Anh Nguyen1. ST2Expected Net Cash Flows

project Xproject Y

0(10,000)(10,000)

1(3,500)(6,500)

2(500)(3,000)

32,500500

43,5004,000

Paybackx = 2 + = 2.17 years

Paybacky = 2 + = 2.86 yearsTo calculate the Net Present Value (NPV) of the project.

NPVx = -$10,000 + + + + = $966.01

NPVy = -$10,000 + + + + = $630.72

project Xproject Y

Payback2.17 years2.86 years

NPV$966.01$630.72

IRR18.0%15.0%

1. Using all methods, project X is preferred over project Y. Because both projects are acceptable under the NPV, IRR, and PI criteria, both projects should be accepted if they are interdependent. 1. Choose the project with the higher NPV at k = 12%, or project X.

1. To determine the effects of changing the cost of capital, plot the NPV profiles of each project. The crossover rate occurs at about 6% to 7%. To find this rate exactly, create a project , which is the difference in cash flows between projects X and Y:

Year Project X - Project Y = Project Net Cash Flow 0 01 30002(500)3(2500)Then find the IRR of Project : IRR = Crossover Rate = 6.2%. Thus, if the firm=s cost of capital is less than 6.2%, a conflict exists, because NPVY > NPVX but IRRX > IRRY.1. The basic cause of conflict is the differing reinvestment rate assumptions between NPV and IRR. The conflict occurs in this situation because the projects differ in their cash flow timing.

Problem 11-7

Project A:CF0 = -6000; CF1-5 = 2000; I/YR = 14.

Solve for NPVA = $866.16. IRRA = 19.86%.

MIRR calculation:012345||||||-6,0002,0002,0002,0002,0002,000

2,280.00

2,599.20

2,963.09

3,377.9213,220.21

Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21; and solve for MIRRA = I/YR = 17.12%.

Payback calculation:012345||||||-6,0002,0002,0002,0002,0002,000Cumulative CF:-6,000-4,000-2,00002,0004,000

Regular PaybackA = 3 years.

Discounted payback calculation:012345||||||-6,0002,0002,0002,0002,0002,000Discounted CF:-6,0001,754.391,538.941,349.941,184.161,038.74Cumulative CF:-6,000-4,245.61-2,706.67-1,356.73-172.57866.17

Discounted PaybackA = 4 + $172.57/$1,038.74 = 4.17 years.

Project B:CF0 = -18000; CF1-5 = 5600; I/YR = 14.

Solve for NPVB = $1,255.25. IRRB = 16.80%.

MIRR calculation:012345||||||-18,0005,6005,6005,6005,6005,600 1.14

6,384.00 (1.14)2

7,277.76 (1.14)3

8,296.65 (1.14)4

9,458.1837,016.59

Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59; and solve for MIRRB = I/YR = 15.51%.

Payback calculation:012345||||||-18,0005,6005,6005,6005,6005,600Cumulative CF:-18,000-12,400-6,800-1,2004,40010,000

Regular PaybackB = 3 + $1,200/$5,600 = 3.21 years.

Discounted payback calculation:012345||||||-18,0005,6005,6005,6005,6005,600Discounted CF:-18,0004,912.284,309.023,779.843,315.652,908.46Cumulative CF:-18,000-13,087.72-8,778.70-4,998.86-1,683.211,225.25

Discounted PaybackB = 4 + $1,683.21/$2,908.46 = 4.58 years.

Summary of capital budgeting rules results:Project AProject BNPV$866.16$1,225.25IRR19.86%16.80%MIRR17.12%15.51%Payback3.0 years3.21 yearsDiscounted payback4.17 years4.58 years

b.If the projects are independent, both projects would be accepted since both of their NPVs are positive.

c.If the projects are mutually exclusive then only one project can be accepted, so the project with the highest positive NPV is chosen. Accept Project B.

d.The conflict between NPV and IRR occurs due to the difference in the size of the projects. Project B is 3 times larger than Project A.