Question

Knight Shades Inc. is considering adding new line of sunglasses to their designer series. The glasses will sell for $1,300 per pair and have a variable cost of $500 per unit. The company has spent $104,000 for a marketing study that estimates the company will sell 80,000 sunglasses per year for seven years. The fixed costs each year to produce the sunglasses will be $5,180,000. The company has also spent $622,000 on research and development for the new glasses. The new plant and equipment will cost $14,000,000 at start-up and will be depreciated on a straight-line basis to zero over the seven years. At the end of the seven years the plant and equipment will be worthless. The new sunglasses will also require an increase in net working capital of $610,000 that will be returned at the end of the project. The tax rate is 37 percent, and the cost of capital is 8 percent. The marketing study also estimates that introducing the new sunglasses will reduce sales of the company's high-priced sunglasses by 20,000 units. The high-priced glasses sell at $2,000 and have variable costs of $900. The study also estimates that the company will increase sales of its cheap sunglasses by 16,000 units. The cheap sunglasses sell for $700 and have variable costs of $300 per unit. Knight Shades Inc. estimates the project's NPV to be $131,360,810.78, but would like to know the sensitivity of NPV to changes in the price of the new sunglasses and the quantity of new sunglasses sold. Note: you may want to verify the base-case NPV to make sure you're setting up the problem correctly.

Required: (a) What is the sensitivity of the NPV to changes in the price of the new sunglasses? Note: In your economics classes you learned that sensitivity (elasticity) is defined as the percent change in one variable due to a percent change in another variable. Hence, it is easiest to estimate the sensitivity by re-calculating the NPV if price increases by 1%. (Do not round your intermediate calculations.)

Answer 1

Base-case NPV

Operating cash flow (OCF) each year = income after tax + depreciation

EBIT = revenues - fixed costs - variable costs - decreased contribution of high-priced sunglasses + increased contribution of cheap sunglasses - depreciation

decreased contribution of high-priced sunglasses = decrease in units sold * (selling price - variable cost)

increased contribution of cheap sunglasses = increase in units sold * (selling price - variable cost)

NPV is calculated using NPV function in Excel

NPV is $131,360,810.78

If price increases by 1%

Selling price = $1,300 * (1 + 1%) = $1,313

NPV is $134,772,024.44

Sensitivity of NPV = ($134,772,024.44 - $131,360,810.78) / $131,360,810.78

Sensitivity of NPV = 2.60%