assuming a world of taxes and a cost for the risk of default. a) Calculate the value of the firm. (4 marks) b) Calculate the WACC for the firm. (1 mark) c) What is the value of the firm if the firm issues $1,000,000 of bonds at a coupon rate of 7.5% ? The beta for the equity of the leveraged firm is 1.22. (7 marks) d) What is the WACC for the firm with its new capital structure?

Answer 1

The value of the firm is approximately $4,787,234.04 and the WACC for the firm is 9.4%. The value of the firm with the new capital structure is approximately $4,177,324.34 and the WACC for the firm with the new capital structure is 9.89%.

a) To calculate the value of the firm, we can use the perpetuity formula. The value of the firm is equal to the earnings before tax (EBIT) divided by the required rate of return:

Value of the Firm = EBIT / Required Rate of Return

In this case, the EBIT is $450,000, and the required rate of return is the risk-free rate plus the market risk premium:

Required Rate of Return = Risk-Free Rate + Beta × Market Risk Premium

The risk-free rate is 4% and the market risk premium is 10% - 4% = 6%:

Required Rate of Return = 4% + 0.90 × 6% = 9.4%

So, the value of the firm is:

Value of the Firm = $450,000 / 9.4% = $4,787,234.04

Therefore, the value of the firm is approximately $4,787,234.04.

b) The Weighted Average Cost of Capital (WACC) is the average rate of return required by all the firm's investors, weighted by the proportion of each source of capital. To calculate the WACC, we need to determine the proportion of equity and debt in the firm's capital structure, and the cost of equity and debt:

Proportion of Equity = Number of Common Shares / Total Capital

Proportion of Debt = 1 - Proportion of Equity

Cost of Equity = Required Rate of Return

Cost of Debt = Coupon Rate × (1 - Tax Rate)

Using the given information, the proportion of equity is 92,656 / 92,656 = 1, and the proportion of debt is 1 - 1 = 0. The cost of equity is 9.4%, and the cost of debt is 7.5% × (1 - 40%) = 4.5%:

WACC = Proportion of Equity × Cost of Equity + Proportion of Debt * Cost of Debt

WACC = 1 × 9.4% + 0 × 4.5% = 9.4%

Therefore, the WACC for the firm is 9.4%.

c) To calculate the value of the firm with the new capital structure, we can use the adjusted present value (APV) approach. The value of the firm is equal to the value of the unlevered firm plus the present value of the tax shield (PVTS). The value of the unlevered firm can be calculated using the perpetuity formula:

Value of the Unlevered Firm = EBIT / Required Rate of Return

The required rate of return is now calculated using the beta for the equity of the leveraged firm:

Required Rate of Return = Risk - Free Rate + Beta × Market Risk Premium

The risk-free rate is 4% and the market risk premium is 10% - 4% = 6%:

Required Rate of Return = 4% + 1.22 × 6% = 10.32%

So, the value of the unlevered firm is:

Value of the Unlevered Firm = $450,000 / 10.32% = $4,360,465.12

The present value of the tax shield can be calculated as the difference between the tax shield on the interest payments and the tax shield on the interest savings:

Present Value of the Tax Shield = (Interest Payments - Interest Savings) / Required Rate of Return

The interest payments are $1,000,000 × 7.5% = $75,000, and the interest savings are $1,000,000 × 9.4% = $94,000:

Present Value of the Tax Shield = ($75,000 - $94,000) / 10.32% = -$183,140.78

Therefore, the value of the firm with the new capital structure is:

Value of the Firm = Value of the Unlevered Firm + Present Value of the Tax Shield

Value of the Firm = $4,360,465.12 + (-$183,140.78) = $4,177,324.34

Therefore, the value of the firm with the new capital structure is approximately $4,177,324.34.

d) To calculate the WACC for the firm with the new capital structure, we need to determine the new proportion of equity and debt in the firm's capital structure, and the new cost of equity and debt. The new proportion of equity is still 1, and the new proportion of debt is the value of the bonds divided by the value of the firm:

New Proportion of Debt = Value of Bonds / Value of the Firm

Using the given information, the value of the bonds is $1,000,000, and the value of the firm is $4,177,324.34:

New Proportion of Debt = $1,000,000 / $4,177,324.34 = 0.2396

The new cost of equity is still 9.4%, and the new cost of debt is the coupon rate of 7.5% × (1 - 40%) = 4.5%:

New WACC = Proportion of Equity × New Cost of Equity + Proportion of Debt * New Cost of Debt

New WACC = 1 × 9.4% + 0.2396 × 4.5% = 9.89%

Therefore, the WACC for the firm with the new capital structure is 9.89%.

Answer 2

a. The value of the firm is $2872340

b. WACC is 9.40%

c. The value of the firm $2987632.51

d. The WACC for the firm with its new capital structure is 9.07%

Given data:

Beta = 0.90

Risk-free rate = 4%

Market return = 10%

EBIT = $450000

Tax rate = 40%

Expected rate of return = Risk fre rate + Beta*(Market return-Risk free rate)

= 4% + 0.90*(10%-4%)

= 4% + 5.4%

= 9.40%

a. The value of the firm = EBIT*(1-Tax rate) / Expected return

= 450000 * (1-0.40)/9.40%

= $2872340

b. WACC equals to Return on equity, so, the cost is 9.40%

c. The beta for the equity of the leveraged firm is = 1.22

Leverage firm of expected return = 4% + 1.22*(10%-4%) = 11.32%

Coupon rate = 7.5%

Interest = 75000 (1000000*7.5%)

Value of equity = (Earnings Interest) * (1 - Tax rate) / Expected rate of return

= (450000 - 75000)*(1-0.40) / 11.32%

= $1987632.50883

= 1987632.51

The value of the firm = Debt + Equity

= $1000000 + $1987633

= $2987632.51

d.

Equity:

Market value = 1987633

Weight = 1987633/2987633 = 67%

After tax cost = 11.32%

Weighted cost = 11.32%*67% = 7.58%

Debt:

Market value = 1000000

Weight = 1000000/2987633 = 33%

After tax cost = 4.50%

Weighted cost = 33%*4.50% = 1.49%

WACC for the firm = Weighted cost of Equity + Weighted cost of Debt

= 7.58% + 1.49%

= 9.07%