Question

RSM Co is considering a project which will require the purchase of $2.7 million in new equipment. The equipment will be depreciated straight-line to a book value of $1 million over the 5-year life of the project. Annual sales from this project are estimated at $2,950,000. The variable cost is 40% of the annual sales and there is an annual fixed cost of $200,000. Sway's Back Store will sell the equipment at the end of the project for 30% of its original cost. New net working capital equal to 15% of sales will be required to support the project. All of the new net working capital will be recouped at the end of the project. The firm’s WACC is 12% per year. The tax rate is 40%.

Please calculate the project NPV, IRR, Discounted Payback Period and Modified IRR (reinvestment return is 10%).

Can I have this answered in "steps" and not in a chart or excel format? Thank You!

Answer 1

1)

Cash flow at year 0 = Sales + net working capital

Cash flow at year 0 = 2,700,000 + ( 0.15 * 2,950,000 )

Cash flow at year 0 = 2,700,000 + 442,500 = $3,142,500

Annual depriciation = ( 2,700,000 - 1,000,000) / 5 = 340,000

Selling price of the equipment = 0.3 * 2,700,000 = 810,000

Variable cost = 0.4 * 2,950,000 = 1,180,000

Annual operating cash flow for 5 years = (sales - variable cost - fixed cost - depreciation)( 1 - tax) + depreciation

Annual operating cash flow for 5 years = ( 2,950,000 - 1,180,000 - 200,000 - 340,000)(1 - 0.4) + 340,000

Annual operating cash flow for 5 years = 1,230,000(0.6) + 340,000

Annual operating cash flow for 5 years = 738,000 + 340,000

Annual operating cash flow for 5 years = 1,078,000

Non-opertaing cash flow at year 5 = sales + Net working capital - tax( sales - book value)

Note: we assume we recover the working capital when the project is completed

Non-opertaing cash flow at year 5 = 810,000 + 442,500 - 0.4( 810,000 - 1,000,000)

Non-opertaing cash flow at year 5 = 1,252,500 - 0.4( -190,000)

Non-opertaing cash flow at year 5 = 1,252,500 + 76,000

Non-opertaing cash flow at year 5 = 1,328,500

NPV = present value of cash inflows - present values of cash outflows

Present value of operating cash flows = 1,078,000 / ( 1 + 0.12)¹ + 1,078,000 / ( 1 + 0.12)² + 1,078,000 / ( 1 + 0.12)³ + 1,078,000 / ( 1 + 0.12)⁴ + 1,078,000 / ( 1 + 0.12)⁵

Present value of operating cash flows = 962,500 + 859,375 + 767,299.11 + 685,088.49 + 611,686.15

Present value of operating cash flows = 3,885,948.75

Present value of non operating cash flow = 1,328,500 / ( 1 + 0.12)⁵

Present value of non operating cash flow = 753,826.58

Total present value of cash inflow = 3,885,948.75 + 753,826.58 = 4,639,775.33

NPV = 4,639,775.33 - 3,142,500

NPV = 1,497,275.33

2)

IRR is the discount rate that makes NPV = 0

Total 5th year cash flow = 1,328,500 + 1,078,000 = 2,406,500

-3,142,500 + 1,078,000 / ( 1 + R)¹ + 1,078,000 / ( 1 + R)² + 1,078,000 / ( 1 + R)³ + 1,078,000 / ( 1 + R)⁴ + 2,406,500 / ( 1 + R)⁵ = 0

Using trial and error method, let's try 27.6196% as R and let's see if we can get NPV as 0:

-3,142,500 + 1,078,000 / ( 1 + 0.276196)¹ + 1,078,000 / ( 1 + 0.276196)² + 1,078,000 / ( 1 + 0.276196)³ + 1,078,000 / ( 1 + 0.276196)⁴ + 2,406,500 / ( 1 + 0.276196)⁵ = 0

-3,142,500 + 844,697.8364 + 661,887.2308 + 518,640.7345 + 406,395.8314 + 710,884.3782 = 0

0 = 0

Therrefore, 27.62 is the IRR

3)

Cumulative cash flow for year 0 = -3,142,500

Cumulative cash flow for year 1 =  -3,142,500 + 962,500 = -2,180,000

Cumulative cash flow for year 2 = -2,180,000 + 859,375 = -1,320,625

Cumulative cash flow for year 3 = -1,320,625 + 767,299.11 = -553,325.89

Cumulative cash flow for year 4 = -553,325.89 + 685,088.49 = 131,762.6

  553,325.89 / 685,088.49 = 0.807

Payback period = 3 + 0.81 = 3.81 years

4)

Future value of year 1 cash flow = 1,078,000 / ( 1 + 0.1)⁴ = 736,288.5049

Future value of year 2 cash flow = 1,078,000 / ( 1 + 0.1)³ = 809,917.3554

Future value of year 3 cash flow = 1,078,000 / ( 1 + 0.1)² = 890,909.091

Future value of year 4 cash flow = 1,078,000 / ( 1 + 0.1)¹ = 980,000

Future value of year 5 cash flow = 2,406,500 / ( 1 + 0.1)⁰ = 2,406,500

Total future value = 2,406,500 + 980,000 + 890,909.091 + 809,917.3554 + 736,288.5049 = 5,823,614.951

FV = PV ( 1+ r)ⁿ

5,823,614.951 = 3,142,500 ( 1 + r)⁵

1.853179 = ( 1 + r)⁵

5th root of 1.853179 is 1.131315

1.131315 =  1 + r

0.131315 = r

MIRR is 13.1315%