In the following problems, you will calculate the “simple metrics” for project selection. For these problems, please use the following data and assume discount rate (interest rate) of 0.06.
Project A
The upfront cost of the project is $500,000. This cost is incurred in year 1. The profits from product sales will come in years 2 through 5. After year 5, the product will be obsolete, so no profits will come in after year 5.
Profits in year 2: $100,000; Profits in year 3: $200,000; Profits in year 4: $250,000; Profits in year 5: $200,000
Project B
The up front cost of the project is $800,000. This cost is incurred in year 1. The profits from product sales will come in years 2 through 5. After year 5, the product will be obsolete, so no profits will come in after year 5.
Profits at end of year 2: $0; Profits at end of year 3: $200,000; Profits at end of year 4: $400,000; Profits at end of year 5: $600,000
1. Calculate ROI for both projects.
2. Calculate NPV for both projects.
3. Calculate IRR for both projects.
4. For E(NPV), we need to change the scenario. Let’s now pretend that Projects A and B are not two different projects but rather are two different estimates of cash flows for the same project. Assuming the probability of each to be 0.5, calculate E(NPV).
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
To calculate the "simple metrics" for project selection, we need to calculate the ROI, NPV, IRR, and E(NPV) for both projects A and B. Let's go through each calculation step by step.
1. Calculating ROI (Return on Investment):
ROI is calculated by dividing the net profit by the initial investment and expressing it as a percentage. The formula for ROI is:
ROI = (Net Profit / Initial Investment) * 100
For Project A:
Net Profit for Project A = Profits in year 2 + Profits in year 3 + Profits in year 4 + Profits in year 5
= $100,000 + $200,000 + $250,000 + $200,000
= $750,000
ROI for Project A = ($750,000 / $500,000) * 100 = 150%
For Project B:
Net Profit for Project B = Profits at the end of year 3 + Profits at the end of year 4 + Profits at the end of year 5
= $200,000 + $400,000 + $600,000
= $1,200,000
ROI for Project B = ($1,200,000 / $800,000) * 100 = 150%
So, the ROI for both projects A and B is 150%.
2. Calculating NPV (Net Present Value):
NPV calculates the present value of future cash flows by discounting them to the present using the discount rate. The formula for NPV is:
NPV = Cash Flow / (1+Discount Rate)^Year
For Project A:
Year 1: Initial Investment = -$500,000 (negative as it's an outflow)
Year 2: Cash Flow = $100,000 / (1+0.06)^2 = $88,757.57
Year 3: Cash Flow = $200,000 / (1+0.06)^3 = $158,493.83
Year 4: Cash Flow = $250,000 / (1+0.06)^4 = $190,569.35
Year 5: Cash Flow = $200,000 / (1+0.06)^5 = $143,084.42
NPV for Project A = Sum of the Present Values - Initial Investment
= $88,757.57 + $158,493.83 + $190,569.35 + $143,084.42 - $500,000
= -$918,095.83
For Project B:
Year 1: Initial Investment = -$800,000 (negative as it's an outflow)
Year 2: Cash Flow = $0 / (1+0.06)^2 = $0
Year 3: Cash Flow = $200,000 / (1+0.06)^3 = $158,493.83
Year 4: Cash Flow = $400,000 / (1+0.06)^4 = $305,775.63
Year 5: Cash Flow = $600,000 / (1+0.06)^5 = $429,300.15
NPV for Project B = Sum of the Present Values - Initial Investment
= $0 + $158,493.83 + $305,775.63 + $429,300.15 - $800,000
= $93,569.61
So, the NPV for Project A is -$918,095.83 and for Project B is $93,569.61.
3. Calculating IRR (Internal Rate of Return):
IRR is the discount rate at which the present value of cash inflows equals the present value of cash outflows. It is the discount rate that makes NPV equal to zero.
Using the NPV formula, we can solve for the discount rate (IRR) that makes NPV = 0:
0 = Cash Flow / (1+IRR)^Year
For Project A:
Solving the equation:
-$500,000 + $100,000 / (1+IRR)^2 + $200,000 / (1+IRR)^3 + $250,000 / (1+IRR)^4 + $200,000 / (1+IRR)^5 = 0
For Project B:
Solving the equation:
-$800,000 + $0 / (1+IRR)^2 + $200,000 / (1+IRR)^3 + $400,000 / (1+IRR)^4 + $600,000 / (1+IRR)^5 = 0
Use numerical methods or financial software to solve for the IRR. The IRR for both projects A and B cannot be determined without solving the equations or using financial software.
4. Calculating E(NPV) (Expected Net Present Value):
E(NPV) is the expected value of NPV taking into account the probability of each scenario. In this case, the probability of each project (A or B) is assumed to be 0.5.
E(NPV) = P(Project A) * NPV of Project A + P(Project B) * NPV of Project B
= 0.5 * (-$918,095.83) + 0.5 * $93,569.61
= -$412,263.11 + $46,784.81
= -$365,478.30
So, the E(NPV) for the scenario where Project A and B are two different estimates of cash flows for the same project is -$365,478.30.