Question

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: $19 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. Show formulas used.

Answers below-

IO = $56 million

Δ D = $2.16 million

NCF1-25 = $7.464 million

NCF25 = $4.4 million

NPV = $17.83 million > 0, so Accept

IRR = 12.75% > 9%, so Accept

PI = 1.32 > 1, so Accept

PB = 7.57 years > 3 so Reject

ACCEPT the project

Answer 1

a). Initial outlay = equipment cost + shipping cost + installation + working capital investment

= 34 + 1 + 19 + 2 = 56 mn

Depreciation per annum = (34+1+19)/25 = 2.16 mn

Net Cash Flow (NCF) from Year 1 to Year 25 = (revenue - cost)*(1-Tax rate) + (depreciation*Tax rate)

= (20-9)*(1-40%) + (2.16*40%) = 7.464 mn

After-tax salvage value in Year 25 (ASV) = salvage value*(1-Tax rate) = 2.40 mn

Terminal value in Year 25 = NCF + ASV + recovery of working capital = 7.464 + 2.40 + 2 = 11.864 mn

NPV = -initial outlay + PV of NCF from Year 1 to Year 24 + PV of terminal value

= -56 + 7.464*PVIFA(9%,24) + 11.864/(1+9%)^25

= -56 + 7.464*9.7066 + 1.376

= -56 + 72.450 + 1.376 = 17.826 mn or 17.83 mn

NPV is positive so project is acceptable.

b). IRR calculated using IRR function with the cash flows: CF0 = -56; CF1 to CF24 = 7.464; CF25 = 11.864

IRR = 12.71% IRR is greater than required rate of 9% so project is acceptable.

c). Profitability index (PI) = sum of PV of future cash flows/initial outlay = [7.464*PVIFA(9%,24) + 11.864/(1+9%)^25]/56

= 73.826/56 = 1.318 or 1.32

PI is greater than one so project can be accepted as it will have a profit.

d). Payback period (PB) = Initial outlay/ annual cash flows (Note: This shortcut method can be used when the PB is annual cash flows are constant.)

= 56/7.464 = 7.50 years

PB is more than the required period of 3 years so project can be accepted.

Note: The answers given in the question for IRR and PB are not entirely accurate. Please check the above solution for correct answers.