Question

A Canadian firm is evaluating a project in the United States. This project involves the establishment of a lumber mill in Wisconsin to process Canadian timber. The factory expects to service clients in the construction industry. All cash flow figures are in thousands. Initial Investment. The initial investment is CAD 48,000. The project is over a period of three years. This investment will be depreciated straight line to zero. Operating Results. The firm expects two likely scenarios for the first year of operations. Under the favorable scenario (probability of 45%), the firm expects to produce and sell 1,400 units of a product. Under the unfavorable scenario (probability of 55%), it expects to produce and sell only 800 units. The selling price is expected to be CAD 55; the variable expense is expected to be CAD 27, and fixed costs excluding depreciation are expected to be CAD 15,000. Additional Investment. If the firm encounters the favorable scenario during year 1, it could make an investment of CAD 25,000 to enable it to produce and sell a total of 2,800 units (double the units) in the second and third years. The cost parameters remain unchanged with the exception of depreciation. This secondary investment will be depreciated equally in years 2 and 3. If the firm chooses not to make the investment in year 1, the results of year 1 will be repeated during years 2 and 3. Discount Rate and Miscellaneous. Assume a discount rate of 11 percent and zero taxes.

a. Estimate the NPV of the project.

b. Estimate the NPV of the option to expand.

Answer 1

question a

• contribution per unit= selling price -variable costs= 55-27= 28 CAD
• cashflow in first year , if 1400 units are sold= (1400x28)-15000= 24200
• cashflow in first year if 800 units are sold= (800x 28)- 15000=7400
• if the firm choose not to make further investments, the cash inflow will be same in years 2 and 3
• applying probability and discounting the cashflows at 11%, the expected value of cash inflows will be (0.45x24200 x present value interest factor of an annuity at 11% for 3 yrs) + (0.55x 7400x PV interest factor of an annuity at 11% for 3 yrs)
• =(0.45x 24200 x2.444) + (0.55x7400x2.444)=26615.16+9947.08= 36562.08
• NPV = present value of cash inflows -present value of cash outflows
• =36562.08-48000= -11437.92

answer b

• If the firm chooses to expand , the cash inflow for the 2nd and 3rd year will be (2800 x28)-15000= 63400 each year.
• The present value of inflows in the 2nd year willbe 63400x PV interest factor at 11% for 2 yrs= 63400 x0.812=51480.8
• the present value of inflows in the 3rd year will be 63400x PV interest factor at 11% for 3 yrs= 63400x 0.731= 46345.4
• present value of investment/cash outflows of 25000 made in the 1st year= 25000x PV interest factor at 11% for 1yr= 25000 x 0.901=22525
• the present value of cash inflows in the 1st year will be
• ,for 1400 units, it will be 24200 x 0.901=21804.2 and for 800 units, it will be 7400 x 0.901=6667.4
• applying probability
• NPV= - 48000+ (0.45x 21804.2+0.55x6667.4) +{ (0.45 x (51.480.8+46345.4 -22525) +( 0.55x 0)}
• = -48000 + 13478.96 +(33885.54 +0)
• =-48000+47364.5= -635.5