FIM Exam: Cost of Capital Practice

Question 5(b) - May 2024: WACC Calculation

Problem Statement: Titan Mining Corporation has 8.7 million shares of common stock outstanding and 230,000 6.4 percent semiannual bonds outstanding, par value Tk. 1,000 each. The common stock currently sells for Tk.37 per share and has a beta of 1.20, and the bonds have 20 years to maturity and sell for 104 percent of par. The market risk premium is 7 percent, T-bills are yielding 3.5 percent, and the company's tax rate is 35 percent.

Required:

(i) What is the firm's market value capital structure?

(ii) If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?

Theoretical Foundation: This problem requires calculating the Weighted Average Cost of Capital (WACC). The WACC is a weighted average of the costs of a company's debt and equity, where the weights are based on the market values of each. The cost of equity is found using the Capital Asset Pricing Model (CAPM), and the cost of debt is the after-tax Yield to Maturity (YTM) of the outstanding bonds.

Step-by-step Solution:

i. Firm's Market Value Capital Structure:

The first step is to find the market value of the company's equity (E) and debt (D).

• Market Value of Equity (E):

  $ E = \text{Shares outstanding} \times \text{Price per share} = 8,700,000 \times \text{Tk. 37} = \textbf{Tk. 321,900,000} $

• Market Value of Debt (D):

  $ D = \text{Bonds outstanding} \times \text{Price per bond} = 230,000 \times (\text{Tk. } 1,000 \times 1.04) = 230,000 \times \text{Tk. } 1,040 = \textbf{Tk. 239,200,000} $

• Total Firm Value (V):

  $ V = E + D = 321,900,000 + 239,200,000 = \textbf{Tk. 561,100,000} $

• Capital Structure Weights:

  $ W_E = E/V = 321,900,000 / 561,100,000 = \textbf{0.5737} $ or 57.37%

  $ W_D = D/V = 239,200,000 / 561,100,000 = \textbf{0.4263} $ or 42.63%

ii. Discount Rate for a New Project (WACC):

The appropriate discount rate for a typical project is the WACC. We need to calculate the cost of equity and the after-tax cost of debt.

• Cost of Equity ($R_E$): Using CAPM, $ R_E = R_f + \beta \times (E(R_M) - R_f) $.

  Given: $R_f = 3.5\%$, $\beta = 1.20$, $E(R_M) - R_f = 7\%$.

  $ R_E = 3.5\% + 1.20 \times 7\% = 3.5\% + 8.4\% = \textbf{11.9\%} $

• Cost of Debt ($R_D$): We must find the YTM of the bonds.

  PV = Tk. 1,040, FV = Tk. 1,000, PMT = $(1,000 \times 0.064) / 2 = \text{Tk. 32}$. N = $20 \times 2 = 40$ periods.

  Tricky Area: When calculating YTM for semiannual bonds, remember to use semiannual payments and periods, and then double the result to get the annual rate.

  Using a financial calculator, the semiannual yield is approximately 3.01%. So the annual pretax cost of debt is $ R_D = 3.01\% \times 2 = \textbf{6.02\%} $

  The after-tax cost of debt is: $ R_D(1-T_C) = 6.02\% \times (1 - 0.35) = 6.02\% \times 0.65 = \textbf{3.91\%} $

• WACC Calculation:

  $ WACC = (W_E \times R_E) + (W_D \times R_D(1-T_C)) $

  $ WACC = (0.5737 \times 11.9\%) + (0.4263 \times 3.91\%) = 6.827\% + 1.667\% = \textbf{8.49\%} $

The firm should use a discount rate of approximately 8.49%.

Question 5(c) - Sep 2023: Capital Structure and Required Return

Problem Statement: Beach Limited is into the provision of online conference call facilities which has become popular due to Covid-19. The company has 10 million issued shares currently at Tk. 50 each, 3 million preference shares trading at Tk. 25 each and 5,000 bonds also trading at Tk. 600 each. Required: (i) Calculate the capital structure of the company. (ii) How much should the company earn annually to achieve a return of 25% per annum on capital employed for equity holders if dividend rate on preference shares per annum is 20% and coupon on the bonds is 18%? Interest paid on debt is tax deductible and corporate tax rate is 25%.

Theoretical Foundation: This problem requires you to calculate the market value weights of a company with three capital components: common equity, preferred stock, and debt. For the second part, you must work backward from the required return on equity to determine the necessary EBIT (Earnings Before Interest and Taxes) to satisfy all investors after tax deductions.

Step-by-step Solution:

i. Capital structure of the company:

First, find the market value of each capital component.

• Market Value of Equity (E) = $10,000,000 \times \text{Tk. 50} = \text{Tk. 500,000,000}$
• Market Value of Preferred Stock (P) = $3,000,000 \times \text{Tk. 25} = \text{Tk. 75,000,000}$
• Market Value of Bonds (D) = $5,000 \times \text{Tk. 600} = \text{Tk. 3,000,000}$
• Total Firm Value (V) = $E + P + D = 500M + 75M + 3M = \textbf{Tk. 578,000,000}$

The capital structure weights are:

• Weight of Equity ($W_E$) = $ 500M / 578M = \textbf{0.865} $ or 86.5%
• Weight of Preferred Stock ($W_P$) = $ 75M / 578M = \textbf{0.130} $ or 13.0%
• Weight of Debt ($W_D$) = $ 3M / 578M = \textbf{0.005} $ or 0.5%

ii. Annual earnings required:

We need to find the EBIT required to achieve a 25% return on equity. The required return on equity is a component of net income, and interest on debt and dividends on preferred stock are paid before the common shareholders receive their return.

• Required Net Income for common shareholders = $ 0.25 \times E = 0.25 \times 500,000,000 = \text{Tk. 125,000,000} $
• Preferred Stock Dividend Payment = $ 0.20 \times \text{Par Value} \times \text{Number of Shares} $

  Tricky Area: The problem states the dividend rate is 20% but doesn't provide a par value. Let's assume the par value is Tk. 25, the same as the market value, as is common for preferred stock in these problems. The market value is what investors pay for the stock, so the return should be based on that. A 20% dividend rate means a 20% return on the par value, not the market value. Let's use the provided market value as the basis for the dividend rate. However, a dividend rate is typically on par value. Since par value is not provided, we have to assume a dividend amount is being specified. Let's re-examine the question. A 20% dividend rate on preferred shares trading at Tk. 25 means the annual dividend is Tk. $25 \times 0.20 = \text{Tk. 5}$ per share. Total preferred dividend is $3,000,000 \times 5 = \text{Tk. 15,000,000}$.

• Interest on bonds = $ \text{Tk. } 3,000,000 \times 0.18 = \text{Tk. 540,000} $
• Earnings After Tax (EAT) = Net Income + Preferred Dividends = $ 125,000,000 + 15,000,000 = \text{Tk. 140,000,000} $
• EBIT After Tax and Interest = $ \text{EBIT} - \text{Interest} = \text{EAT} / (1 - T) = 140M / (1 - 0.25) = 140M / 0.75 \approx \text{Tk. 186,666,667} $
• Required EBIT = $ 186,666,667 + \text{Interest} = 186,666,667 + 540,000 = \textbf{Tk. 187,206,667} $.

Question 5(c) - Jan 2024: WACC and Debt-Equity Ratio

Problem Statement: Fekdil Pic has a weighted average cost of capital of 9.1 percent. The company's cost of equity is 11 percent and its cost of debt is 6.4 percent. The tax rate is 21 percent. What is the company's debt-equity ratio?

Theoretical Foundation: This problem requires you to use the WACC formula and solve for the unknown capital structure weights. The debt-equity ratio, $D/E$, can be derived from the weights, $D/V$ and $E/V$.

Step-by-step Solution:

Let the debt-equity ratio be $x = D/E$. We can express the capital structure weights in terms of $x$:

• $ \frac{E}{V} = \frac{E}{E+D} = \frac{1}{1 + D/E} = \frac{1}{1+x} $
• $ \frac{D}{V} = \frac{D}{E+D} = \frac{D/E}{1 + D/E} = \frac{x}{1+x} $

Now, substitute these into the WACC formula: $WACC = (\frac{E}{V}) \times R_E + (\frac{D}{V}) \times R_D(1-T_C)$.

The company's debt-equity ratio is approximately 0.47.

Question 5(c) - May 2023: WACC Calculation with DVM and CAPM

Problem Statement: A colleague has been taken ill. Your managing director has asked you to take over from the colleague and to provide urgently-needed estimates of the discount rate to be used in appraising a large new capital investment. You have been given your colleague's working notes, which you believe to be numerically accurate. Working notes: Estimates for the next five years (annual averages): Stock market total return on equity: 16%, Own company dividend yield: 7%, Own company share price rise: 14%, Standard deviation of total stock market return on equity: 10%, Systematic risk of own company return on equity: 14%, Growth rate of own company earnings: 12%, Growth rate of own company dividends: 11%, Growth rate of own company sales: 13%, Treasury bill yield: 12%. The company's gearing level (by market values) is 1:2 debt to equity, and after-tax earnings available to ordinary shareholders in the most recent year were Tk. 54,000,000, of which Tk. 21,400,000 was distributed as ordinary dividends. The company has 1 million issued ordinary shares which are currently trading on the Stock Exchange at Tk. 3.21. Corporate debt may be assumed to be risk-free. The company pays tax at 30% and personal taxation may be ignored. Required: Estimate the company's weighted average cost of capital using: (i) The dividend valuation model; (ii) The capital asset pricing model. State clearly any assumptions that you make. Under what circumstances these models would be expected to produce similar values for the weighted average cost of capital?

Theoretical Foundation: This is a comprehensive problem that requires you to use both the Dividend Valuation Model (DVM) and the Capital Asset Pricing Model (CAPM) to calculate the cost of equity. You must then use the calculated cost of equity and cost of debt to find the WACC under both scenarios and compare the results.

Step-by-step Solution:

Assumptions:

• The given growth rates are assumed to be stable and will continue indefinitely.
• The market is in equilibrium, meaning the cost of capital is consistent across different models.
• The firm's beta (systematic risk) is constant.
• The debt is assumed to be risk-free.

i. WACC using the Dividend Valuation Model (DVM):

The cost of equity ($k_e$) is the sum of the dividend yield and the dividend growth rate. The working notes give: Dividend Yield = 7%, Dividend Growth Rate = 11%.

Next, we find the market values for debt and equity. Gearing level is 1:2 debt to equity.

• Market Value of Equity (E) = $1,000,000 \times \text{Tk. 3.21} = \text{Tk. 3,210,000}$
• Market Value of Debt (D) = $E \times (1/2) = 3,210,000 \times 0.5 = \text{Tk. 1,605,000}$
• Total Firm Value (V) = $E + D = 3,210,000 + 1,605,000 = \text{Tk. 4,815,000}$

The cost of debt ($k_d$) is the Treasury Bill Yield, which is 12%. The after-tax cost is $12\% \times (1-0.30) = \textbf{8.4\%}$.

WACC = $(W_E \times k_e) + (W_D \times k_d(1-T))$

ii. WACC using the Capital Asset Pricing Model (CAPM):

First, we find the cost of equity ($k_e$) using the CAPM. We are given: $R_f = 12\%$, $E(R_M) = 16\%$, and the systematic risk is 14%. As beta is a factor, we assume the beta is 1.40.

Using the same market values and after-tax cost of debt as in part (i):

Circumstances for similar values:

The two models would produce similar values for the WACC if the assumptions of both models hold true. The key link is that the expected return from the DVM model ($k_e = \frac{D_1}{P_0} + g$) should be consistent with the required return from the CAPM ($k_e = R_f + \beta \times (R_M - R_f)$). This is a hallmark of a market in equilibrium. If the inputs for both models are accurate and consistent with each other, their resulting WACC values should be very close.

Question 5(c) - May 2022: After-Tax Cost of Borrowing

Problem Statement: Rick and Stacy Stark, a married couple, are interested in purchasing their first boat. They have decided to borrow the boat's purchase price of Tk. 100,000. The family is in the 28% income tax bracket. There are two choices for the Stark family: They can borrow the money from the boat dealer at an annual interest rate of 8%, or they could take out a Tk. 100,000 second mortgage on their home. Currently, home equity loans are at rates of 9.2%. There is no problem securing either of these two alternative financing choices. Rick and Stacy learn that if they borrow from the boat dealership, the interest will not be tax deductible. However, the interest on the second mortgage will qualify as being tax deductible on their federal income tax return. Required: (i) Calculate the after-tax cost of borrowing from the boat dealership. (ii) Calculate the after-tax cost of borrowing through a second mortgage on their home. (iii) Which source of borrowing is less costly for the Stark family?

Theoretical Foundation: This problem illustrates the importance of the tax shield in determining the true cost of debt. The after-tax cost of borrowing is the relevant metric for decision-making. If interest is tax-deductible, the effective cost of the loan is reduced.

Step-by-step Solution:

i. After-tax cost of borrowing from the boat dealership:

The interest on this loan is not tax deductible. Therefore, the after-tax cost is the same as the before-tax cost.

ii. After-tax cost of borrowing through a second mortgage:

The interest on this loan is tax deductible. We use the formula: $\text{After-tax cost} = \text{Interest Rate} \times (1 - \text{Tax Rate})$.

iii. Less costly source of borrowing:

The after-tax cost of borrowing from the boat dealership is 8%, while the after-tax cost of the second mortgage is 6.624%. Since the after-tax cost of the second mortgage is lower, it is the less costly source of borrowing for the Stark family.

Question 5(b) - May 2025: Cost of Capital for Various Sources

Problem Statement: Humble Manufacturing is measuring its overall cost of capital with a tax rate of 40% and a target capital structure.

A new issue of 10-year bonds with a Tk. 1,000 par value and 10% coupon will be sold at a Tk. 30 discount from par and will incur a Tk. 20 flotation cost. The company's 11% preferred stock is Tk. 100 par value, with flotation costs of Tk. 4. A new issue of common stock is expected to have a Tk. 6 dividend in the coming year, sells for Tk. 80, is underpriced by Tk. 4, and will incur flotation costs of Tk. 4 per share. The company's stock has a constant growth rate of 6% and the retained earnings amount to Tk. 50 million. The target capital structure is 40% debt, 15% preferred stock, and 45% common stock. The corporate tax rate is 40%.

i. Calculate the individual cost of each source of financing.

ii. Calculate the firm's weighted average cost of capital (WACC).

Theoretical Foundation: This is a comprehensive problem that requires calculating the cost of all three capital components (debt, preferred stock, and equity) while properly accounting for issuance costs. The problem highlights the difference between the cost of new equity and retained earnings, as well as the importance of using the correct net proceeds when calculating cost.

Step-by-step Solution:

i. Calculate the individual cost of each source of financing.

• Cost of Debt ($R_D$):

  We need to find the YTM of the bond. We use the net proceeds as the PV, which is the par value less the discount. The flotation costs are handled separately as a cost of the project itself, not as a reduction in the initial proceeds for YTM calculation.

  PV = Tk. $1,000 - 30 = 970$. FV = Tk. 1,000. PMT = $10\% \times 1,000 = \text{Tk. 100}$. N = 10 years. Using a financial calculator, the YTM is approximately 10.42%.

  After-tax cost of debt = \( R_D(1 - T_C) = 10.42\% \times (1 - 0.40) = 10.42\% \times 0.60 = \textbf{6.25\%} \)

• Cost of Preferred Stock ($R_P$):

  The cost of preferred stock is the dividend divided by the net price to the company (price less flotation costs and underpricing).

  Net price = $100 - 4 = \text{Tk. 96}$. Annual dividend = $11\% \times 100 = \text{Tk. 11}$.

  $ R_P = \frac{\text{Annual Dividend}}{\text{Net Price}} = \frac{11}{96} \approx \textbf{11.46\%} $

  Tricky Area: Flotation costs for the preferred stock are given as a specific amount (Tk. 4) rather than a percentage. This amount should be deducted from the selling price to get the net proceeds.

• Cost of Retained Earnings ($R_{RE}$):

  We use the dividend growth model with the stock's current price.

  $ R_{RE} = \frac{D_1}{P_0} + g = \frac{6}{80} + 0.06 = 0.075 + 0.06 = \textbf{13.5\%} $
• Cost of New Common Stock ($R_N$):

  The new stock is underpriced and has flotation costs. We must use the net proceeds, which is the current price less underpricing and flotation costs.

  Net Proceeds = $80 - 4 - 4 = \text{Tk. 72}$ per share.

  $ R_N = \frac{D_1}{\text{Net Proceeds}} + g = \frac{6}{72} + 0.06 \approx 0.0833 + 0.06 = \textbf{14.33\%} $

ii. Calculate the firm's weighted average cost of capital (WACC).

We assume the firm will use retained earnings first, and then new common stock if needed. Since the problem asks for the WACC without specifying the amount of new capital to be raised, we will calculate the WACC based on the cost of retained earnings. If the retained earnings are insufficient, the cost of equity would be higher, leading to a higher WACC.

Target weights: \( W_D = 0.40 \), \( W_P = 0.15 \), \( W_E = 0.45 \).

WACC = $(0.40 \times 6.25\%) + (0.15 \times 11.46\%) + (0.45 \times 13.5\%)$

The firm's WACC is 10.3% when using retained earnings.