# Calculating IRR, MIRR, Payback Period, NPV and AFN for Business Projects: A Comprehensive Guide

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1. A project has an initial cost of $50,000, expected net cash inflows of $11,000 per year for 9 years, and a cost of capital of 8%. What is the project’s IRR? Round your answer to two decimal places.

1. A project has an initial cost of $50,000, expected net cash inflows of $11,000 per year for 9 years, and a cost of capital of 8%. What is the project’s IRR? Round your answer to two decimal places.

1. A project has an initial cost of $50,000, expected net cash inflows of $11,000 per year for 9 years, and a cost of capital of 8%. What is the project’s IRR? Round your answer to two decimal places.

IRR?_______________

2. A project has an initial cost of $55,000, expected net cash inflows of $13,000 per year for 10 years, and a cost of capital of 8%. What is the project’s MIRR? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to two decimal places.

MIRR?______________

3. A project has an initial cost of $40,000, expected net cash inflows of $11,000 per year for 7 years, and a cost of capital of 13%. What is the project’s payback period? Round your answer to two decimal places.

project’s payback period?________________

4. Although the Chen Company’s milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so the company is considering replacing it. The new milling machine, at a cost of $110,000 delivered and installed, would also last for 10 years and would produce after-tax cash flows (labor savings and depreciation tax savings) of $19,300 per year. It would have zero salvage value at the end of its life. The project cost of capital is 10%, and its marginal tax rate is 25%. Should Chen buy the new machine? Do not round intermediate calculations. Round your answer to the nearest cent. Negative value, if any, should be indicated by a minus sign.

NPV: $ _______________

Should Chen purchase the new machine?__________

5. The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer’s base price is $860,000, and it would cost another $18,000 to install it. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $468,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. The machine would require an increase in net working capital (inventory) of $14,000. The sprayer would not change revenues, but it is expected to save the firm $341,000 per year in before-tax operating costs, mainly labor. Campbell’s marginal tax rate is 25%. (Ignore the half-year convention for the straight-line method.) Cash outflows, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest dollar.

What is the Year-0 net cash flow?

$ _______________

What are the net operating cash flows in Years 1, 2, and 3?

Year 1:$ _________ Year 2:$ ______ Year 3:$_______

What is the additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital)?

$ ___________

If the project’s cost of capital is 10%, what is the NPV of the project?

$__________

Should the machine be purchased?___________

6. Broussard Skateboard’s sales are expected to increase by 15% from $9.0 million in 2019 to $10.35 million in 2020. Its assets totaled $3 million at the end of 2019.

Broussard is already at full capacity, so its assets must grow at the same rate as projected sales. At the end of 2019, current liabilities were $1.4 million, consisting of $450,000 of accounts payable, $500,000 of notes payable, and $450,000 of accruals. The after-tax profit margin is forecasted to be 3%, and the forecasted payout ratio is 55%. Use the AFN equation to forecast Broussard’s additional funds needed for the coming year. Enter your answer in dollars. For example, an answer of $1.2 million should be entered as $1,200,000. Do not round intermediate calculations. Round your answer to the nearest dollar.

$_________________

## Assignment Preview:

A project’s internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project’s cash flows equal to zero. In other words, it’s the rate at which the present value of the future cash inflows from the project is equal to the initial investment. To calculate the IRR, you would need to use trial and error or a financial calculator to find the rate that makes the NPV equal to zero.

To calculate the modified internal rate of return (MIRR) for this project, you would first need to construct a time line that shows the project’s cash flows over time. The MIRR is calculated as the rate at which the future value of the project’s cash flows, discounted back to their present value, is equal to the initial investment. The formula for MIRR is:

FV = (CF1/(1+r)^1) + (CF2/(1+r)^2) + … + (CFn/(1+r)^n)

Where: FV = future value of cash flows CF = cash flow r = discount rate n = number of periods

The payback period is the amount of time it takes for a project to recoup its initial investment from its cash flows. To calculate the payback period, you would need to divide the initial investment by the annual net cash inflow, and then round to the nearest whole number.

To determine whether Chen should buy the new machine, you would need to calculate the net present value (NPV) of the project’s cash flows. The NPV is the present value of the cash flows, minus the initial investment, with all the value discounted back to the present at the project cost of capital. The formula is:

NPV = (CF0 + (CF1/(1+r)^1) + (CF2/(1+r)^2) + … + (CFn/(1+r)^n)) – I

Where: CF0 = Initial investment CF = Annual net cash flow r = Discount rate n = number of years

For the Campbell Company a. Year-0 net cash flow = $860,000+$18,000-$14,000 = $864,000 b. Year 1 net cash flow = -($860,000 – ($860,000*(1-0.3333)) + $341,000*(1-0.25)) = $234,195.5 c. Year 2 net cash flow = -($860,000 – ($860,000*(1-0.4445)) + $341,000*(1-0.25)) = $182,118.86 d. Year 3 net cash flow = -($860,000 – ($860,000*(1-0.1481)) + $341,000*(1-0.25) – $468,000) = $50,729.78 e. Year 3 additional cash flow = $468,000*0.75 = $351,000 f. NPV = $864,000 + ($234,195.5/(1+0.1)^1) + ($182,118.86/(1+0.1)^2) + ($50,729.78 + $351,000)/(1+0.1)^3 = $532,144.24

To forecast additional funds needed (AFN) you need to use the following formula: AFN = (S x (1 + g) – A) / (1 – (1 – t) x p)

Where: S = Sales forecasted for the coming year g = Growth rate in sales A = Assets t = Tax rate p = Profit margin

So in this case, AFN = ($10,350,000 x (1 + 0.15) – $3,000,000) / (1 – (1 – 0.25) x 0.03) = $2,080,417

This is the forecasted additional funds needed by Broussard Skateboard for the coming year.