Question

Problem 1

A company is considering manufacturing new elliptical trainers. This company did a marketing research 2 years ago, paying $750,000 consulting fees and found that the market is ripe for such a new product. The company feels that they can sell 5,000 of these per year for 5 years (after which time this project is expected to shut down). The elliptical trainers would sell for $ 2,000 each and have a variable cost of $500 each. The annual fixed costs associated with production would be $1,000,000. In addition, there would be a $5,000,000 initial expenditure associated with the purchase of new production equipment. It is assumed that this initial expenditure will be depreciated using the straight- line method down to zero over 5 years. This project will also require a one- time initial investment of $1,000,000 in working capital associated with inventory. The introduction of this new elliptical trainer will reduce the sales of an existing training machine that the company currently sells. The company estimates that $250,000 per year before tax basis will be lost on this existing training machine if the new elliptical trainer is introduced. At the end of the 5th year, the company estimates selling the production equipment for $150,000. Finally, assume that the firm’s marginal tax rate is 34 percent.

a) What is the initial outlay associated with this project?

b) What are the annual after- tax operating cash flows associated with this project for years 1 through 4?

c) What is the non-operating cash flow in year 5 or the terminal value?

d) What is the project’s NPV given a 10 percent cost of capital?

Answer 1

a) What is the initial outlay associated with this project?

Initial outlay will have following components:

• Purchase price for new machine = $ 5,000,000
• Initial investment in working capital = $ 1,000,000
• Hence, total initial outlay = 5,000,000 + 1,000,000 = $ 6,000,000

b) What are the annual after- tax operating cash flows associated with this project for years 1 through 4?

Annual after tax operating cash flows = NOPAT + Annual depreciation

Annual depreciation = Purchase price / Useful life = 5,000,000 / 5 = 1,000,000

NOPAT = (Sale - Variable cost - Fixed cost - Depreciation - Lost sales) x (1 - tax rate) = (5,000 x 2,000 - 5,000 x 500 - 1,000,000 - 1,000,000 - 250,000) x (1 - 34%) =  3,465,000

Hence, Annual after tax operating cash flows = NOPAT + Annual depreciation = 3,465,000 + 1,000,000 = 4,465,000

c) What is the non-operating cash flow in year 5 or the terminal value?

Terminal value will comprise of the following:

• Release of working capital = $ 1,000,000
• Post tax salvage value
  • Salvage value = 150,000
  • Gain on sale = salvage value - accumulated depreciation = 150,000 - 0 = 150,000
  • Tax on gain on sale = Gain on sale x Tax rate = 150,000 x 34% =  51,000
  • Hence, post tax salvage value = 150,000 - 51,000 = $ 99,000

Hence terminal value = 1,000,000 + 99,000 = $ 1,099,000

d) What is the project’s NPV given a 10 percent cost of capital?

Cost of capital = Discount rate = R = 10%

NPV = -Initial investment + PV of annual cash flows as annuity + PV of terminal value = - 6,000,000 + 4,465,000 / R x [1 - (1 + R)^-N] + 1,099,000 / (1 + R)^N where N = life of the project = 5 years

Hence, NPV = - 6,000,000 + 4,465,000 / 10% x [1 - (1 + 10)^-5] + 1,099,000 / (1 + 10%)⁵ =  11,608,255