Question

A venture under review costs $950,000, has a five-year life, and has no salvage value. Depreciation is straight-line to zero. The required return is 18 percent, and the tax rate is 40 percent. Sales are projected at 700 units per year. Price per unit is $4,500, variable cost per unit is $3,500, and fixed costs are $400,000 per year. Suppose you think that the unit sales, price, variable cost, and fixed cost projections given here are accurate to within 10 percent. What are the upper and lower bounds for these projections? What are the best- and worst-case scenario NPVS?

Answer 1

Answer:

Working:

Initial investment = $950,000

Annual depreciation = (Cost - salvage value) / Useful life = ($950000 - 0)/ 5 = $190,000

Depreciation tax shield = 190000 * 40% = $76,000

BEST CASE:

Best case will be when price and quantity increases by 10% and

Variable costs, and fixed costs decreases by 10 percent.

Price = 4500 + 4500 * 10% =$4,950

Quantity = 700 + 700* 10% = 770

Variable cost per unit = 3500 - 3500 * 10% =$3,150

Fixed cost = 400000 - 400000 * 10% = $360,000

Annual cash flow = ((4950 - 3150)* 770 - 360000) *(1 - 40%) + 76000 = $691,600

NPV = Annual cash flow * Pv of $1 annuity for 6 years at 9% - Initial investment

= 691600* (1 - 1/(1+18%)^5)/18% - 950000

= $1,212,751.48

Best-case NPV = $1,212,751.48

WORST CASE:

Worst case will be when price and quantity decreases by 10% and

Variable costs, and fixed costs increases by 10 percent.

Price = 4500 - 4500 * 10% =$4050

Quantity = 700 - 700 *10% = 630

Variable cost per unit = 3500 + 3500 * 10% =$3850

Fixed cost = 400000 + 400000 * 10% = $440,000

Annual cash flow = ((4050 - 3850)* 630 - 440000) * (1 - 40%) + 76000 = -$112,400

NPV = Annual cash flow * Pv of $1 annuity for 6 years at 9% - Initial investment

= -112400* (1 - 1/(1+18%)^5)/18% - 950000

= - $1301494.02

Worst-case NPV = - $1,301,494.02