Question

Problem 4 After paying $3 million for a feasibility study, Stanley wrote a proposal with the following cash flow estimates for a 25-year capital project. Equipment cost: $34 million, Shipping costs: $1 million, Installation: S19 million, Salvage: $4, Working capital investment: $2 million, Revenues are expected to increase by $20 million per year and cash operating expenses by $9 million per year. The firm's marginal tax rate is 40 percent, its weighted average cost of capital is 9%, and the firm requires a 3 year payback. Assume straight line depreciation. Evaluate the project using NPV, IRR, PI, and PB. #4 IO = $56 million AD=$2 million NCF-25 = $7.4 million NCF25 = $6 million NPV = $17.38 million > 0, so Accept IRR = 12.60% > 9%, so Accept PI = 1.31 > 1, so Accept PB = 7.57 years > 3 so Reject ACCEPT the project These are the correct answers, however, I am more concerned with the process of solving. Please show formulas and all work. Thank You!

Edit: Please do not use Excel as I need to learn to solve without it. thank you.

Answer 1

Calculation of Initial Outflow (IO)= Equipment Cost + Shipping Cost + Installation Cost + Working Capital Investment

= $ 34 million + $ 1 million + $ 19 million + $ 2 million

= $ 56 million

Note : Amount for feasibility study is never included in initial outflow.

Calculation of Depreciation = [ Equipment Cost + Shipping Cost + Installation Cost - Salvage Value] / Life of equipment

= [ $ 34 million + $ 1 million + $ 19 million - $ 4 million] / 25

= $ 2 million

Calculation of Net Cash Flow for Year 1 to Year 25

= (Incremental Revenue - Cash Operating Expense - Depreciation) * (1- Tax Rate) + Depreciation

= ($ 20 million - $ 9 million - $ 2 million) * (1 - 0.40) + $ 2 million

= ($ 9 million * 0.60) + $ 2 million

= $ 7.4 million

Calculation of Net Cash Flow for Year 25

= Salvage Value + Release of Working Capital

= $ 4 million + $ 2 million

= $ 6 million

Calculation of NPV

= (Net Cash Flow for Year 1 to Year 25) * PVIFA (9% , 25 years) + (Net Cash Flow for Year 25) PVIF (9% , 25 years) - Initial Outflow

= ($ 7.4 million * 9.8226 + $ 6 million * 0.116 ) - $ 56 million

= $ 72.68 million + $ 0.70 million - $ 56 million

= $ 17.38 million

Calculation of IRR

At IRR, NPV =0

Take two random discount rates (10% and 15%)

NPV at 10% = (Net Cash Flow for Year 1 to Year 25) * PVIFA (10% , 25 years) + (Net Cash Flow for Year 25) PVIF (10% , 25 years) - Initial Outflow

= ($ 7.4 million * 9.077 + $ 6 million * 0.0923) - $ 56 million

= $ 11.72 million

NPV at 15% = (Net Cash Flow for Year 1 to Year 25) * PVIFA (15% , 25 years) + (Net Cash Flow for Year 25) PVIF (15% , 25 years) - Initial Outflow

= ($ 7.4 million * 6.4641 + $ 6 million * 0.0304) - $ 56 million

= - $ 7.98 million

This means the IRR lies between 10% to 15% where NPV becomes zero.

By interpolation,

IRR = R1 + [ ( R2 - R1) * NPV1 ] / (NPV 1 - NPV 2) *100

= 10% + [ ( 15% - 10%) * $ 11.72 million ] / [$ 11.72 million - (- $ 7.98 million)] *100

= 10 % + (  $ 0.586 million / $ 19.7 million ) * 100

= 12.60 %

Calculation of Profitability Index

= PV of Future Inflows / Initial Investment

= [ (Net Cash Flow for Year 1 to Year 25) * PVIFA (9% , 25 years) + (Net Cash Flow for Year 25) PVIF (9% , 25 years) ] /   Initial Investment

= ($ 7.4 million * 9.8226 + $ 6 million * 0.116 ) / $ 56 million

= ($ 72.68 million + $ 0.70 million) / $ 56 million

= 1.31

Calculation of Payback Period

= Initial Investment / Cash Inflows

= $ 56 million / $ 7.4 million

= 7.57 years