Exam 3 March 10-10-15, questions and answers PDF

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11. Caledonia is considering two investments with one-year lives. The more expensive of the two is the better and will produce more savings. Assume these projects are mutually exclusive and that the required rate of return is 10 percent. Given the following after-tax net cash flows: YEAR PROJECT A PROJECT B 0 –$195,000 –$1,200,000 1 240,000 1,650,000 1. Calculate the net present value. 2. Calculate the profitability index. 3. Calculate the internal rate of return. 4. If there is no capital-rationing constraint, which project should be selected? If there is a capital-rationing constraint, how should the decision be made?

1. Calculate the net present value NPV Project A= -195000 + (240000/1.10) = -195000 + 218182 = $23,182

NPV Project B= -1200000 + (1650000/1.10) = -1200,000 + 1500,000 = 300,000

2. Calculate the profitability index.

Profitability index for Project A = Present Value of Inflow/Initial Investment = 218182/195000 = 1.12

Profitability index for Project B = Present Value of Inflow/Initial Investment = 1500000/1200000 = 1.25

3. Calculate the internal rate of return. For Project A $195,000=$240,000/(1+r) So Solving for r r= .2308 or 23.08%

We can also solve this $195,000=$240,000 [PVIFIRR %,1 yr] A [PVIFIRR %,1 yr] = .8125 A

So getting value for Present Value Table =IRR A = 23% (Approx)

For Project B $1200,000=$1650,000/(1+r) So Solving for r r= .355 or 35.50% We can also solve this $1200,000=$1650,000 [PVIFIRR %,1 yr] A [PVIFIRR %,1 yr] = .7273 A So getting value for Present Value Table =IRRA = 35.5% (Approx)

4. If there is no capital-rationing constraint, which project should be selected? If there is a capital-rationing constraint, how should the decision be made?

If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $1,005,000 freed up if project A is chosen. If Caledonia can earn more on project A, plus the project financed with the additional $1,005,000, than it can on project B, then project A and the marginal project should be accepted

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12.

Caledonia is considering two additional mutually exclusive projects. The cash flows

associated with these projects are as follows: YEAR PROJECT A PROJECT B 0 –$100,000 – $100,000 1 32,000 0 2 32,000 0 3 32,000 0 4 32,000 0 5 32,000 $200,000 The required rate of return on these projects is 11 percent. 1. What is each project’s payback period? Project A Payback=3+ (4000/32000) = 3.125 Years (Till Third year total cash accumulate = 96000 so remaining accumulated in 4 year)

Project B Payback = =4+(100000/200000) = 4.5 years (Till 4th year total cash accumulate = 0 so remaining accumulated in 5 year) 2. What is each project’s net present value? NPV Project A = -100000 + 32000/(1.11) + 32000/(1.11^2) + 32000/(1.11^3) + 32000/ (1.11^4) + + 32000/(1.11^5) = $18269

NPV Project B = -100000 + 200000/(1.11^5) = $18690 3. What is each project’s internal rate of return? Project A 100000 = 32000/(1+r) + 32000/(1+r)^2 + 32000/(1+r)^3 + 32000/(1+r)^4)+ 32000/ (1+r)^5 Solving for r = 18.03% Alternatively $100,000=$32,000 [PVIFAIRR %,5 yrs] A 3.125=PVIFAIRR %,5 yrs A (Getting Values form Present value annuity table) IRRA

Project B

= 18.03%

100000 = 200000/(1+r)^5 Solving for r r = 14.87% Alternatively

$100,000=$200,000 [PVIFIRR %,5 yrs] B .50

=PVIFIRR %,5 yrs B

So getting value for Present Value Table =IRRB = 14.87% (Approx) 4. What has caused the ranking conflict? Ranking conflict arises when one project has higher NPV that other project but lower IRR. This happens because NPV criterion assume that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows can be reinvested at the internal rate of return.

5. Which project should be accepted? Why?

Since project B has higher NPV, hence project B should be accepted.

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13.

The final two mutually exclusive projects that Caledonia is considering involve

mutually exclusive pieces of machinery that perform the same task. The two alternatives

available provide the following set of after-tax net cash flows: YEAR EQUIPMENT A EQUIPMENT B 0 –$100,000 –$100,000 1 65,000 32,500 2 65,000 32,500 3 65,000 32,500 4 Â 32,500 5 Â 32,500 6 Â 32,500 7 Â 32,500 8 Â 32,500 9 Â 32,500 Equipment A has an expected life of three years, whereas equipment B has an expected life of nine years. Assume a required rate of return of 14 percent. 1. Calculate each project’s payback period. Equipment A Payback=1+ 35000/65000= 1.538 Years (Till 1 year total cash accumulate = 65000 so remaining accumulated in 2 year)

Equipment B Payback=3+ 2500/32500= 3.08 Years (Till 3 year total cash accumulate = 97500 so remaining accumulated in 2 year)

2.

Calculate each project’s net present value.

Equipment A NPV = -100000 + 65000/1.14 + 65000/1.14^2 + + 65000/1.14^3 = $50906.08 Equipment B NPV = -100000 + 32500/1.14 + 32500/1.14^2 + 32500/1.14^3 + 32500/1.14^4 + 32500/1.14^5 + 32500/1.14^6 + 32500/1.14^7 + 32500/1.14^8 + 32500/1.14^9 = $60757.08 3. Calculate each project’s internal rate of return. Equipment A IRR 100000 = 65000/(1+r) + 65000/(1+r)^2 + + 65000/(1+r)^3 Solving for r r = .4257 or 42.57%

Equipment B IRR

100000 = 32500/(1+r)+ 32500/(1+r)^2 + 32500/(1+r)^3 + 32500/(1+r)^4 + 32500/ (1+r)^5 + 32500/(1+r)^6 + 32500/(1+r)^7 + 32500/(1+r)^8 + 32500/(1+r)^9 Solving for r r = .2928 or 29.28%

Or Alternatively

$100,000 =$65,000 [PVIFAIRR %,3 yrs] A IRRA = 42.57% $100,000=

$32,500 [PVIFAIRR %,9 yrs] B

IRRB=29 .28% 4. Are these projects comparable? These projects are not comparable because they have uneqal project life. equipment A life is 3 years whereas equipment B life is 9 years. So if company accept equipment A so at the end of 3 years it can replace it with other equipment A and can derive the future benefits, such an option is not available for equipment B.

5. Compare these projects using replacement chains and EAAs. Which project should be selected? Support your recommendation. Under Replacement chain method cash flow under equipment A would change and they would be as follows

Year 0 1 2 3 4 5 6 7 8

EQUIPMENT A -100000 65000 65000 -35000 65000 65000 -35000 65000 65000

So NPV Equipment A = -100000 + 65000/1.14 + 65000/1.14^2 + -35000/1.14^3 + 65000/1.14^4 + 65000/1.14^5 + -35000/1.14^6 + 65000/1.14^7 + 65000/1.14^8 + 65000/1.14^9 = $108458.36

So NPV of project A would be increased to $108458.36 which is higher than equipment B NPV. So equipment A should be selected.

Under EAA Approach Project A (NPV) from Part 2 = 50906.08 Project A EAA= NPV/PVIFA (14%, 3 period) = 50906.08/2.3216 = $21927.15

Project B (NPV) from Part 2 = 60757.08 Project B EAA= NPV/PVIFA (14%, 9 period) = 60757.08/4.9464 = $12283.09

Under EAA Approach project A should be accepted as it has higher EAA....