What is the risk adjusted npv of each project

P12–3 Breakeven cash inflows and risk Blair Gasses and Chemicals is a supplier of highly purified gases to semiconductor manufacturers. A large chip producer has asked Blair to build a new gas production facility close to an existing semiconductor plant. Once the new gas plant is in place, Blair will be the exclusive supplier for that semiconductor fabrication plant for the subsequent 5 years. Blair is considering one of two plant designs. The first is Blair’s “standard” plant, which will cost $30 million to build. The second is for a “custom” plant, which will cost $40 million to build. The custom plant will allow Blair to produce the highly specialized gases that are required for an emerging semiconductor manufacturing process. Blair estimates that its client will order $10 million of product per year if the traditional plant is constructed, but if the customized design is put in place, Blair expects to sell $15 million worth of product annually to its client. Blair has enough money to build either type of plant, and, in the absence of risk differences, accepts the project with the highest NPV. The cost of capital is 12%. a. Find the NPV for each project. Are the projects acceptable? b. Find the breakeven cash inflow for each project. c. The firm has estimated the probabilities of achieving various ranges of cash inflows for the two projects as shown in the following table. What is the probability that each project will achieve at least the breakeven cash inflow found in part b? d. Which project is more risky? Which project has the potentially higher NPV? Discuss the risk–return trade-offs of the two projects. e. If the firm wished to minimize losses (that is, NPV < $0), which project would you recommend? Which would you recommend if the goal were to achieve a higher NPV?
5 Year
30 Million
40 Million
10 Million
15 Million
12%
Probability of achieving
cash inflow in given range
Range of cash inflow ($ millions) Standard Plant Custom Plant
$0 to $5 0% 5%
$5 to $8 10 10
$8 to $11 60 15
$11 to $14 25 25
$14 to $17 5 20
$17 to $20 0 15
Above $20 0 10
SOLUTION:
a. Find the NPV for each project. Are the projects acceptable?
Standard Plant
Millions $
Year Investment Revenue Cash flow Disc rate -12% Present value
A B C D C*D
A+B
0 -30 0 -30 1 -30
1 0 10 10 0.89 8.93
2 0 10 10 0.80 7.97
3 0 10 10 0.71 7.12
4 0 10 10 0.64 6.36
5 0 10 10 0.57 5.67
NPV 6.05
Custom Plant
Millions $
Year Investment revenue Cash flow Disc rate -12% Present value
A B C D C*D
A+B
0 -40 0 -40 1 -40
1 0 15 15 0.89 13.39
2 0 15 15 0.80 11.96
3 0 15 15 0.71 10.68
4 0 15 15 0.64 9.53
5 0 15 15 0.57 8.51
NPV 14.07
b. Find the breakeven cash inflow for each project.
Break even cash inflow Amount
Standard Plant 30
Custom Plant 40
c. The firm has estimated the probabilities of achieving various ranges of cash inflows for the two projects as shown in the following table. What is the probability that each project will achieve at least the breakeven cash inflow found in part b?
Standard Plant
Million
Year Investment Revenue Cash flow Disc rate -12% Present value
A B C D C*D
A+B
0 -30 0 -30 1 -30
1 0 8 8 0.89 7.14
2 0 8 8 0.80 6.38
3 0 8 8 0.71 5.69
4 0 8 8 0.64 5.08
5 0 8 8 0.57 4.54
NPV -1.16
Standard Plant
Million
Year Investment Revenue Cashflow Disc rate -12% Present value
A B C D C*D
A+B
0 -30 0 -30 1 -30
1 0 11 11 0.89 9.82
2 0 11 11 0.80 8.77
3 0 11 11 0.71 7.83
4 0 11 11 0.64 6.99
5 0 11 11 0.57 6.24
NPV 9.65
Custom Plant
Millions
Year Investment revenue Cash flow Disc rate -12% Present value
A B C D C*D
A+B
0 -40 0 -40 1 -40
1 0 11 11 0.89 9.82
2 0 11 11 0.80 8.77
3 0 11 11 0.71 7.83
4 0 11 11 0.64 6.99
5 0 11 11 0.57 6.24
NPV -0.35
Custom Plant
Millions
Year Investment revenue Cashflow Disc rate -12% Present value
A B C D C*D
A+B
0 -40 0 -40 1 -40
1 0 14 14 0.89 12.5
2 0 14 14 0.80 11.16
3 0 14 14 0.71 9.96
4 0 14 14 0.64 8.90
5 0 14 14 0.57 7.94
NPV 10.47
Million $
Break even cash inflow Amount Probability for achievement
Standard Plant 30 30% (25+5)
Custom Plant 40 45% (20+15+10)
d. Which project is more risky? Which project has the potentially higher NPV? Discuss the risk–return trade-offs of the two projects.
Standard plant project is more risky because it has only 30% probability of achieving breakeven cash inflow compared to custom plant has 45% probability of achieving breakeven cash inflow. Custom plant has NPV of $ 14.07 million (with 45% probability) compared to standard plant has NPV of $ 6.05 million (with 30% probability). So Custom plant has potential higher NPV.
e. If the firm wished to minimize losses (that is, NPV < $0), which project would you recommend? Which would you recommend if the goal were to achieve a higher NPV?
If firm wished to minimise losses , then I would recommend custom project because it has higher probability(45%) of achieving break even cash inflow compared to standard project (30%). Custom plant has NPV of $ 14.07 million compared to standard plant has NPV of $ 6.05 million. So I will recommend Custom plant.
P12–4
P12–4 Basic scenario analysis Murdock Paints is in the process of evaluating two mutually exclusive additions to its processing capacity. The firm’s financial analysts have developed pessimistic, most likely, and optimistic estimates of the annual cash inflows associated with each project. These estimates are shown in the following table. a. Determine the range of annual cash inflows for each of the two projects. b. Assume that the firm’s cost of capital is 10% and that both projects have 20-year lives. Construct a table similar to this one for the NPVs for each project. Include the range of NPVs for each project. c. Do parts a and b provide consistent views of the two projects? Explain. d. Which project do you recommend? Why?
Year 20
Capital 10%
Project A Project B
Initial investment (CF0) -8000 -8000
Outcome Annual cash inflows (CF)
Pessimistic 200 900
Most likely 1000 1000
Optimistic 1800 1100
SOLUTION:
a. Determine the range of annual cash inflows for each of the two projects.
Range = Highest value - Lowest value
Cash inflows
Outcome Project A Project B
Pessimistic 200 900
Most likely 1000 1000
Optimistic 1800 1100
Range 1,600 200
b. Assume that the firm’s cost of capital is 10% and that both projects have 20-year lives. Construct a table similar to this one for the NPVs for each project. Include the range of NPVs for each project.
Project A:
Pessimistic: Most likely: Optimistic:
Rate 10% Rate 10% Rate 10%
Nper 20 Nper 20 Nper 20
PMT -200 PMT -1,000 PMT -1,800
PV $1,702.71 PV $8,513.56 PV $15,324.41
Cash outflow -8,000 Cash outflow -8,000 Cash outflow -8,000
NPV -$6,297.29 NPV $513.56 NPV $7,324.41
Project B:
Pessimistic: Most likely: Optimistic:
Rate = 10% Rate 10% Rate 10%
Nper 20 Nper 20 Nper 20
PMT -900 PMT -1,000 PMT -1,100
PV $7,662.21 PV $8,513.56 PV $9,364.92
Cash outflow -8,000 Cash outflow -8,000 Cash outflow -8,000
NPV -$337.79 NPV $513.56 NPV $1,364.92
NPVs of project A and Project B under different outcomes:
NPV
Outcome Project A Project B
Pessimistic -$6,297.29 -$337.79
Most likely 513.56 513.56
Optimistic 7,324.41 1,364.92
Range 13,622 1,703
c. Do parts a and b provide consistent views of the two projects? Explain.
Yes both the projects provide consistent view as the initial investment and the years of the project are same.
From the above we notice that project A is riskier than project B aas the range is high for project A.
d. Which project do you recommend? Why?
The decision depends upon the investors risk aversion.
If the company is interested to earn higher returns and willing to take up greater risk, then the company should select Project A as the NPV is higher than B.
If the company is risk averse then select project B as the range or deviation is less.
P12–8
P12–8 Risk-adjusted discount rates: Basic Country Wallpapers is considering investing in one of three mutually exclusive projects, E, F, and G. The firm’s cost of capital, r, is 15%, and the risk-free rate, RF, is 10%. The firm has gathered the basic cash flow and risk index data for each project as shown in the following table. a. Find the net present value (NPV) of each project using the firm’s cost of capital. Which project is preferred in this situation? b. The firm uses the following equation to determine the risk-adjusted discount rate, RADRj, for each project j: RADRj = RF + 3RIj * (r - RF) 4 Where RF = risk-free rate of return RIj = risk index for project j r = cost of capital Substitute each project’s risk index into this equation to determine its RADR. c. Use the RADR for each project to determine its risk-adjusted NPV. Which project is preferable in this situation? d. Compare and discuss your findings in parts a and c. Which project do you recommend that the firm accept?
r 15%
RF 10%
Project (j)
E F G
Initial investment (CF0) -15000 -11000 -19000
Year (t) Cash inflows (CFt)
1 $6,000 $6,000 $4,000
2 6,000 4,000 6,000
3 6,000 5,000 8,000
4 6,000 2,000 12,000
Risk index (RIj) 1.8 1 0.6
SOLUTION:
a. Find the net present value (NPV) of each project using the firm’s cost of capital. Which project is preferred in this situation?
Project E F G
Initial Investment (CF0) -15,000 -11,000 -19,000
Year (t)
1 6,000 6,000 4,000
2 6,000 4,000 6,000
3 6,000 5,000 8,000
4 6,000 2,000 12,000
NPV 2,129.87 1,673.05 1,136.29
On comparing the NPV of the above project , project E has highest NPV and thus , it has to be selected
Project E NPV 2,129.87
Project F NPV 1,673.05
Project G NPV 1,136.29
b. The firm uses the following equation to determine the risk-adjusted discount rate, RADRj, for each project j:
Rf = Risk-free rate of return
Rij = Risk index for project j
r = Cost of capital
Project E RADR :
10% + (1.80*(15%-10%))
Project E RADR : 19%
Project F RADR :
10% + (1.00*(15%-10%))
Project F RADR : 15%
Project G RADR :
10% + (0.60*(15%-10%))
Project G RADR : 13%
E RADR 19%
F RADR 15%
G RADR 13%
c. Use the RADR for each project to determine its risk-adjusted NPV. Which project is preferable in this situation?
Project E F G
Initial Investment (CF0) -15,000 -11,000 -19,000
Year (t)
1 6,000 6,000 4,000
2 6,000 4,000 6,000
3 6,000 5,000 8,000
4 6,000 2,000 12,000
NPV 831.51 1,673.05 2,142.93
On comparing the NPV of the above projects, project G has the highest NPV following by project F and project E.
Project E NPV 831.51
Project F NPV 1,673.05
Project G NPV 2,142.93
d. Compare and discuss your findings in parts a and c. Which project do you recommend that the firm accept?
NPV of all the projects are positive. After the adjustment in the discount rates also, the NPV of the project remained to be positive. But it is preferable to consider the NPV calculation of RADR than the straight rate, because risk adjusted discount rate stands ahead than the cost of capital. On this basis, the NPV of Project G is higher than all other projects and thus, Project G should be selected.
P12–12
P12–12 Risk classes and RADR Moses Manufacturing is attempting to select the best of three mutually exclusive projects, X, Y, and Z. Although all the projects have 5-year lives, they possess differing degrees of risk. Project X is in class V, the highest-risk class; project Y is in class II, the below-average-risk class; and project Z is in class III, the average-risk class. The basic cash flow data for each project and the risk classes and risk-adjusted discount rates (RADRs) used by the firm are shown in the following tables. a. Find the risk-adjusted NPV for each project. b. Which project, if any, would you recommend that the firm undertake?
Project X Project Y Project Z
Initial investment (CF0) -180000 -235000 -310000
Year (t) Cash inflows (CFt)
1 80000 50000 90000
2 70000 60000 90000
3 60000 70000 90000
4 60000 80000 90000
5 60000 90000 90000
Risk Classes and RADRs
Risk class Description Risk-adjusted discount rate (RADR)
I Lowest risk 10%
II Below-average risk 13%
III Average risk 15%
IV Above-average risk 19%
V Highest risk 22%
SOLUTION:
a. Find the risk-adjusted NPV for each project.
Year Cash flows PVIF at 22% Present value of cash flows
1 80000 0.820 65573.77
2 70000 0.672 47030.37
3 60000 0.551 33042.41
4 60000 0.451 27083.95
5 60000 0.370 22199.96
Present value of cash inflows 194930.45
NPV = - Initial cash flow + Present value of all cash flows
NPV -180000 194930.45
NPV project X 14930.45
Year Cash flows PVIF at 13% Present value of cash flows
1 50000 0.8850 44247.79
2 60000 0.7831 46988.80
3 70000 0.6931 48513.51
4 80000 0.6133 49065.50
5 90000 0.5428 48848.39
Present value of cash inflows 237663.99
NPV = - Initial cash flow + Present value of all cash flows
NPV -235000 237663.99
NPV project Y 2663.99
Year Cash flows PVIF at 13% Present value of cash flows
1 90000 0.870 78260.87
2 90000 0.756 68052.93
3 90000 0.658 59176.46
4 90000 0.572 51457.79
5 90000 0.497 44745.91
Present value of cash inflows 301693.96
NPV = - Initial cash flow + Present value of all cash flows
NPV -310000 301693.96
NPV project Y -8306.04
b. Which project, if any, would you recommend that the firm undertake?
If we compare the NPV of all the three projects, Project X and Y only has positive NPV and Project Z is having negative NPV. It is clear that, Project Z will be rejected because of negative NPV. On comparing the NPV of Project X and Y, Project X should be selected because it has higher NPV than other projects.
P12–14
P12–14 Unequal lives: ANPV approach Portland Products is considering the purchase of one of three mutually exclusive projects for increasing production efficiency. The firm plans to use a 14% cost of capital to evaluate these equal-risk projects. The initial investment and annual cash inflows over the life of each project are shown in the following table. a. Calculate the NPV for each project over its life. Rank the projects in descending order on the basis of NPV. b. Use the annualized net present value (ANPV) approach to evaluate and rank the projects in descending order on the basis of ANPV. c. Compare and contrast your findings in parts a and b. Which project would you recommend that the firm purchase? Why?
Project X Project Y Project Z
Initial investment (CF0) -78000 -52000 -66000
Year (t) Cash inflows (CFt)
1 17000 28000 15000
2 25000 38000 15000
3 33000 0 15000
4 41000 0 15000
5 0 0 15000
6 0 0 15000
7 0 0 15000
8 0 0 15000
Capital 14%
SOLUTION:
a. Calculate the NPV for each project over its life. Rank the projects in descending order on the basis of NPV.
NPV For Project X:
Year Cash flow PV factor at 14% Net present value
0 -78000 1 -78000
1 17000 0.87719 14912.28
2 25000 0.76947 19236.69
3 33000 0.67497 22274.06
4 41000 0.59208 24275.29
5 0 0.51937 0.00
6 0 0.45559 0.00
7 0 0.39964 0.00
8 0 0.35056 0.00
NPV 2698.32
NPV For Project Y:
Year Cash flow PV factor at 14% Net present value
0 -52000 1 -52000
1 28000 0.87719 24561.404
2 38000 0.76947 29239.766
3 0 0.67497 0.000
4 0 0.59208 0.000
5 0 0.51937 0.000
6 0 0.45559 0.000
7 0 0.39964 0.000
8 0 0.35056 0.000
NPV 1801.17
NPV For Project Z:
Year Cash flow PV factor at 14% Net present value
0 -66000 1 -66000
1 15000 0.87719 13157.89
2 15000 0.76947 11542.01
3 15000 0.67497 10124.57
4 15000 0.59208 8881.20
5 15000 0.51937 7790.53
6 15000 0.45559 6833.80
7 15000 0.39964 5994.56
8 15000 0.35056 5258.39
NPV 3582.96
Ranking of proposals using NPV the project with highest positive NPV is gien the top priority over the positive NPV project.
Rank Project NPV
1 Z 3582.96
2 X 2698.32
3 Y 1801.17
b. Use the annualized net present value (ANPV) approach to evaluate and rank the projects in descending order on the basis of ANPV.
Annualized NPV (ANPV) = NPV / PVIFAk%,n
ANPV X 2698.32 2.9137123045 926.08
ANPV Y 1801.17 1.6466605109 1093.83
ANPV Z 3582.96 4.6388638939 772.38
on comparing the calculated ANPV all project have positive Anpv. Project Y has the highest ANPV followed by Project Xand Project Z.
Rank Project
1 Y
2 X
3 Z
c. Compare and contrast your findings in parts a and b. Which project would you recommend that the firm purchase? Why?
Project Y only should be selected because it is having highest ANPV. All the projects have different lives, therefore ANPV will be a better measure for making decision. In case of unequal lives, the result will vary with the life of the project. Therefore, it is always better to choose an alternative using a method which will be affected with the time period of the project.
P12–18
P12–18 Capital rationing: IRR and NPV approaches Valley Corporation is attempting to select the best of a group of independent projects competing for the firm’s fixed capital budget of $4.5 million. The firm recognizes that any unused portion of this budget will earn less than its 15% cost of capital, thereby resulting in a present value of inflows that is less than the initial investment. The firm has summarized, in the following table, the key data to be used in selecting the best group of projects. a. Use the internal rate of return (IRR) approach to select the best group of projects. b. Use the net present value (NPV) approach to select the best group of projects. c. Compare, contrast, and discuss your findings in parts a and b. d. Which projects should the firm implement? Why?
Budget 4.5
Cost 15%
Project Initial investment IRR Present value of inflows at 15%
A -5000000 17% 5400000
B -800000 18% 1100000
C -2000000 19% 2300000
D -1500000 16% 1600000
E -800000 22% 900000
F -2500000 23% 3000000
G -1200000 20% 1300000
SOLUTION:
a. Use the internal rate of return (IRR) approach to select the best group of projects.
Project Initial Investement Present value of inflows at 15% IRR Net present value
F -2500000 3000000 23% 500000
E -800000 900000 22% 100000
G -1200000 1300000 20% 100000
Total -4500000 5200000 700000
The project E,F and G are the best project according to IRR approach. The total intial investement of the project is $4500000 and the project have IRR greater than cost of capital of 15%
b. Use the net present value (NPV) approach to select the best group of projects.
Project Initial Investement Present value of inflows at 15% IRR Net present value
F -2500000 3000000 23% 500000
B -800000 1100000 18% 300000
E -800000 900000 22% 100000
Total -4100000 5000000 900000
The project F,Band E are the best projects accoring to NPV approach. The total intial investement of the project is $4100000. the present value is $5000000 and the NPV is $900000. the total NPV for these 3 projects is highest.
c. Compare, contrast, and discuss your findings in parts a and b.
Comparing the results from sub-part (a) and (b), the projects as per each approach is different. As per IRR approach, the Projects with IRR greater than cost of capital and under the capital budget are considered. As per NPV approach, project with highest NPV and under the capital budget is considered. The selection for the Project under both the approaches is different. This makes the best group of projects different.
d. Which projects should the firm implement? Why?
The company should implement project as per NPV approach. As per NPV approach, the initial investment is $4,100.000 which is less than the capital budget. Also the Net Present Value as per NPV approach is $900,000 which is greater than the NPV as per IRR approach which is $700.000. NPV is a more realistic approach to select a project considering the inflows and outflows measured in terms of present dollars.
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