Dde 321 - Solutions Exercise 5
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Dde 321 - Solutions Exercise 5 as PDF for free.
More details
- Words: 784
- Pages: 3
Advanced Corporate Finance
Leonidas Rompolis
EXERCISES -5 (SOLUTIONS) 4. We make three adjustments to the balance sheet: • Ignore deferred taxes; this is an accounting entry and represents neither a liability nor a source of funds • ‘Net out’ accounts payable against current assets • Use the market value of equity (7.46 million x $46) Now the right-hand side of the balance sheet (in thousands) is: Short-term debt Long-term debt Shareholders’ equity Total
$75,600 208,600 343,160 $627,360
The after-tax weighted-average cost of capital formula, with one element for each source of funding, is: WACC = (1 − τc )rDL
D DL E + (1 − τc )rDS S + rE V V V
WACC = [0.06×(1 – 0.35)×(75,600/627,360)]+[0.08×(1 –0.35)×(208,600/627,360)] + [0.15×(343,160/627,360)] = 0.004700 + 0.017290 + 0.082049 = 0.1040 = 10.40%
5. Assume that short-term debt is temporary. From Practice Question 4: Long-term debt Share holder equity Total
$208,600 343,160 $551,760
Therefore: D/V = $208,600/$551,760 = 0.378 E/V = $343,160/$551,760 = 0.622 Step 1: r = rD (D/V) + rE (E/V) = (0.08 × 0.378) + (0.15 × 0.622) = 0.1235 Step 2: rE = r + (r – rD) (D/E) = 0.1235 + (0.1235 – 0.08) × (0.403) = 0.1410 Step 3: WACC = [rD × (1 – TC) × (D/V)] + [rE × (E/V)] = (0.08 × 0.65 × 0.287) + (0.1410 × 0.713) = 0.1155 = 11.55%
1
Advanced Corporate Finance
Leonidas Rompolis
6. Base case NPV = –$1,000 + ($600/1.12) + ($700/1.122) = $93.75 or $93,750 The dept outstanding at the beginning of year 1 is $300,000 and at the beginning of year 2 is $150,000. The interest paid the 1st year is 300,000 × 0.08 = $24,000 while that paid the 2nd year is 150,000 × 0.08 = $12,000. The interest tax shield is 24,000 × 0.3 = $7,200 for the 1st year and 12,000 × 0.3 = $3,600 for the second year. The present values of these two tax shields are: 7.2 = 6.67 1.08 3.6 PV2 = = 3.09 1.082
PV1 =
Therefore, APV = $93.75 + $6.67 + $3.09 = 103.5 or $103,500
7.
a.
Base-case NPV = –$1,000,000 + ($85,000/0.10) = –$150,000 PV(tax shields) = 0.35 × $400,000 = $140,000 APV = –$150,000 + $140,000 = –$10,000
b.
PV(tax shields, approximate) = (0.35 × 0.07 × $400,000)/0.10 = $98,000 APV = -$150,000 + $98,000 = –$52,000
The present value of the tax shield is higher when the debt is fixed and therefore the tax shield is certain. When borrowing a constant proportion of the market value of the project, the interest tax shields are as uncertain as the value of the project, and therefore must be discounted at the project’s opportunity cost of capital. 13. a. Assume that the expected future Treasury-bill rate is equal to the 20-year Treasury bond rate (5.2%) less the average historical premium of Treasury bonds over Treasury bills (1.8%), so that the risk-free rate (rf) is 3.4%. Also assume that the market risk premium (rm – rf) is 8%. Then, using the CAPM, we find rE as follows: rE = rf + βA × [rm – rf] = 3.4% + (0.46 × 8%) = 7.08% Market value of equity (E) is equal to: 324.5 × $40.59 = $13,171.5 so that: V = $2,327 + $13,171.5 = $15,498.5 D/V = $2,327/$15,498.5 = 0.150
2
Advanced Corporate Finance
Leonidas Rompolis
E/V = $13,171.5/$15,498.5 = 0.850 WACC = (0.850 × 7.08%) + (0.150 × 0.65 × 7.0%) = 6.70% b. The opportunity cost of capital is: r = rD × (D/V) + rE × (E/V) = 7.0% × 0.150 + 7.08% × 0.850 = 7.07%
14.
1. 2. 3. 4. 5. 6. 7. 8.
Sales Cost of Goods Sold Other Costs EBITDA (1 – 2 – 3) Depreciation and Amortization EBIT (Pretax profit) (4 – 5) Tax at 35% Profit after tax (6 – 7)
9.
Investment (change in Gross PP&E) Change in working capital Free Cash Flow (8 + 5 – 9 – 10)
10. 11.
PV Free cash flow, years 1-4 PV Horizon value PV of company
Latest year 0 40,123.0 22,879.0 8,025.0 9,219.0 5,678.0 3,541.0 1,239.4 2,301.7
1 36,351.0 21,678.0 6,797.0 7,876.0 5,890.0 1,986.0 695.1 1,290.9
2 30,155.0 17,560.0 5,078.0 7,517.0 5,670.0 1,847.0 646.5 1,200.6
Forecast 3 28,345.0 16,459.0 4,678.0 7,208.0 5,908.0 1,300.0 455.0 845.0
4 29,982.0 15,631.0 4,987.0 9,364.0 6,107.0 3,257.0 1,140.0 2,117.1
5 30,450.0 14,987.0 5,134.0 10,329.0 5,908.0 4,421.0 1,547.4 2,873.7
6,547.0
7,345.0
5,398.0
5,470.0
6,420.0
6,598.0
784.0 648.7
-54.0 -110.1
-342.0 1,814.6
3,501.6 15,480.0 18,981.7
-245.0 1,528.0
127.0 1,677.1
235.0 1,948.7
Horizon value in year 4 24,358.1
The total value of the equity is: $18,981.7 – $5,000 = $13,981.7 Value per share = $13,981.7/865 = $16.16
3
Leonidas Rompolis
EXERCISES -5 (SOLUTIONS) 4. We make three adjustments to the balance sheet: • Ignore deferred taxes; this is an accounting entry and represents neither a liability nor a source of funds • ‘Net out’ accounts payable against current assets • Use the market value of equity (7.46 million x $46) Now the right-hand side of the balance sheet (in thousands) is: Short-term debt Long-term debt Shareholders’ equity Total
$75,600 208,600 343,160 $627,360
The after-tax weighted-average cost of capital formula, with one element for each source of funding, is: WACC = (1 − τc )rDL
D DL E + (1 − τc )rDS S + rE V V V
WACC = [0.06×(1 – 0.35)×(75,600/627,360)]+[0.08×(1 –0.35)×(208,600/627,360)] + [0.15×(343,160/627,360)] = 0.004700 + 0.017290 + 0.082049 = 0.1040 = 10.40%
5. Assume that short-term debt is temporary. From Practice Question 4: Long-term debt Share holder equity Total
$208,600 343,160 $551,760
Therefore: D/V = $208,600/$551,760 = 0.378 E/V = $343,160/$551,760 = 0.622 Step 1: r = rD (D/V) + rE (E/V) = (0.08 × 0.378) + (0.15 × 0.622) = 0.1235 Step 2: rE = r + (r – rD) (D/E) = 0.1235 + (0.1235 – 0.08) × (0.403) = 0.1410 Step 3: WACC = [rD × (1 – TC) × (D/V)] + [rE × (E/V)] = (0.08 × 0.65 × 0.287) + (0.1410 × 0.713) = 0.1155 = 11.55%
1
Advanced Corporate Finance
Leonidas Rompolis
6. Base case NPV = –$1,000 + ($600/1.12) + ($700/1.122) = $93.75 or $93,750 The dept outstanding at the beginning of year 1 is $300,000 and at the beginning of year 2 is $150,000. The interest paid the 1st year is 300,000 × 0.08 = $24,000 while that paid the 2nd year is 150,000 × 0.08 = $12,000. The interest tax shield is 24,000 × 0.3 = $7,200 for the 1st year and 12,000 × 0.3 = $3,600 for the second year. The present values of these two tax shields are: 7.2 = 6.67 1.08 3.6 PV2 = = 3.09 1.082
PV1 =
Therefore, APV = $93.75 + $6.67 + $3.09 = 103.5 or $103,500
7.
a.
Base-case NPV = –$1,000,000 + ($85,000/0.10) = –$150,000 PV(tax shields) = 0.35 × $400,000 = $140,000 APV = –$150,000 + $140,000 = –$10,000
b.
PV(tax shields, approximate) = (0.35 × 0.07 × $400,000)/0.10 = $98,000 APV = -$150,000 + $98,000 = –$52,000
The present value of the tax shield is higher when the debt is fixed and therefore the tax shield is certain. When borrowing a constant proportion of the market value of the project, the interest tax shields are as uncertain as the value of the project, and therefore must be discounted at the project’s opportunity cost of capital. 13. a. Assume that the expected future Treasury-bill rate is equal to the 20-year Treasury bond rate (5.2%) less the average historical premium of Treasury bonds over Treasury bills (1.8%), so that the risk-free rate (rf) is 3.4%. Also assume that the market risk premium (rm – rf) is 8%. Then, using the CAPM, we find rE as follows: rE = rf + βA × [rm – rf] = 3.4% + (0.46 × 8%) = 7.08% Market value of equity (E) is equal to: 324.5 × $40.59 = $13,171.5 so that: V = $2,327 + $13,171.5 = $15,498.5 D/V = $2,327/$15,498.5 = 0.150
2
Advanced Corporate Finance
Leonidas Rompolis
E/V = $13,171.5/$15,498.5 = 0.850 WACC = (0.850 × 7.08%) + (0.150 × 0.65 × 7.0%) = 6.70% b. The opportunity cost of capital is: r = rD × (D/V) + rE × (E/V) = 7.0% × 0.150 + 7.08% × 0.850 = 7.07%
14.
1. 2. 3. 4. 5. 6. 7. 8.
Sales Cost of Goods Sold Other Costs EBITDA (1 – 2 – 3) Depreciation and Amortization EBIT (Pretax profit) (4 – 5) Tax at 35% Profit after tax (6 – 7)
9.
Investment (change in Gross PP&E) Change in working capital Free Cash Flow (8 + 5 – 9 – 10)
10. 11.
PV Free cash flow, years 1-4 PV Horizon value PV of company
Latest year 0 40,123.0 22,879.0 8,025.0 9,219.0 5,678.0 3,541.0 1,239.4 2,301.7
1 36,351.0 21,678.0 6,797.0 7,876.0 5,890.0 1,986.0 695.1 1,290.9
2 30,155.0 17,560.0 5,078.0 7,517.0 5,670.0 1,847.0 646.5 1,200.6
Forecast 3 28,345.0 16,459.0 4,678.0 7,208.0 5,908.0 1,300.0 455.0 845.0
4 29,982.0 15,631.0 4,987.0 9,364.0 6,107.0 3,257.0 1,140.0 2,117.1
5 30,450.0 14,987.0 5,134.0 10,329.0 5,908.0 4,421.0 1,547.4 2,873.7
6,547.0
7,345.0
5,398.0
5,470.0
6,420.0
6,598.0
784.0 648.7
-54.0 -110.1
-342.0 1,814.6
3,501.6 15,480.0 18,981.7
-245.0 1,528.0
127.0 1,677.1
235.0 1,948.7
Horizon value in year 4 24,358.1
The total value of the equity is: $18,981.7 – $5,000 = $13,981.7 Value per share = $13,981.7/865 = $16.16
3
Related Documents
Dde 321 - Solutions Exercise 5
June 2020 4
Dde 321 - Solutions Exercise 2
June 2020 0
Dde 321 - Solutions Exercise 3
June 2020 0
Dde 321 - Solutions Exercise 1
June 2020 2
Dde 321 - Solutions Exercise 4
June 2020 0