Concept explainers
a.
To determine: Expected present value,
a.
Explanation of Solution
Table that shows the calculation of the expected present values of the cash flow is as follows:
Condition | Probability | Cash Flows ($) | Present value ($) |
Good | 30% | 9 | 2.70 |
Medium | 40% | 4 | 1.60 |
Bad | 30% | -1 | -0.30 |
Expected present value | 4 |
Table (1)
Table that shows calculation of the Net present value is as follows:
Particulars | Cash Flow | Present value factor | Present value |
Initial Cost (A) | 4 | 1 | 4 |
Cash Flows: (B) | |||
Year 1 | 4 | 0.893 | 3.572 |
Year 2 | 4 | 0.797 | 3.188 |
Year 3 | 4 | 0.711 | 2.844 |
NPV | 0.396 |
Table (2)
b.
To decide: If the project should be accepted with the scrap value of $6 million and cash flow in first year only.
b.
Explanation of Solution
Table that shows calculation of the NPV with current scenario is as follows:
Cost | Probability | Future cash flows | NPV | |||
1 ($) | 2 ($) | 3 ($) | ||||
-$10 | 30% | 9 | 9 | 9 | 11.62 | 3.48 |
40% | 4 | 4 | 4 | -0.39 | -0.16 | |
30% | 5 | -5.54 | -1.66 | |||
Expected NPV of future Cash flows | 1.67 |
Table (3)
With the abandonment factor, the expected NPV becomes positive but NPV of medium is negative but higher than the NPV of the medium factor if the project will be abandoned in the year 1 itself.
c.
Estimate: The value of the project.
c.
Explanation of Solution
Table that shows calculation of the Expected NPV is as follows:
Cost | Future operating cash flows | NPV ($) | |||||||
0 | Probability | 1 ($) | 2 ($) | 3 ($) | 4 ($) | 5 ($) | 6 ($) | ||
-10 | 30% | 9 | 9 | 9 | 9 | 9 | 9 | 27 | 8.10 |
40% | 4 | 4 | 4 | 0 | 0 | 0 | -0.39 | -0.16 | |
30% | -1 | -1 | -1 | 0 | 0 | 0 | -12.40 | -3.72 | |
Expected NPV | 4.22 |
Table (4)
Table that shows calculation of expected NPV after the implementation of additional project is as follows:
Future operating cash flows | NPV ($) | ||||||||
0 | Probability | 1 ($) | 2 ($) | 3 ($) | 4 ($) | 5 ($) | 6 ($) | ||
30% | 0 | 0 | -10 | 0 | 0 | 0 | -8.40 | -2.52 | |
40% | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
30% | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Expected NPV | -2.52 |
Table (5)
Total of the NPV of the future operating cash flows and NPV after the implementation of additional project is $1.70.
Hence, as with the additional project the NPV gets positive, therefore, the project with additional projects should be accepted.
d.
Estimate: The value of the project if it is delayed for one year.
d.
Explanation of Solution
Table that shows calculation of expected NPV of future cash flows with risk-free rate of 6% and WACC of 12% is as follows:
Future operating cash flows | NPV ($) | ||||||
0 | Probability | 1 ($) | 2 ($) | 3 ($) | 4 ($) | ||
Cost | |||||||
30% | 9 | 9 | 9 | 21.62 | 6.48 | ||
40% | 0 | 0 | 0 | 0 | 0 | ||
30% | 0 | 0 | 0 | 0 | 0 | ||
Expected NPV | 6.48 |
Table (6)
Future operating cash flows | NPV ($) | ||||||
0 | Probability | 1 ($) | 2 ($) | 3 ($) | 4 ($) | ||
Cost | |||||||
30% | 0 | 0 | 0 | -9.43 | -2.83 | ||
40% | 0 | 0 | 0 | 0 | 0 | ||
30% | 0 | 0 | 0 | 0 | 0 | ||
Expected NPV | -2.83 |
Table (7)
Total of both the expected NPV is $3.65, which is positive; hence, the project should be accepted without any delaying 1 year.
e.
Estimate: The value of the growth option using Black-Scholes model.
e.
Explanation of Solution
Table that shows calculation of the expected NPV is as follows:
Cost | Future operating cash flows | NPV ($) | |||||||
0 | Probability | 1 ($) | 2 ($) | 3 ($) | 4 ($) | 5 ($) | 6 ($) | ||
30% | 0 | 0 | 0 | 9 | 9 | 9 | 15.39 | 4.62 | |
40% | 0 | 0 | 0 | 4 | 4 | 4 | 6.84 | 2.74 | |
30% | 0 | 0 | 0 | -1 | -1 | -1 | -1.71 | -0.51 | |
Expected NPV | 6.84 |
Table (8)
Formula to calculate total value is as follows:
Substituting the equation with $6.84 for P, 0.56 for N(d1), 0.26 for N(d2) and $10.00 for X to calculate value of growth option.
Formula to calculate total value is as follows:
Substituting the Equation with -$0.39 for the value of original project and $1.71 for the value of growth option to calculate total value.
Hence, the project should be accepted even if the value of original project is negative; as the total value with the growth option is greater than 0.
Working Note:
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