cost of capital lecture examples

COST OF CAPITAL

LECTURE EXAMPLES

Prepared by Sara du Toit CA (SA)

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CAPITAL STRUCTURE RATIOS

Example 1.1: The following information relates to Cersei Limited: Market value of equity R500 000 Market value of debt R300 000 Debt: Equity ratio = Non-current liabilities / Equity = 300 000 / 500 000 = 60% The calculation above does not give us the capital structure of a company. It simply tells us that debt is 60% of equity. This does not mean that the company has 60% debt and 40% equity in its capital structure. It is therefore preferable to calculate the gearing ratio as follows: Gearing ratio = Long-term debt / (Long-term debt + Equity)

= 300 000 / (300 000 + 500 000) = 37.5% The gearing ratio gives us the capital structure of the company. It indicates the degree to which a company’s operations are funded by debt (i.e. a gearing ratio of 37.5% means that Cersei Limited has 37.5% debt and 62.5% equity in its capital structure). If you are told that a company is highly geared it means that the company has a significant amount of debt in its capital structure.

Example 1.2: As an alternative the debt: equity ratio can be presented as follows: Debt: Equity ratio = Non-current liabilities : Equity = 300 000 : 500 000 = 0.6: 1 Once again, this calculation does not give us the capital structure of a company. It simply tells us that debt is 60% of equity. It does not mean that the company has 60% debt and 40% equity in its capital structure. It is therefore preferable to calculate the gearing ratio: Gearing ratio = Long-term debt / (Long-term debt + Equity) = 0.6 / (0.6 + 1) = 37.5% Therefore Cersei Limited has 37.5% debt and 62.5% equity in its capital structure.


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Example 1.3:

The debt: equity ratio is sometimes presented as follows: Debt: Equity ratio = 37.5: 62.5 In this example the debt: equity ratio has been presented in a format that we can work with. The above ratio tells us that Cersei Limited has 37.5% debt and 62.5% equity in its capital structure. You therefore don’t need to calculate the gearing ratio!

How to determine if the ratio provided gives you the capital structure?

1. If the ratio is presented :1 (or :100) it does not provide the capital structure.

2. You can double check this by adding the amounts together:

If the total is not 100 (or 1) you don’t have the capital structure.

If the total is 100 (or 1) you have the capital structure.

Example 1.2:

Debt: Equity ratio = 0.6: 1 The ratio is presented :1 and if we add the amounts together the total is not 1: 0.6 + 1 = 1.6 This is therefore not the capital structure of Cersei Limited and you should calculate the gearing ratio.

Example 1.3:

Debt: Equity ratio = 37.5: 62.5 Ratio is not presented :100 and if we add the amounts together the total is 100: 37.5 + 62.5 = 100. This is therefore the capital structure of Cersei Limited and you do not need to calculate the

gearing ratio.


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THE ADVANTAGES & DISADVANTAGES OF DEBT

Example 2.1: Tyrion Limited is currently financed by R200 000 equity. Profit after tax for the financial year ending 28 February 20X6 was R40 000. Tyrion Limited wants to expand by investing a further R100 000 in a new project with expected returns of R25 000 before tax. The shareholders required rate of return (Ke) is 18% and the cost of debt (Kd) is 12% before tax. The tax rate is 28%. Return from the new project:

Equity Finance Debt Finance

Profit before interest and tax 25 000 25 000 Interest expense (100 000 x 12%) - (12 000)

Profit before tax 25 000 13 000 Tax @ 28% (7 000) (3 640) Profit after tax 18 000 9 360

Total return from business:

Equity Finance Debt Finance Existing profit after tax 40 000 40 000 New project profit after tax 18 000 9 360 Total profit after tax 58 000 49 360

Return on shareholder’s investment:

Equity Finance Debt Finance

Total return 58 000 49 360 Shareholder’s investment 300 000 200 000 Shareholder’s return on investment 19.33% 24.68%

This example illustrates how debt can be used to improve returns to shareholders. The ordinary shareholders would be better off by financing the new project using debt as their return on investment increases to 24.68% without any additional investment. However, the shareholders required rate of return (Ke) of 18% relates to business risk only as the company was previously financed purely through equity:

If the project is financed through equity the shareholders will receive a return of 19.33% which is higher than their required return of 18%.

If the new project is financed through debt the shareholders will need to be compensated for financial risk and hence the cost of equity (Ke) will increase above 18%. The project should only be financed through debt if the return of 24.68% is sufficient to compensate shareholders for both business risk and financial risk.


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GORDON’S DIVIDEND GROWTH MODEL

Example 3.1:

Why is this example important? Shows you how to calculate the cost of equity (Ke) when the market value (PV) is given.

Drogo Limited recently paid a dividend of R5 per share which is expected to grow by 6% indefinitely. The shares are currently trading at R40 each. Calculate the cost of equity. Ke = D1/PV + g = (5 x 1.06)/40 + 0.06 = 19.25%

Example 3.2:

Why is this example important? Shows you how to calculate the market value of equity (PV) when the cost (Ke) is given.

Drogo Limited has 500 000 shares in issue and recently paid a dividend of R5 per share. The ordinary dividend is expected to grow by 6% indefinitely. The company’s cost of equity has recently been calculated at 19.25%. Calculate the market value of equity. This calculation can either be performed in total or per share:

IN TOTAL PER SHARE

PV = D1/(Ke – g) = (R5 x 500 000 x 1.06) / (19.25% - 6%) = R20 000 000

PV = D1/(Ke – g) = (R5 x 1.06) / ((19.25% - 6%) = R40 x 500 000 = R20 000 000


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Example 3.3:

Why is this example important?

Shows you how to deal with authorised and issued shares.

Shows you how to calculate the cost of equity (Ke) when D1 is provided.

Ordinary share capital includes 1 000 000 authorised shares of which 500 000 shares have been issued. A large block of ordinary shares were recently traded between non-connected parties at a price of R40 per share. The next dividend planned is R5.30 per share with an expected growth rate of 6% thereafter. Calculate the cost of equity. This calculation can either be performed in total or per share:

IN TOTAL PER SHARE Ke = D1/PV + g = (R5.30 x 500 000) / (R40 x 500 000) + 0.06 = 19.25%

Ke = D1/PV + g = R5.30 / R40 + 0.06 = 19.25%

You have been given the next dividend (D1) therefore don’t adjust for growth!


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Example 3.4:

Why is this example important? Shows you how to deal with a situation where you don’t have consistent growth in perpetuity.

Drogo Limited has 500 000 shares in issue and recently paid a dividend of R5 per share. The shareholders required rate of return is 19.25% and the directors believe that dividends will grow by 10% for the next three years and then by 6% indefinitely. Calculate the market value of equity. Gordon’s dividend growth model can only be used where there is consistent growth in perpetuity. Where there is inconsistent growth (in the first 3 years) the calculation must be done as follows:

0 1 2 3

Dividend in year 1: (5 x 1.10 x 500 000)

2 750 000

Dividend in year 2: (2 750 000 x 1.10)

3 025 000

Dividend in year 3: (3 025 000 x 1.10)

3 327 500

Dividends from year 4 onwards: PV = D4 / Ke – g

= (3 327 500 x 1.06) / (19.25% - 6%)

= 26 620 000

26 620 000

0 cfj

2 750 000 cfj

3 025 000 cfj

29 947 500 cfj

i = 19.25% (Ke) NPC = R22 093 066 (market value)


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Example 3.5:

Why is this example important? Shows you how to calculate a growth rate when you are provided with the return on investment and percentage of earnings not paid out as a dividend.

g = r x b Where:

r = return on investment

b = percentage of earnings retained and reinvested (earnings not paid out as a dividend) Assume the Drogo Limited has a return on investment of 15% and a dividend payout ratio of 80%. What is the growth rate? If Drogo Limited has a dividend payout ratio of 80% it means that 20% of earnings are retained and reinvested. Earnings retained in the business will contribute towards the growth of the company: g = r x b = 15% (20%) = 3%


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Example 3.6:

Why is this example important? Shows you how to calculate a growth rate when you are provided with historical dividends and earnings.

Dividend and earnings per share information (cents):

Dividend history Earnings history 20X5 360 2 800

20X4 320 2 450

20X3 280 2 380

20X2 250 2 150 Calculate the growth rate in dividends and earnings as follows:

Dividends: PV = - 250 FV = 360 n = 3 i = 12.9%

Earnings: PV = - 2 150 FV = 2 800 n = 3 i = 9.2%

NOTES: 1. To perform this calculation on your financial calculator either the PV

or FV must be negative. 2. You are provided with information for 4 years. However, there are only

3 periods of growth:

Period 1: 20X2 – 20X3

Period 2: 20X3 – 20X4

Period 3: 20X4 – 20X5 3. g = growth in perpetuity. If the growth rate in dividends exceeds the

growth rate in earnings this dividend will not be sustainable in perpetuity (eventually the company will not have enough earnings to pay the dividend). You should therefore limit the growth in dividends to the growth in earnings and use 9.2% as “g” in your calculation.


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Calculate the cost of equity (Ke) at 31 December 20X5 assuming that the shares are currently trading at R120 each:

USING CENTS USING RANDS

R120 x 100 = 12 000 cents Ke = D1/PV + g = (360 x 1.092)/12 000 + 0.092 = 12.48%

360 cents / 100 = R3.60 Ke = D1/PV + g = (3.6 x 1.092)/120 + 0.092 = 12.48%

BE CONSISTENT: The calculation is performed using either Rands OR cents and not a combination of the two!

Example 3.7:

Why is this example important? Shows you how to calculate a growth rate when you are provided with anticipated growth rates and probabilities.

The directors anticipate the following growth in the share price:

Annual % increase Probability

8% 45%

15% 55% Expected growth rate = (8 x 45%) + (15 x 55%) = 11.85%


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CAPITAL ASSET PRICING MODEL (CAPM)

Example 4.1:

Why is this example important? Shows you how to calculate the cost of equity (Ke) using the capital asset pricing model.

The risk-free rate on RSA treasury bonds is 8%. The market risk premium is 4%. Calculate the cost of equity for Sansa Limited:

IF BETA = 1 IF BETA = 1.3 IF BETA = 0.8

Ke = Rf + β (Rm – Rf) = 8 + 1 (4) = 12% Sansa’s share price will move in line with the market and therefore the Ke = the market rate.

Ke = Rf + β (Rm – Rf) = 8 + 1.3 (4) = 13.2% Sansa’s share price is more volatile than the market. Since the investment is more risky shareholders will require a higher return.

Ke = Rf + β (Rm – Rf) = 8 + 0.8 (4) = 11.2% Sansa’s share price is less volatile than the market. Since the investment is less risky shareholders will require a lower return.

Example 4.2:


Shows you how to select the correct risk-free rate.

Shows you how to select the correct beta.

Shows you how to deal with a situation where you are provided with the market rate / return instead of the market risk premium.

Current yield on R186 RSA bond with expiry date in 5 years: 5%. Current yield on R153 RSA bond with expiry date in 10 years: 8%. The beta for Sansa Limited is 1.3 and the beta for the industry is 0.8. The market rate is 12%. Calculate the cost of equity for Sansa Limited. Ke = Rf + β (Rm – Rf) = 8 + 1.3 (12 - 8) = 13.2%


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Example 4.3:


Shows you how to select the correct risk-free rate.

Shows you how to adjust beta for risk if you are given the beta of a similar company.

The average 5 year government bond yield is 8%. The three month treasury bill rate is 5%. A company similar to Sansa Limited has a beta of 1.2. The auditors have advised that Sansa Limited’s risk profile warrants an 8% premium. The market return is currently 12% per annum. Calculate the cost of equity for Sansa Limited. Beta of Sansa Limited = 1.2 + 8% = 1.3 Ke = Rf + β (Rm – Rf) = 8 + 1.3 (12 - 8) = 13.2%

Example 4.4:

Why is this example important? Includes a discussion around why the cost of equity calculated using Gordon’s Dividend Growth Model is different to the cost of equity calculated using the Capital Asset Pricing Model.

Why would the cost of equity calculated using Gordon’s Dividend Growth Model be different to the cost of equity calculated using the Capital Asset Pricing Model?

GORDON’S DIVIDEND GROWTH MODEL CAPITAL ASSET PRICING MODEL

This calculation is performed using information relating to the specific company.

This calculation is performed using market information and is thus based on market perceptions.

This calculation takes total risk into account.

This calculation only takes systematic risk into account.

This calculation uses the market value of shares which is based on future projections.

This calculation uses beta which is computed on a historical basis.

This calculation uses the market value of shares and the market value is not always a true reflection of the value of the company.


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Example 4.5:

Why is this example important? Shows you how to calculate beta for an unlisted (private) company if you are provided with the beta of a similar listed company as well as the capital structures of both companies.

Samwell (Pty) Ltd is a company operating in the furniture manufacturing industry and is 60% debt funded. Theon Ltd, a company operating in the same industry, is 80% debt funded and has a beta of 0.7. Calculate the beta for Samwell (Pty) Ltd. If you need to calculate beta for an unlisted (private) company you will use a proxy beta of a similar listed company as your starting point. The entities have different capital structures, therefore, first calculate the asset beta of Theon Ltd: β (ungeared / asset beta) = β (geared) x E . E + D(1 – t) = 0.7 x 20 . 20 + 80(0.72) = 0.18 The asset beta (ignoring financial risk) for Theon Ltd is 0.18. Now calculate the equity beta for Samwell (Pty) Ltd: β (geared / equity beta) = β (ungeared) x E + D (1 – t) E = 0.18 x 40 + 60(0.72) 40 = 0.37 The equity beta (taking financial risk into account) of Samwell (Pty) Ltd is 0.37. Why does Samwell (Pty) Ltd have a lower equity beta (0.37) than Theon Ltd (0.7)? Samwell (Pty) Ltd has less debt in its capital structure and is therefore less risky than Theon Ltd.


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PREFERENCE SHARES

Example 5.1:

Why is this example important? Shows you how to calculate the market value of non-redeemable preference shares (PV) when the cost (Kp) is given.

Lannister Limited issued preference shares without par value for a total consideration of R2 000 000 (there are 20 000 shares in issue). These preference shares carry a 15% dividend payable annually in arrears and they are not redeemable. A fair rate of return for preference shares with a similar risk profile is 15.3%. Calculate the market value of the preference shares. This calculation can either be performed in total or per share:

IN TOTAL PER SHARE

PV = D / Kp = (R2 000 000 x 15%) / 15.3% = R1 960 784

Par value per share = R2 000 000 / 20 000 = R100 PV = D / Kp = (R100 x 15%) / 15.3% = R98 x 20 000 = R1 960 000

The difference above is as a result of rounding. Rounding differences will be marked through.


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Example 5.2:

Why is this example important? Shows you how to calculate the cost of non-redeemable preference shares (Kp) when the market value (PV) is given.

Lannister Limited has in issue 15% preference shares with a nominal value of R2 000 000. The shares were issued in 20X5 at R100 per share. The preference shares are not redeemable and are currently trading at R98 each. Calculate the total market value of the preference shares as well as the cost of the preference shares at 31 December 20X8. Number of shares = R2 000 000 / R100 = 20 000 Total market value at 31 December 20X8: R98 x 20 000 = R1 960 000 Cost of the preference shares at 31 December 20X8 (this calculation can either be performed in total or per share):

IN TOTAL PER SHARE

Kp = D / PV = (R2 000 000 x 15%) / 1 960 000 = 15.3%

Kp = D / PV = (R100 x 15%) / 98 = 15.3%


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Example 5.3:

Why is this example important? Shows you how to calculate the cost of redeemable preference shares (Kp) when the market value (PV) is given.

Lannister Limited has in issue 20 000 15% preference shares. The preference shares were issued at R100 per share on 1 October 20X1 are redeemable at a discount of 8% on 30 September 20X7. Calculate the cost of the preference shares at 1 October 20X3 if they are currently trading at R98. 1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

1 OCT

20X3

30 SEP

20X4

30 SEP

20X5

30 SEP

20X6

30 SEP

20X7

Dividends (R100 x 20 000 x 15%) (300 000) (300 000) (300 000) (300 000)

Redemption (R100 x 20 000) - 8% (1 840 000)

Present value (R98 x 20 000) 1 960 000

Total cash flows 1 960 000 (300 000) (300 000) (300 000) (2 140 000)

cfj cfj cfj cfj cfj

i = 14.06% (Kp) 2. SHORTCUT: PMT = R100 x 20 000 x 15% = - 300 000 FV = (R100 x 20 000) - 8% = - 1 840 000 PV = R98 x 20 000 = 1 960 000 n = 4 i = 14.06% (Kp)


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Example 5.4:


Shows you how to calculate the market value of redeemable preference shares (PV) when the cost (Kp) is given.

Shows you how to deal with a missed dividend.

Preference shares were issued at a par value of R100 per share (there are 20 000 shares are in issue). These shares are redeemable in 4 years’ time at a discount of 8%. These preference shares carry a non-cumulative dividend that is payable annually at 15% of the par value. A fair rate of return for similar preference shares with a similar risk profile is currently equal to 18% per annum. The directors expect that all dividends will be declared and paid except for dividends in the final redemption year due to expected cash flow shortages. Calculate the market value of the preference shares. 1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

0 1 2 3 4

Dividends (R100 x 20 000 x 15%) (300 000) (300 000) (300 000) -

Redemption (R100 x 20 000) - 8% (1 840 000)

Total cash flows 0 (300 000) (300 000) (300 000) (1 840 000)

cfj cfj cfj cfj cfj

i = 18% (Kp) NPC = R1 601 333 (market value)

Shortcut cannot be used as annual cash flows (PMT) are not equal (there is no dividend in final year).


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Example 5.5:

Why is this example important? Shows you how to deal with convertible preference shares.

Lannister Limited has 500 000 R2 preference shares in issue with a coupon rate of 12%. The

preference shares are convertible into ordinary shares at a rate of 1 ordinary share for every

8 preference shares in 4 years’ time at the option of the holders. Preference shares not

converted will be redeemed at a premium of 8%. Preference shares in a similar risk class are

yielding 14% per annum. The last dividend declared was 95 cents per share. Lannister Limited

expects annual growth in dividends of 10% per annum, forecast to continue for the

foreseeable future. The cost of equity is 15%.

Calculate the market value of the preference shares.

STEP 1: CALCULATE THE FUTURE VALUE OF EACH ALTERNATIVE (IN FOUR YEARS’ TIME)

1. If the preference shares convert into ordinary shares:

Number of shares = 500 000 / 8 = 62 500

D5 = 95 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 = 153 cents per share

PV = D5 / (Ke – g) = 153 / (15% - 10%)

= 3 060 cents per share / 100 = R30.60 x 62 500 = R1 912 500

Rounding differences will be marked through.

2. If the preference shares are redeemed:

R2 x 500 000 = R1 000 000 + 8% = R1 080 000

The shareholders would select the alternative with the highest value (they would opt for

conversion).


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STEP 2: CALCULATE THE MARKET VALUE OF THE PREFERENCE SHARES

1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

0 1 2 3 4

Dividends (R1 000 000 x 12%) (120 000) (120 000) (120 000) (120 000)

Ordinary shares (1 912 500)

Total cash flows 0 (120 000) (120 000) (120 000) (2 032 500)

cfj cfj cfj cfj cfj

i = 14% (Kp) NPC = R1 481 999 (market value)

2. SHORTCUT:

FV = - 1 912 500

PMT = R1 000 000 x 12% = - 120 000

n = 4

i = 14%

PV = R1 481 999

NOTES:

The above cash flows are discounted at 14% (Kp) because they will still be preference shares for the next 4 years.

In the long-term (from year 5 onwards) the preference shares will be classified as equity (as they will convert) and therefore the cost of equity will be used in the WACC calculation.


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DEBT

Example 6.1:

Why is this example important? Shows you how to calculate the market value of non-redeemable debt (PV) when the cost (Kd) is given.

Daenerys Limited obtained a loan to the value of R4 000 000 two years ago. Interest at a rate of 10% per annum is payable on this loan. The loan is for an indefinite period with no fixed repayment date (i.e. it is non-redeemable). The loan is not publicly traded, however, analysts believe that the effective pre-tax cost is 8% per annum. Calculate the market value of the loan. PV = I / Kd = (R4 000 000 x 10% x 72%) / (8% x 72%) = R288 000 / 5.76% = R5 000 000

Example 6.2:

Why is this example important? Shows you how to calculate the cost of non-redeemable debt (Kd) when the market value (PV) is given.

Daenerys Limited has 100 000 R40 debentures in issue. Interest at 10% is paid annually. The debentures are non-redeemable and are currently trading at R50 each. Calculate the cost of the debentures. This calculation can either be performed in total or per share:

IN TOTAL PER SHARE Nominal value = R40 x 100 000 = R4 000 000 PV (market value) = R50 x 100 000 = R5 000 000 Kd = I / PV = (R4 000 000 x 10% x 72%) / R5 000 000 = R288 000 / R5 000 000 = 5.76% (after tax cost)

Kd = I / PV = (R40 x 10% x 72%) / R50 = R2.88 / R50 = 5.76% (after tax cost)


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Example 6.3:

Why is this example important? Shows you how to calculate the cost of redeemable debentures (Kd) when the market value (PV) is given.

Daenerys Limited issued 100 000 debentures on 1 July 20X2 at an interest rate of 10%. The debentures have a coupon value of R40 each. The debentures are redeemable at a 5% premium on 30 June 20X9. Calculate the cost of the debentures (Kd) at 30 June 20X6 if the current market value is R38 per debenture. 1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

30 JUNE

20X6

30 JUNE

20X7

30 JUNE

20X8

30 JUNE

20X9

Interest (R40 x 100 000 x 10% x 72%) (288 000) (288 000) (288 000)

Redemption (R40 x 100 000) + 5% (4 200 000)

Present value (R38 x 100 000) 3 800 000

Total cash flows 3 800 000 (288 000) (288 000) (4 488 000)

cfj cfj cfj cfj

i = 10.74% (after tax Kd) 2. SHORTCUT: PMT = R40 x 100 000 x 10% x 72% = - 288 000 FV = (R40 x 100 000) + 5% = - 4 200 000 (30 June 20X9) PV = R38 x 100 000 = 3 800 000 (30 June 20X6) n = 3 i = 10.74% (after tax Kd)


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Example 6.4:

Why is this example important? Shows you how to calculate the market value of redeemable debentures (PV) when the cost (Kd) is given.

Daenerys Limited issued 100 000 debentures of R40 each on 1 July 20X2. The debentures are redeemable on 30 June 20X9 at a 5% premium. Interest at a rate of 10% per annum is payable on these debentures. The pre-tax rate on similar debentures is 15%. Calculate the market value of the debentures at 30 June 20X6. 1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

30 JUNE

20X6

30 JUNE

20X7

30 JUNE

20X8

30 JUNE

20X9

Interest (R40 x 100 000 x 10% x 72%) (288 000) (288 000) (288 000)

Redemption (R40 x 100 000) + 5% (4 200 000)

Total cash flows 0 (288 000) (288 000) (4 488 000)

cfj cfj cfj cfj

i = 15% x 72% = 10.8% (Kd) NPC = R3 793 909 (market value) 2. SHORTCUT: PMT = R40 x 100 000 x 10% x 72% = - 288 000 FV = (R40 x 100 000) + 5% = - 4 200 000 (30 June 20X9) n = 3 i = 15% x 75% = 10.8% (Kd) PV = R3 793 909 (30 June 20X6)


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Example 6.5:

Why is this example important? Shows you how to calculate the market value of a loan (PV) when the cost (Kd) is given:

Loan capital and interest is repayable in a single bullet.

Incorporates section 24J of the Income Tax Act.

Daenerys Limited obtained a loan from Eden Bank SA on 1 January 20X3 for an original amount of R1 million. The interest rate on the loan is 1% above the current market-related rate of 8%. The loan capital and interest are repayable in a single bullet payment on 31 December 20X7. The loan qualifies as an instrument and is deductible for tax purposes in terms of section 24J of the Income Tax Act. Calculate the market value of the loan at 31 December 20X4.

If the question is silent you should assume that section 24J is applicable.

STEP 1 - CALCULATE THE CASH FLOWS: Ignore tax and transaction costs in this step!! PV = 1 000 000 (1 January 20X3) i = 8% + 1% = 9% n = 5 PMT = 0 FV = - 1 538 624 (31 December 20X7)

Before we can calculate the market value we need the cash flows!! We applied the same logic to all other sections – the cash flows were just easier to calculate and didn’t require a separate step


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STEP 2 – ANSWER THE REQUIRED (CALCULATE THE MARKET VALUE):

31 DEC

20X4

31 DEC

20X5

31 DEC

20X6

31 DEC

20X7

Bullet payment (1 538 624)

Tax effect of S24J at 28% (C1) 29 940 32 635 35 572

24J accrual amount (A = B x C) 106 929 116 553 127 042

Pre-tax YTM (B) 9% 9% 9%

Adjusted initial amount (C) 1 188 100 1 295 029 1 411 582

Total cash flows 0 29 940 32 635 (1 503 052)

cfj cfj cfj cfj

i = 8% x 72% = 5.76% (Kd) NPC = R1 213 116 (market value) Calculations: C1: Financial calculator: Period 3 Amort = interest of R106 929 x 28% = R29 940 Period 4 Amort = interest of R116 553 x 28% = R32 635 Period 5 Amort = interest of R127 042 x 28% = R35 572 AMORTISATION TABLE:

Opening balance Accrued interest (9%) Annual payment Closing balance

1 000 000 90 000 0 1 090 000

1 090 000 98 100 0 1 188 100 1 188 100 106 929 0 1 295 029

1 295 029 116 553 0 1 411 582

1 411 582 127 042 0 1 538 624

Shortcut cannot be used as annual cash flows (PMT) are not equal.


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Example 6.6:

Why is this example important? Shows you how the calculation changes where are you specifically told to ignore section 24J of the Income Tax Act.

Daenerys Limited obtained a loan from Eden Bank SA on 1 January 20X3 for an original amount of R1 million. The interest rate on the loan is 1% above the current market-related rate of 8%. The loan capital and interest are repayable in a single bullet payment on 31 December 20X7. You can ignore the impact of section 24J of the Income Tax Act in your answer. Calculate the market value of the loan at 31 December 20X4. STEP 1 - CALCULATE THE CASH FLOWS:

Ignore tax and transaction costs in this step!!

PV = 1 000 000 (1 January 20X3) i = 8% + 1% = 9% n = 5 PMT = 0 FV = - 1 538 624 (31 December 20X7) STEP 2 – ANSWER THE REQUIRED (CALCULATE THE MARKET VALUE):

1. USING THE CASH FLOW FUNCTION ON YOUR CALCULATOR:

31 DEC

20X4

31 DEC

20X5

31 DEC

20X6

31 DEC

20X7

Bullet payment (1 538 624)

Tax benefit of interest (538 624 x 28%) 150 815

Total cash flows 0 0 0 (1 387 809)

cfj cfj cfj cfj

i = 8% x 72% = 5.76% (Kd) NPC = R1 173 182 (market value) 2. SHORTCUT:

FV = - 1 387 809 PMT = 0 n = 3 i = 5.76% PV = R1 173 182


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Example 6.7:

Why is this example important? Shows you how the calculation changes when the loan is repayable in equal annual instalments comprising capital and interest.

Daenerys Limited obtained a loan from Eden Bank SA on 1 January 20X3 for an original amount of R1 million. The period of the loan is 5 years and the loan is repayable in equal annual instalments comprising capital and interest. Interest is charged at 9% per annum. The loan is not publicly traded, however, analysts believe that the effective pre-tax cost is 8% per annum. The loan qualifies as an instrument and is deductible for tax purposes in terms of section 24J of the Income Tax Act. Calculate the market value of the loan at 31 December 20X4. STEP 1 - CALCULATE THE CASH FLOWS: Ignore tax and transaction costs in this step!! PV = 1 000 000 (1 January 20X3) n = 5 i = 9% FV = 0 PMT = - 257 092 STEP 2 – ANSWER THE REQUIRED (CALCULATE THE MARKET VALUE):

31 DEC

20X4

31 DEC

20X5

31 DEC

20X6

31 DEC

20X7

Interest & capital payments (257 092) (257 092) (257 092)



Pre-tax YTM (B) 9% 9% 9%

Adjusted initial amount (C) 650 778 452 256 235 867

Total cash flows 0 (240 692) (245 695) (251 115)

cfj cfj cfj cfj

i = 8% x 72% = 5.76% (Kd) NPC = R659 524 (market value)


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Calculations: C1: Financial calculator: Period 3 Amort = interest of R58 570 x 28% = R16 400 Period 4 Amort = interest of R40 703 x 28% = R11 397 Period 5 Amort = interest of R21 228 x 28% = R5 944 AMORTISATION TABLE:

Opening balance Accrued interest (9%) Annual payment Closing balance

1 000 000 90 000 (257 092) 832 908

832 908 74 962 (257 092) 650 778

650 778 58 570 (257 092) 452 256 452 256 40 703 (257 092) 235 867

235 867 21 228 (257 092) 0



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Example 6.8:

Why is this example important? Shows you how the calculation changes when the loan is repayable in bi-annual equal annual instalments comprising capital and interest.

Daenerys Limited obtained a loan from Eden Bank SA on 1 January 20X3 for an original amount of R1 million. The period of the loan is 5 years and the loan is repayable, in arrears, in 10 bi-annual equal instalments comprising capital and interest. The interest rate on the loan is 9% per annum. The rate on similar loans is 8% (this is an annual percentage rate for two repayments per annum). The loan qualifies as an instrument and is deductible for tax purposes in terms of section 24J of the Income Tax Act. Calculate the market value of the loan at 30 June 20X6. STEP 1 - CALCULATE THE CASH FLOWS: Ignore tax and transaction costs in this step!! PV = 1 000 000 (1 January 20X3) n = 5 x 2 = 10 i = 9% / 2 = 4.5% FV = 0 (31 December 20X7) PMT = - 126 379 STEP 2 – ANSWER THE REQUIRED (CALCULATE THE MARKET VALUE):

30 JUNE

20X6

31 DEC

20X6

30 JUNE

20X7

31 DEC

20X7

Interest & capital payments (126 379) (126 379) (126 379)



Pre-tax YTM (B) 4.5% 4.5% 4.5%

Adjusted initial amount (C) 347 409 236 664 120 935

Total cash flows 0 (122 002) (123 397) (124 855)

cfj cfj cfj cfj

i = 8% x 72% = 5.76% / 2 = 2.88% (Kd) NPC = R349 832 (market value) Calculations: C1: Financial calculator: Period 8 Amort = interest of R15 633 x 28% = R4 377 Period 9 Amort = interest of R10 650 x 28% = R2 982 Period 10 Amort = interest of R5 442 x 28% = R1 524


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AMORTISATION TABLE:

Opening balance Accrued interest (4.5%)

Bi-annual payment

Closing balance

1 000 000 45 000 (126 379) 918 621

918 621 41 338 (126 379) 833 560

833 560 37 511 (126 379) 744 712

744 712 33 512 (126 379) 651 845

651 845 29 333 (126 379) 554 799

554 799 24 966 (126 379) 453 386 453 386 20 402 (126 379) 347 409

347 409 15 633 (126 379) 236 664

236 664 10 650 (126 379) 120 935

120 935 5 442 (126 379) 0



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Example 6.9:

Why is this example important? Shows you how to deal with convertible debentures.

Three years ago Daenerys Limited issued 100 000 convertible debentures with a total nominal value of R6 000 000. Interest is paid at a rate of 12% compared to the market return of 10% for similar debentures. The debentures mature in 3 years’ time with the following options available to the company:

Redeem the debentures at a 10% premium.

Convert the debentures into ordinary shares at a rate of 1 ordinary share for every 5 debentures held. The directors anticipate that one ordinary share will be worth R120 in 3 years’ time.

Convert the debentures into new debentures with the same nominal value. The new debentures will be redeemed 5 years after issue at a premium of 5%. Interest will be paid at a rate of 14% per annum.

Debentures will continue as indefinite debentures at 8% per annum.

Calculate the current market value of the debentures. STEP 1: CALCULATE THE FUTURE VALUE OF EACH ALTERNATIVE (IN THREE YEARS’ TIME)

1. Redeem the debentures at a 10% premium:

R6 000 000 + 10% = R6 600 000

2. Convert the debentures into ordinary shares: Number of shares = 100 000 / 5 = 20 000

Value = R120 x 20 000 = R2 400 000

3. Convert the debentures into new debentures:

FV = R6 000 000 + 5% = - 6 300 000

n = 5

PMT = R6 000 000 x 14% x 72% = - 604 800

i = 10% x 72% = 7.2%

PV = R6 916 644

4. Indefinite debentures:

PV = I / Kd = (R6 000 000 x 8% x 72%) / (10% x 72%)

= R4 800 000

The company will select the alternative with the lowest cost (convert the debentures into

ordinary shares).


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STEP 2: CALCULATE THE MARKET VALUE OF THE DEBENTURES

FV = - 2 400 000

n = 3

i = 10% x 72% = 7.2%

PMT = R6 000 000 x 12% x 72% = - 518 400

PV = R3 303 660

As an alternative you can use the cash flow function on your calculator instead of the above shortcut.

NOTES:

The above cash flows are discounted at 7.2% (Kd) because they will still be debentures for the next 3 years.

In the long-term (from year 4 onwards) the debentures will be classified as equity (as they will convert) and therefore the cost of equity will be used in the WACC calculation.


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WEIGHTED AVERAGE COST OF CAPITAL (WACC)

Example 7.1:

Why is this example important? Shows you how the market value of equity is calculated where both the issue price and current market value are provided.

Equity consists of 100 000 ordinary shares issued at 150 cents per share plus accumulated reserves. The shares are currently trading at 250 cents per share. Calculate the market value of equity. Market value = 100 000 x 250/100 = R250 000

Example 7.2:

Why is this example important? Shows you how the market value of equity is calculated where you are provided with authorised and issued shares as well as other capital reserves.

Equity consists of:

1 000 000 authorised shares with 400 000 shares currently in issue. The current share price is 680 cents per share.

Retained income: R250 000

Non-distributable reserves: R100 000 Calculate the market value of equity. Market value = 400 000 x 680/100 = R2 720 000


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Example 7.3:

Why is this example important? Shows you how to calculate the WACC if the target capital structure is provided.

Stark Limited has the following target capital structure: Equity 40% Preference shares 25% Debt 35% Assume that you calculated the following costs: Equity (Ke) 25% Preference shares (Kp) 18% Debt (Kd) - after tax 12% Calculate the weighted average cost of capital:

Weighting Cost WACC

Equity 40% 25% 10% Preference shares 25% 18% 4.5% Debt 35% 12% 4.2%

100% 18.7%

Example 7.4:

Why is this example important? Shows you how to calculate the WACC if the target capital structure is not provided.

Assume that you calculated the following for Snow Limited:

Cost Market value Equity 25% R400 000 Preference shares 18% R250 000 Debt 12% (after tax) R350 000

Market value Weighting Cost WACC

Equity R400 000 40% 25% 10% Preference shares R250 000 25% 18% 4.5% Debt R350 000 35% 12% 4.2%

R1 000 000 100% 18.7%


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Example 7.5:

Why is this example important? Shows you how to calculate the WACC if preference shares are going to convert into ordinary shares.

Bran Limited has the following target capital structure: Equity 40% Preference shares 25% Debt 35% Assume that you calculated the following costs: Equity (Ke) 25% Preference shares (Kp) 18% Debt (Kd) - after tax 12% The preference shares will convert into ordinary shares in 3 years’ time. Calculate the weighted average cost of capital:

Weighting Cost WACC

Equity 40% 25% 10% Preference shares 25% 25% 6.25% Debt 35% 12% 4.2% 100% 20.45%

Therefore the WACC = 20.45%.


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Example 7.6:

Why is this example important? Shows you how to work backwards and calculate the cost of a specific type of finance if the WACC has been provided.

Arya Limited has a weighted average cost of capital of 18%. The market value of equity is R1 500 000 and the market value of debt is R900 000. The cost of equity is 24%. Calculate the cost of debt. There is not enough information to calculate the cost of debt directly and you are therefore required to work backwards in this example:

Market value Weighting

Equity R1 500 000 62.5% Debt R900 000 37.5%

R2 400 000 100%

Therefore working backwards:

Market value Weighting Cost WACC

Equity R1 500 000 62.5% 24% 15% (C1) Debt R900 000 37.5% 8% (C3) 3% (C2)

R2 400 000 100% 18% Calculations: C1: 24 x 62.5% = 15% C2: 18% - 15% = 3% C3: 3 / 37.5% = 8% (proof: 8 x 37.5% = 3%) Therefore the cost of debt is 8%.


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Example 7.7:

Why is this example important? Shows you how to calculate the target and actual WACC, explain the reason for the difference and methods to align the actual WACC with the target WACC.

The target debt: equity ratio is 60:40 The required return on equity is 24% The targeted cost of debt is 13% after tax You have also calculated the following:

Cost Market value

Equity 26% R1 500 000 Debt 12% (after tax) R900 000

Calculate the target and actual WACC for Tarly Limited based on the information provided. If the question is asked in this way you should perform the calculation as follows: Target WACC:

Weighting Cost WACC

Equity 40% 24% 9.6% Debt 60% 13% 7.8%

100% 17.4% Actual WACC:

Market value Weighting Cost WACC Equity R1 500 000 62.5% 26% 16.25% Debt R900 000 37.5% 12% 4.5% R2 400 000 100% 20.75%

Explain the reason for the difference and methods to align the actual WACC with the target WACC. Reason for the difference:

Current debt: equity ratio is 37.5: 62.5

Target debt: equity ratio is 60: 40

Tarly Limited currently has too much equity in their capital structure when compared to the target.

The cost of equity is higher than the cost of debt and therefore the actual WACC is higher than the target WACC.


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Methods to align the actual WACC with the target WACC:

A position of temporary disequilibrium is normal. However, Tarly Limited should strive to move towards the target: o Tarly Limited should take on more debt (future projects should be financed using

debt). o Alternatively Tarly Limited should reduce the amount of equity capital. This could be

done through a share buyback.

This will cause the WACC to decrease because debt is cheaper than equity.

cost of capital lecture examples

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