Dde 321 - Solutions Exercise 1
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Advanced Corporate Finance
Leonidas Rompolis
EXERCISES -1 (SOLUTIONS) 1. NPV = −$1,300,000 + ($1,500,000/1.10) = +$63,636 Since the NPV is positive, you would construct the motel.
2. a. Expected cash flow (Project B) = ($4 million + $6 million + $8 million)/3 Expected cash flow (Project B) = $6 million Expected cash flow (Project C) = ($5 million + $5.5 million + $6 million)/3 Expected cash flow (Project C) = $5.5 million b. Expected rate of return (Stock X) = ($110/$95.65) –1 = 0.15 = 15.0% Expected rate of return (Stock Y) = ($44/$40) –1 = 0.10 = 10.0% Expected rate of return (Stock Z) = ($12/$10) –1 = 0.20 = 20.0% c. Percentage Differences Slump v. Normal Boom v. Normal Project B 4/6 = 66.67% 8/6 = 133.33% Project C 5/5.5 = 90.91% 6/5.5 = 109.09% Stock X 80/110 = 72.73% 140/110 = 127.27% Stock Y 40/44 = 90.91% 48/44 = 109.09% Stock Z 8/12 = 66.67% 16/12 = 133.33% Project B has the same risk as Stock Z, so the cost of capital for Project B is 20%. Project C has the same risk as Stock Y, so the cost of capital for Project C is 10%. d. NPV (Project B) = −$5,000,000 + ($6,000,000/1.20) = 0 NPV (Project C) = −$5,000,000 + ($5,500,000/1.10) = 0 e. The two projects will add nothing to the total market value of the company’s shares.
2.3 2.6 2.8 3.0 3.1 2.9 + + + + + = 1.57 , 2 3 4 5 1.06 1.06 1.06 1.06 1.06 1.066 should be accepted.
3. NPV = −12 +
and the project
⎡1 1 ⎤ 4. PV = C ⎢ − ⇒ 500, 000 = C × 9.7122 ⇒ C = 51, 481 t ⎥ ⎣ r r(1 + r) ⎦ C 51, 481 PV = = = 858, 023 r 0.06
5. a. PV =
C 2, 000, 000 = = 14, 285, 714 r + g 0.1 + 0.04
1
Advanced Corporate Finance
Leonidas Rompolis
⎡ 1 1 (1 − 0.04) 20 ⎤ − = 13,347,131 b. PV = 2, 000, 000 ⎢ 20 ⎥ ⎣ 0.1 + 0.04 0.1 + 0.04 (1 + 0.1) ⎦
6.
After one year: FVA = $1,000 × (1 + 0.12)1 = $1,120 FVB = $1,000 × (1 + 0.0585)2 = $1,120.4 FVC = $1,000 × e(0.115 × 1) = $1,121.9 After five years: FVA = $1,000 × (1 + 0.12)5 = $1,762.3 FVB = $1,000× (1 + 0.0585)10= $1,765.7 FVC = $1,000 × e(0.115 × 5) = $1,777.1 After twenty years: FVA = $1,000 × (1 + 0.12)20 = $9,646.3 FVB = $1,000 × (1 + 0.0585)40= $9,719.3 FVC = $1,000 × e(0.115 × 20) = $9,974.2 The preferred investment is C.
7. a. NPVA = 39.06, IRRA = 19.71% and NPVB = 54.96, IRRB = 15.97%. The better investment is B. b. NPVA = 5.38, IRRA = 19.71% and NPVB = -13.74, IRRB = 15.97%. The better investment is A.
8. 1000
NPV
500
-0.40
-0.20
0 0.00 -500
0.20
0.40
0.60 NPV
-1000 -1500 -2000 Discount rates
The IRR are -17.5% and 45.5%. If the OCC lies between these two values the NPV is positive
2
Leonidas Rompolis
EXERCISES -1 (SOLUTIONS) 1. NPV = −$1,300,000 + ($1,500,000/1.10) = +$63,636 Since the NPV is positive, you would construct the motel.
2. a. Expected cash flow (Project B) = ($4 million + $6 million + $8 million)/3 Expected cash flow (Project B) = $6 million Expected cash flow (Project C) = ($5 million + $5.5 million + $6 million)/3 Expected cash flow (Project C) = $5.5 million b. Expected rate of return (Stock X) = ($110/$95.65) –1 = 0.15 = 15.0% Expected rate of return (Stock Y) = ($44/$40) –1 = 0.10 = 10.0% Expected rate of return (Stock Z) = ($12/$10) –1 = 0.20 = 20.0% c. Percentage Differences Slump v. Normal Boom v. Normal Project B 4/6 = 66.67% 8/6 = 133.33% Project C 5/5.5 = 90.91% 6/5.5 = 109.09% Stock X 80/110 = 72.73% 140/110 = 127.27% Stock Y 40/44 = 90.91% 48/44 = 109.09% Stock Z 8/12 = 66.67% 16/12 = 133.33% Project B has the same risk as Stock Z, so the cost of capital for Project B is 20%. Project C has the same risk as Stock Y, so the cost of capital for Project C is 10%. d. NPV (Project B) = −$5,000,000 + ($6,000,000/1.20) = 0 NPV (Project C) = −$5,000,000 + ($5,500,000/1.10) = 0 e. The two projects will add nothing to the total market value of the company’s shares.
2.3 2.6 2.8 3.0 3.1 2.9 + + + + + = 1.57 , 2 3 4 5 1.06 1.06 1.06 1.06 1.06 1.066 should be accepted.
3. NPV = −12 +
and the project
⎡1 1 ⎤ 4. PV = C ⎢ − ⇒ 500, 000 = C × 9.7122 ⇒ C = 51, 481 t ⎥ ⎣ r r(1 + r) ⎦ C 51, 481 PV = = = 858, 023 r 0.06
5. a. PV =
C 2, 000, 000 = = 14, 285, 714 r + g 0.1 + 0.04
1
Advanced Corporate Finance
Leonidas Rompolis
⎡ 1 1 (1 − 0.04) 20 ⎤ − = 13,347,131 b. PV = 2, 000, 000 ⎢ 20 ⎥ ⎣ 0.1 + 0.04 0.1 + 0.04 (1 + 0.1) ⎦
6.
After one year: FVA = $1,000 × (1 + 0.12)1 = $1,120 FVB = $1,000 × (1 + 0.0585)2 = $1,120.4 FVC = $1,000 × e(0.115 × 1) = $1,121.9 After five years: FVA = $1,000 × (1 + 0.12)5 = $1,762.3 FVB = $1,000× (1 + 0.0585)10= $1,765.7 FVC = $1,000 × e(0.115 × 5) = $1,777.1 After twenty years: FVA = $1,000 × (1 + 0.12)20 = $9,646.3 FVB = $1,000 × (1 + 0.0585)40= $9,719.3 FVC = $1,000 × e(0.115 × 20) = $9,974.2 The preferred investment is C.
7. a. NPVA = 39.06, IRRA = 19.71% and NPVB = 54.96, IRRB = 15.97%. The better investment is B. b. NPVA = 5.38, IRRA = 19.71% and NPVB = -13.74, IRRB = 15.97%. The better investment is A.
8. 1000
NPV
500
-0.40
-0.20
0 0.00 -500
0.20
0.40
0.60 NPV
-1000 -1500 -2000 Discount rates
The IRR are -17.5% and 45.5%. If the OCC lies between these two values the NPV is positive
2
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