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Anita Johri
Anita Johri

CJ Manufacturing LLC is evaluating two mutually exclusive projects, Project A and Project B, to purchase a new machine. Both projects produce the same product but one machine is more efficient. The company will use the payback period, net present value (NPV), and internal rate of return (IRR) methods to evaluate the projects. Based on the payback period, the company will select Project A, which has a shorter payback period of 5.43 years compared to Project B's 5.57 years. However, based on the NPV and IRR methods, the company will select Project B, which has a higher NPV and IRR of 11% compared to Project A's NPV and IRR of

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Capital Budgeting Project (Evaluate two mutually exclusive projects) CJ Manufacturing LLC. By Anita Johri
1 Capital Budgeting Project About our company: CJ Manufacturing LLC., Was formed in year 2000 by Anita Johri and Xianmei Chen. We are partners with limited liability. We are planning to go public because we wish to expand our business and raise more capital. We currently manufacture fruit juices. We are planning to purchase of one of two machines, A or B. They are mutually exclusive projects, ie we can either go with project A or project B but not both. The machine will be installed in the manufacturer¡¯s factory and will produce items for sale. Both machines take exactly the same input and produce exactly the same final product. The only difference between the machines is that one is more efficient and therefore has lower operating costs, resulting in higher net cash flows. Our Shadow Company: We assume that the required rate of return is 3.8% (From our shadow company Coca- Cola). Capital budget Proposal:
2 Capital Budgeting Project The cash flows of each of the projects are as follows: ? Purchase Date 1/1/2014, Sale date 1/1/2023. Time line:
3 Capital Budgeting Project Our decision is going to be based by evaluating the two projects based on below methods. ? Payback Period ? Net Present Value (NPV) ? Internal Rate of Return (IRR) Payback Period Method: Payback period method is the number of years it takes to recover the initial cost of the investment. The project that takes the least amount of time is the one we pick. Formula: The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is: Payback Period = Initial Investment Cash Inflow per Period When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period: Payback Period = A + B C In the above formula, A is the last period with a negative cumulative cash flow;
4 Capital Budgeting Project B is the absolute value of cumulative cash flow at the end of the period A; C is the total cash flow during the period after A. Using the formula for payback we get the below: Payback period for Project A is 5.43 yrs. and Payback period for Project B is 5.57 yrs. Based on payback period we decide to go with project A as it takes less time to recover the initial cost of investment, when compared to project B.
5 Capital Budgeting Project Net Present Value Method: (NPV) Net present value is the present value of net cash inflows generated by a project including salvage value, if any, less the initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts for time by using discounted cash inflows. Before calculating NPV, a target rate of return is set which is used to discount the net cash inflows from a project. Net cash inflow equals total cash inflow during a period less the expenses directly incurred on generating the cash inflow. Calculation Methods and Formulas The first step involved in the calculation of NPV is the determination of the present value of net cash inflows from a project or asset. The net cash flows may be even (i.e. equal cash inflows in different periods) or uneven (i.e. different cash flows in different periods). When they are even, present value can be easily calculated by using the present value formula of annuity. However, if they are uneven, we need to calculate the present value of each individual net cash inflow separately. In the second step we subtract the initial investment on the project from the total present value of inflows to arrive at net present value. Thus we have the following two formulas for the calculation of NPV: When cash inflows are even: NPV = R ¡Á 1 ? (1 + i)-n ? Initial Investment I In the above formula, R is the net cash inflow expected to be received each period; i is the required rate of return per period; n are the number of periods during which the project is expected to operate and generate cash inflows. When cash inflows are uneven: NPV = R1 + R2 + R3 + ... ? Initial Investment (1 + i)1 (1 + i)2 (1 + i)3 Where, i is the target rate of return per period; R1 is the net cash inflow during the first period; R2 is the net cash inflow during the second period; R3 is the net cash inflow during the third period, and so on ...
6 Capital Budgeting Project Decision Rule Accept the project only if it¡¯s NPV is positive or zero. Reject the project having negative NPV. While comparing two or more exclusive projects having positive NPVs, accept the one with highest NPV. Based on NPV method we pick the project if NPV > 0 or if NPV = 0. A positive NPV means the project is expected to add value to the firm and will increase the wealth of the owners. With two mutually exclusive projects, the project which has higher NPV is picked. We use our shadow company YTM, which is 3.8%. We pick project B as the NPV of project B is higher than project A at 3.8% return. Based on the NPV profile below we see that at the crossover rate, the NPV for project ¡®A¡¯ equals Project ¡®B¡¯. Left to the crossover rate, Project B yields higher NPV than Project A, so we choose Project B over Project A
7 Capital Budgeting Project Internal Rate of Return (IRR) method: Internal rate of return (IRR) is the discount rate at which the net present value of an investment becomes zero. In other words, IRR is the discount rate which equates the present value of the future cash flows of an investment with the initial investment. It is one of the several measures used for investment appraisal. Decision Rule A project should only be accepted if its IRR is NOT less than the target internal rate of return. When comparing two or more mutually exclusive projects, the project having highest value of IRR should be accepted. IRR Calculation The calculation of IRR is a bit complex than other capital budgeting techniques. We know that at IRR, Net Present Value (NPV) is zero, thus: NPV = 0; or PV of future cash flows ? Initial Investment = 0; or
8 Capital Budgeting Project CF1 + CF2 + CF3 + ... ? Initial Investment = 0 ( 1 + r )1 ( 1 + r )2 ( 1 + r )3 Where, r is the internal rate of return; CF1 is the period one net cash inflow; CF2 is the period two net cash inflow, CF3 is the period three net cash inflow, and so on ... But the problem is, we cannot isolate the variable r (=internal rate of return) on one side of the above equation. However, there are alternative procedures which can be followed to find IRR. The simplest of them is described below: 1. Guess the value of r and calculate the NPV of the project at that value. 2. If NPV is close to zero then IRR is equal to r. 3. If NPV is greater than 0 then increase r and jump to step 5. 4. If NPV is smaller than 0 then decrease r and jump to step 5. 5. Recalculate NPV using the new value of r and go back to step 2. Internal rate of a project¡¯s is the expected rate of return on its investment. It¡¯s the rate of return that the firm will earn if it invests in the project and receives the given cash inflows. In case of mutually exclusive projects we accept the project with highest IRR. ? Project A : 12% ? Project B: 11% We will go with Project A based on IRR calculation as it gives higher rate of return. While NPV and IRR methods are useful methods for determining whether to accept a project, both have their advantages and disadvantages. Advantages and Disadvantages: Payback Method: Advantages ? Easy to calculate ? Easy to explain ? For companies facing liquidity problems, it provides a good ranking of projects that would return money early. Disadvantages ? Does not consider time value of money ? It does not take into account, the cash flows that occur after the payback period.
9 Capital Budgeting Project NPV Advantages: ? It considers time value of money. ? NPV measures how much wealth a project creates for the firm and investors. It is the ¡°gold standard¡± for evaluating investment opportunities. Disadvantages ? Does not give visibility into how long a project will take to generate a positive NPV ? Model assumes that capital is abundant - that is there is no capital rationing. This is overcome by IRR IRR: Advantages: ? Considers the time value of money. ? More intuitive and appealing to business owners to think in terms of rate of return rather than actual dollar returns. Disadvantages ? Multiple or no Rates of Return - if you're evaluating a project that has more than one change in sign for the cash flow stream, then the project may have multiple IRRs or no IRR at all. ? Changes in Discount Rates ? If IRR > WACC Accept. But if this discount rate changes each year then it's impossible to make this comparison. ? IRRs Do Not Add Up - one of the strengths of the NPV approach is that if you need to add one project to an existing project you can simply add the NPVs together to evaluate the entire project. IRRs on the other hand cannot be added together so projects must be combined or evaluated on an incremental basis. Overall, NPV is the best and preferred method.
10 Capital Budgeting Project Citations: ? Textbook: Principles of Managerial Finance by Lawrence and Chad ? Images: "GoThinkBig.co.uk." 5 Foolproof Questions to Ask in Your Job Interview. N.p., n.d. Web. 13 Nov. 2013. ? "Benefits Realization and Business Cases." : Pros and Cons of NPV, IRR and Payback Calculations. N.p., n.d. Web. 22 Nov. 2013. ? "NPV vs IRR." YouTube. YouTube, 18 Sept. 2013. Web. 22 Nov. 2013. <https://www.youtube.com/watch?v=6RztxNwerOA>.

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  • 1. Capital Budgeting Project (Evaluate two mutually exclusive projects) CJ Manufacturing LLC. By Anita Johri
  • 2. 1 Capital Budgeting Project About our company: CJ Manufacturing LLC., Was formed in year 2000 by Anita Johri and Xianmei Chen. We are partners with limited liability. We are planning to go public because we wish to expand our business and raise more capital. We currently manufacture fruit juices. We are planning to purchase of one of two machines, A or B. They are mutually exclusive projects, ie we can either go with project A or project B but not both. The machine will be installed in the manufacturer¡¯s factory and will produce items for sale. Both machines take exactly the same input and produce exactly the same final product. The only difference between the machines is that one is more efficient and therefore has lower operating costs, resulting in higher net cash flows. Our Shadow Company: We assume that the required rate of return is 3.8% (From our shadow company Coca- Cola). Capital budget Proposal:
  • 3. 2 Capital Budgeting Project The cash flows of each of the projects are as follows: ? Purchase Date 1/1/2014, Sale date 1/1/2023. Time line:
  • 4. 3 Capital Budgeting Project Our decision is going to be based by evaluating the two projects based on below methods. ? Payback Period ? Net Present Value (NPV) ? Internal Rate of Return (IRR) Payback Period Method: Payback period method is the number of years it takes to recover the initial cost of the investment. The project that takes the least amount of time is the one we pick. Formula: The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is: Payback Period = Initial Investment Cash Inflow per Period When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period: Payback Period = A + B C In the above formula, A is the last period with a negative cumulative cash flow;
  • 5. 4 Capital Budgeting Project B is the absolute value of cumulative cash flow at the end of the period A; C is the total cash flow during the period after A. Using the formula for payback we get the below: Payback period for Project A is 5.43 yrs. and Payback period for Project B is 5.57 yrs. Based on payback period we decide to go with project A as it takes less time to recover the initial cost of investment, when compared to project B.
  • 6. 5 Capital Budgeting Project Net Present Value Method: (NPV) Net present value is the present value of net cash inflows generated by a project including salvage value, if any, less the initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts for time by using discounted cash inflows. Before calculating NPV, a target rate of return is set which is used to discount the net cash inflows from a project. Net cash inflow equals total cash inflow during a period less the expenses directly incurred on generating the cash inflow. Calculation Methods and Formulas The first step involved in the calculation of NPV is the determination of the present value of net cash inflows from a project or asset. The net cash flows may be even (i.e. equal cash inflows in different periods) or uneven (i.e. different cash flows in different periods). When they are even, present value can be easily calculated by using the present value formula of annuity. However, if they are uneven, we need to calculate the present value of each individual net cash inflow separately. In the second step we subtract the initial investment on the project from the total present value of inflows to arrive at net present value. Thus we have the following two formulas for the calculation of NPV: When cash inflows are even: NPV = R ¡Á 1 ? (1 + i)-n ? Initial Investment I In the above formula, R is the net cash inflow expected to be received each period; i is the required rate of return per period; n are the number of periods during which the project is expected to operate and generate cash inflows. When cash inflows are uneven: NPV = R1 + R2 + R3 + ... ? Initial Investment (1 + i)1 (1 + i)2 (1 + i)3 Where, i is the target rate of return per period; R1 is the net cash inflow during the first period; R2 is the net cash inflow during the second period; R3 is the net cash inflow during the third period, and so on ...
  • 7. 6 Capital Budgeting Project Decision Rule Accept the project only if it¡¯s NPV is positive or zero. Reject the project having negative NPV. While comparing two or more exclusive projects having positive NPVs, accept the one with highest NPV. Based on NPV method we pick the project if NPV > 0 or if NPV = 0. A positive NPV means the project is expected to add value to the firm and will increase the wealth of the owners. With two mutually exclusive projects, the project which has higher NPV is picked. We use our shadow company YTM, which is 3.8%. We pick project B as the NPV of project B is higher than project A at 3.8% return. Based on the NPV profile below we see that at the crossover rate, the NPV for project ¡®A¡¯ equals Project ¡®B¡¯. Left to the crossover rate, Project B yields higher NPV than Project A, so we choose Project B over Project A
  • 8. 7 Capital Budgeting Project Internal Rate of Return (IRR) method: Internal rate of return (IRR) is the discount rate at which the net present value of an investment becomes zero. In other words, IRR is the discount rate which equates the present value of the future cash flows of an investment with the initial investment. It is one of the several measures used for investment appraisal. Decision Rule A project should only be accepted if its IRR is NOT less than the target internal rate of return. When comparing two or more mutually exclusive projects, the project having highest value of IRR should be accepted. IRR Calculation The calculation of IRR is a bit complex than other capital budgeting techniques. We know that at IRR, Net Present Value (NPV) is zero, thus: NPV = 0; or PV of future cash flows ? Initial Investment = 0; or
  • 9. 8 Capital Budgeting Project CF1 + CF2 + CF3 + ... ? Initial Investment = 0 ( 1 + r )1 ( 1 + r )2 ( 1 + r )3 Where, r is the internal rate of return; CF1 is the period one net cash inflow; CF2 is the period two net cash inflow, CF3 is the period three net cash inflow, and so on ... But the problem is, we cannot isolate the variable r (=internal rate of return) on one side of the above equation. However, there are alternative procedures which can be followed to find IRR. The simplest of them is described below: 1. Guess the value of r and calculate the NPV of the project at that value. 2. If NPV is close to zero then IRR is equal to r. 3. If NPV is greater than 0 then increase r and jump to step 5. 4. If NPV is smaller than 0 then decrease r and jump to step 5. 5. Recalculate NPV using the new value of r and go back to step 2. Internal rate of a project¡¯s is the expected rate of return on its investment. It¡¯s the rate of return that the firm will earn if it invests in the project and receives the given cash inflows. In case of mutually exclusive projects we accept the project with highest IRR. ? Project A : 12% ? Project B: 11% We will go with Project A based on IRR calculation as it gives higher rate of return. While NPV and IRR methods are useful methods for determining whether to accept a project, both have their advantages and disadvantages. Advantages and Disadvantages: Payback Method: Advantages ? Easy to calculate ? Easy to explain ? For companies facing liquidity problems, it provides a good ranking of projects that would return money early. Disadvantages ? Does not consider time value of money ? It does not take into account, the cash flows that occur after the payback period.
  • 10. 9 Capital Budgeting Project NPV Advantages: ? It considers time value of money. ? NPV measures how much wealth a project creates for the firm and investors. It is the ¡°gold standard¡± for evaluating investment opportunities. Disadvantages ? Does not give visibility into how long a project will take to generate a positive NPV ? Model assumes that capital is abundant - that is there is no capital rationing. This is overcome by IRR IRR: Advantages: ? Considers the time value of money. ? More intuitive and appealing to business owners to think in terms of rate of return rather than actual dollar returns. Disadvantages ? Multiple or no Rates of Return - if you're evaluating a project that has more than one change in sign for the cash flow stream, then the project may have multiple IRRs or no IRR at all. ? Changes in Discount Rates ? If IRR > WACC Accept. But if this discount rate changes each year then it's impossible to make this comparison. ? IRRs Do Not Add Up - one of the strengths of the NPV approach is that if you need to add one project to an existing project you can simply add the NPVs together to evaluate the entire project. IRRs on the other hand cannot be added together so projects must be combined or evaluated on an incremental basis. Overall, NPV is the best and preferred method.
  • 11. 10 Capital Budgeting Project Citations: ? Textbook: Principles of Managerial Finance by Lawrence and Chad ? Images: "GoThinkBig.co.uk." 5 Foolproof Questions to Ask in Your Job Interview. N.p., n.d. Web. 13 Nov. 2013. ? "Benefits Realization and Business Cases." : Pros and Cons of NPV, IRR and Payback Calculations. N.p., n.d. Web. 22 Nov. 2013. ? "NPV vs IRR." YouTube. YouTube, 18 Sept. 2013. Web. 22 Nov. 2013. <https://www.youtube.com/watch?v=6RztxNwerOA>.