Need Solution of FIN-450(Principles of Managerail finance-14th edition)

P12–3

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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