Question

AAA Corp. currently has one​ product, high-priced lawn mowers. AAA Corp. has decided to sell a new line of​ medium-priced lawn mowers. The building and machinery for producing this new line is estimated to cost ​$10 comma 000 comma 000 and it will be depreciated down to zero over 20 years using​ straight-line depreciation.​ Also, an investment today on working capital in the amount of ​$2 comma 000 comma 000 is needed. The working capital will be recovered at the end of the project. Sales for the new line of lawn mowers are estimated at ​$19 million a year. Annual variable costs are 60​% of sales. The project is expected to last 5 years. In addition to the production variable​ costs, the fixed costs each year will be ​$2 comma 000 comma 000. The company has spent ​$1 comma 500 comma 000 in a marketing study that determined the company will lose ​$10 million in sales a year of its existing​ high-priced lawn mowers. The production variable cost of these sales is ​$8 million a year. It is expected that at the end of the​ project, the building and machinery can be sold for ​$8 comma 000 comma 000. The tax rate is 30 percent and the cost of capital is 10​%.

a. What is the initial outlay​ (IO) for this​ project?

b. What is the operating cash flows​ (OCF) for each of the years for this​ project?

c. What is the termination value​ (TV) cash flow​ (aka recovery cost or​ after-tax salvage​ value, or liquidation value of the​ assets) at the end of the​ project?

d. What is the NPV of this​ project?

Answer 1

a). Initial outlay = cost of building and equipment + investment in working capital

= 10,000,000 + 2,000,000 = 12,000,000

b). Depreciation per year = cost of building and equipment/20 = 10,000,000/20 = 500,000

Operating cash flows (OCF) = (revenue from sale of new mowers - revenue loss from sale of old mowers - variable expense for new mowers + variable expense for old mowers - fixed cost)*(1 - tax rate) + (depreciation*tax rate)

= (19,000,000 - 10,000,000 - (60%*19,000,000) + 8,000,000 - 2,000,000)*(1-30%) + (500,000*30%) = 2,670,000

c). Termination value (TV) = after-tax salvage value + recovery of working capital

After-tax salvage value = salvage value - (salvage value - book value at the end of 5 years)*tax rate

= 8,000,000 - (8,000,000 - (10,000,000 - (500,000*5))*30% = 8,000,000 - (8,000,000 - 7,500,000)*30%

= 8,000,000 - (500,000*30%) = 7,850,000

TV = 7,850,000 + 2,000,000 = 9,850,000

d). NPV = - initial outlay + Present Value (PV) of OCFs for 5 years + PV of Termination value

PV of OCF: PMT = 2,670,000; N = 5; rate = 10%, CPT PV. PV = 10,121,400.67

PV of Termination value = 9,850,000/(1+10%)^5 = 6,116,075.03

NPV = - 12,000,000 + 10,121,400.67 + 6,116,075.03 = 4,237,475.71