You are a consultant to a large manufacturing corporation considering a project
ID: 1174531 • Letter: Y
Question
You are a consultant to a large manufacturing corporation considering a project with the following net after-tax cash flows (in millions of dollars):
The project's beta is 1.6. Assuming rf = 4% and E(rM) = 14%
a. What is the net present value of the project? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)
b. What is the highest possible beta estimate for the project before its NPV becomes negative? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
YEARS FROM NOW AFTER TAX CF 0 -27 1-9 16 10 32Explanation / Answer
a. NPV = $42.66
Working:
For calculating the NPV we should know cost of capital or discounting rate.
We can use CAPM equation to get Cost of capital or equity.
.
Cost of equity or discount rate = Risk-free rate + Beta x (Market return - Risk-free rate)
Cost of equity or discount rate =4%+1.6*(14%-4%)
Cost of equity or discount rate = 20.00%
Now, we can calculate the NPV:
NPV working below:
Discount rate = WACC = R = 20%
Present Values
Year
Cash flows
Discount factor or PV factors = Df = 1/(1+R)^Year
PV of cash flows = Cash flows x Df
0
-$27.00
1.000000
-$27.00
1
$16.00
0.833333
$13.33
2
$16.00
0.694444
$11.11
3
$16.00
0.578704
$9.26
4
$16.00
0.482253
$7.72
5
$16.00
0.401878
$6.43
6
$16.00
0.334898
$5.36
7
$16.00
0.279082
$4.47
8
$16.00
0.232568
$3.72
9
$16.00
0.193807
$3.10
10
$32.00
0.161506
$5.17
Total of Present values = NPV =
$42.66
b. Beta = 5.50
Working:
IRR is the rate where NPV becomes Zero hence it is a point before negative NPV hence, lets calculate IRR.
IRR is obtained with trial error and we keep trying different values for IRR where we get NPV = 0
Working for Zero NPV at IRR = 59.024%
Discount rate = R = 59.024%
Present Values
Year
Cash flows
Discount factor or PV factors = Df = 1/(1+R)^Year
PV of cash flows = Cash flows x Df
0
-$27.00
1.000000
-$27.00
1
$16.00
0.628836
$10.06
2
$16.00
0.395435
$6.33
3
$16.00
0.248663
$3.98
4
$16.00
0.156369
$2.50
5
$16.00
0.098330
$1.57
6
$16.00
0.061834
$0.99
7
$16.00
0.038883
$0.62
8
$16.00
0.024451
$0.39
9
$16.00
0.015376
$0.25
10
$32.00
0.009669
$0.31
Total of Present values = NPV =
$0.00
Now, we can use CAPM model to get Beta for project or highest beta:
Expected rate or IRR = Risk free rate + Beta x (Market rate – Risk free rate)
Beta = (IRR-Risk free rate)/(Market rate – Risk free rate)
Beta = (59.024%-4%)/(14%-4%)
Beta = 5.50
Discount rate = WACC = R = 20%
Present Values
Year
Cash flows
Discount factor or PV factors = Df = 1/(1+R)^Year
PV of cash flows = Cash flows x Df
0
-$27.00
1.000000
-$27.00
1
$16.00
0.833333
$13.33
2
$16.00
0.694444
$11.11
3
$16.00
0.578704
$9.26
4
$16.00
0.482253
$7.72
5
$16.00
0.401878
$6.43
6
$16.00
0.334898
$5.36
7
$16.00
0.279082
$4.47
8
$16.00
0.232568
$3.72
9
$16.00
0.193807
$3.10
10
$32.00
0.161506
$5.17
Total of Present values = NPV =
$42.66
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