Bundle: Financial Management: Theory & Practice, 16th + MindTap, 1 term Printed Access Card
Bundle: Financial Management: Theory & Practice, 16th + MindTap, 1 term Printed Access Card
16th Edition
ISBN: 9780357252673
Author: Brigham, Eugene F., EHRHARDT, Michael C.
Publisher: Cengage Learning
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Chapter 26, Problem 9SP

a.

Summary Introduction

To determine: Expected present value, NPV and the coefficient of variation of the present value.

a.

Expert Solution
Check Mark

Explanation of Solution

Table that shows the calculation of the expected present values of the cash flow is as follows:

ConditionProbabilityCash Flows ($)Present value ($)
Good30%92.70
Medium40%41.60
Bad30%-1-0.30
Expected present value  4

Table (1)

Table that shows calculation of the Net present value is as follows:

ParticularsCash FlowPresent value factorPresent value
Initial Cost (A)414
Cash Flows: (B)   
Year 140.8933.572
Year 240.7973.188
Year 340.7112.844
NPV (A)(B)  0.396

Table (2)

b.

Summary Introduction

To decide: If the project should be accepted with the scrap value of $6 million and cash flow in first year only.

b.

Expert Solution
Check Mark

Explanation of Solution

Table that shows calculation of the NPV with current scenario is as follows:

CostProbabilityFuture cash flowsNPVProbability×NPV
  1 ($)2 ($)3 ($)  
-$1030%99911.623.48
40%444-0.39-0.16
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.

Summary Introduction

Estimate: The value of the project.

c.

Expert Solution
Check Mark

Explanation of Solution

Table that shows calculation of the Expected NPV is as follows:

Cost Future operating cash flowsNPV ($)Probability×NPV ($)
0Probability1 ($)2 ($)3 ($)4 ($)5 ($)6 ($)  
-1030%999999278.10
40%444000-0.39-0.16
30%-1-1-1000-12.40-3.72
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 flowsNPV ($)Probability×NPV ($)
0Probability1 ($)2 ($)3 ($)4 ($)5 ($)6 ($)  
 30%00-10000-8.40-2.52
40%00000000
30%00000000
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.

Summary Introduction

Estimate: The value of the project if it is delayed for one year.

d.

Expert Solution
Check Mark

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 flowsNPV ($)Probability×NPV ($)
0Probability1 ($)2 ($)3 ($)4 ($)  
  Cost     
 30% 99921.626.48
40% 00000
30% 00000
Expected NPV     6.48

Table (6)

  Future operating cash flowsNPV ($)Probability×NPV ($)
0Probability1 ($)2 ($)3 ($)4 ($)  
  Cost     
 30% 000-9.43-2.83
40% 00000
30% 00000
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.

Summary Introduction

Estimate: The value of the growth option using Black-Scholes model.

e.

Expert Solution
Check Mark

Explanation of Solution

Table that shows calculation of the expected NPV is as follows:

Cost Future operating cash flowsNPV ($)Probability×NPV ($)
0Probability1 ($)2 ($)3 ($)4 ($)5 ($)6 ($)  
 30%00099915.394.62
40%0004446.842.74
30%000-1-1-1-1.71-0.51
Expected NPV       6.84

Table (8)

Formula to calculate total value is as follows:

V=P[N(d1)]XerRFt[N(d2)]

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.

V=P[N(d1)]XerRFt[N(d2)]=$6.84(0.56)$10e0.06×3(0.26)=$1.71

Formula to calculate total value is as follows:

Total Value=Value of original project+Value of growth option

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.

Total Value=$0.39+$1.71=$1.31

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:

d1={In(PX)+[rRF+σ22]t}σ(t12)=0.160

d2=d1σ(t12)=0.65

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