Question

You are considering a new product launch. The project will cost $750,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 180 units per year; price per unit will be $18,500, variable cost per unit will be $11,400, and fixed costs will be $522,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 28 percent.

a) Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±13 percent. What are the best and worst cases for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

b) Evaluate the sensitivity of your base-case NPV to changes in fixed costs.

Please show all steps for credit.

Answer 1

Base Case NPV:

A B H. M | 1 Year Operating profit (Sales unit*(price-VC)-FC Depreciation Taxable income Tax (1*28%) PAT (1-) 0 59 omto 00 Initial Cost Sales unit per year Price per unit VC per unit Fixed Cost 750,000 180 18,500 11,400 522,000 180 18,500 11,400 522,000 180 18,500 11,400 522,000 180 18,500 11,400 522,000 756,000 756,000 756,000 756,000 187,500 187,500 187,500 187,500 568,500 568,500 568,500 568,500 159,180 159,180 159,180 159,180 409,320 409,320 409,320 409,320 Cash flow Present Value fo cash flow (K+H-B) (cash flow/1.12^year) (750,000) (750,000) 596,820 532,875 596,820 475,781 596,820 424,805 596,820 379,290 Total (NPV) 1,062,751

For Best Case NPV : Sales=180*1.13=203 (Approx), Price=18500*1.13=$20905 and VC= $11400*(1-.13)=9918, FC= 522000*(1-.13)=$454140

Best Case NPV Calculation: Year Operating profit (Sales unit* (price-VC)-FC Depreciation Taxable income Tax (1*28%) PAT (1-1) 0 WNA Initial Cost Sales unit per year Price per unit VC per unit Fixed Cost 750,000 203 20,905 9,918 454,140 203 20,905 9,918 454,140 203 20,905 9,918 454,140 203 20,905 9,918 454,140 1,776,221 1,776,221 1,776,221 1,776,221 187,500 187,500 187,500 187,500 1,588,721 1,588,721) 1,588,721 1,588,721 444,842 444,842 444,842 444,842 1,143,879 1,143,879 1,143,879 1,143,879 Cash flow Present Value fo cash flow (K+H-B) (cash flow/1.12^year) (750,000) (750,000) 1,331,379 1,188,731 1,331,379 1,061,367 1,331,379 947,649 1,331,379 846,115 Total (NPV) 3,293,864

For Worst case NPV:

Sales=180*(1-.13)=157 (Approx), Price=18500*(1-.13)=$16095 and VC= $11400*(1+.13)=12882, FC= 522000*(1+.13)=$589860

Worst Case NPV Calculation: Year 0 Initial Cost Sales unit per year Price per unit VC per unit Fixed Cost 750,000 157 16,095 12,882 589,860 157 16,095 12,882 589,860 157 16,095 12,882 589,860 157 16,095 12,882 589,860 Operating profit Cash flow Present Value fo cash flow (Sales unit*(price-VC)-FC Depreciation Taxable income Tax (1*28%) PAT (1-) (K+H-B) (cash flow/1.12^year) (750,000) (750,000) (85,419) 187,500 (272,919) (76,417) (196,502) (9,002) (8,037) (85,419) 187,500 (272,919) (76,417) (196,502) (9,002) (7,176) (85,419) 187,500 (272,919) (76,417) (196,502) (9,002) (6,407) (85,419) 187,500 (272,919) (76,417) (196,502) (9,002) (5,721) Total (NPV) (777,341)

b) If you increase FC of base case by 1%, the NPV= $1051335, calculation is given below:

C E B Base Case NPV Calculation: Operating profit (Sales unit*(price-VC)-FC 2 Year Sales unit per year Price per unit VC per unit Fixed Cost Depreciation Taxable income Tax (1*28%) PAT (1-1) Initial Cost 750,000 180 180 180 180 18,500 18,500 18,500 18,500 11,400 11,400 11,400 11,400 527,220 527,220 527,220 527,220 750,780 750,780 750,780 750,780 187,500 187,500 187,500 187,500 563,280 563,280 563,280 563,280 157,718 157,718 157,718 157,718 405,562 405,562 405,562 405,562 Cash flow Present Value fo cash flow (K+H-B) (cash flow/1.12^year) (750,000) (750,000) 593,062 529,519 593,062 472,785 593,062 422,130 593,062 376,901 Total (NPV) 1,051,335 Doct Caco MDV Calculation

Hence, Sensitivity of NPV=(1062751-1051335)/1062751= 1.074%