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.

Answers:

IO = $56 million

Δ D = $2 million

NCF1-25 = $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

Please show work and formula while avoiding Excel/spreadsheet programs. Thank you

Answer 1

Solution:

Initial Investment:

Cost of Equipment (in Millions) : 34

Add:Shipping Cost                   : 1

Add: Installation Cost              : 19

Cost of the Project                 : 54

Add: Working Capital Employed : 2

Initial Investment               : 56

Net Annual Cash Flow:

Annual Revenues                  : 20

Less: Cash Operating Expenses : 9

Annual Profit                           : 11

Less : Depreciation                : 2               Here , Depreciation per year = (Initial Cost - Salvage value)/ Life = (54-4)/25 = 2

Profit before tax                      : 9

Less : Tax @ 40%                  : 3.6

Profit after Tax                      : 5.4

Add: Depreciation                 :2

Net Annual Cash Flow        : 7.4

Terminal Cash Inflow

Working Capital Released : 2

Add: Salvage Value          : 4

Terminal Cash Inflow        : 6

Payback Period = Initial Investment/Net Annual Cash Flow = 56/7.4 = 7.57 Years

Since Payback period of 7.57 > 3 years i.e. acceptance level. Therefore , according to this we should reject the project.

NPV = Aggregate of PV of cash Inflows - Aggregate of PV of cash Outflows

Year	Cash Flow	PV Factor @ 9%	PV
0	-56	1	-56
Net Annual Cash Flow (Year 1-25)	7.4	9.823	72.6902
Terminal Cash Inflow	6	0.116	0.696
		NPV	17.3862

Since NPV is positive, therefore we can accept the project.

Profitability Index (PI) = Aggregate of PV of cash Inflows / Aggregate of PV of cash Outflows

                          PI = 73.3862/56 = 1.31

PI is greater than 1, we should accept the project.

For IRR Calculation:

Discount Rate	NPV
12%	2.3922
13%	-1.476

IRR is the rate where NPV becomes zero. From calculation we come to know that NPV is negative at 13% and posititve at the discount rate of 12%. Therefore the value of IRR lies in between 12% and 13%.

Lower Discount Rate (LDR) = 12%

Higher Discount Rate (HDR) = 13%

NPV 1(at LDR) = 2.3922

NPV 2 (at HDR) = -1.476

IRR = LDR + (NPV 1 )* (HDR - LDR) / (NPV 1 - NPV 2)

        = 12 + (2.3922) *(13-12) / (2.3922 + 1.476)

IRR = 12.61%

IRR is greater than cost of capital i.e. 9%. therefore we should accept the project.