Question

​It's been 2 months since you took a position as an assistant financial analyst at Caledonia Products. Although your boss has been pleased with your​ work, he is still a bit hesitant about unleashing you without supervision. Your next assignment involves both the calculation of the cash flows associated with a new investment under consideration and the evaluation of several mutually exclusive projects. Given your lack of tenure at​ Caledonia, you have been asked not only to provide a recommendation but also to respond to a number of questions aimed at judging your understanding of the​ capital-budgeting process. The memorandum you received outlining your assignment​ follows:

​To: The Assistant Financial Analyst

​From: Mr. V.​ Morrison, CEO, Caledonia Products

​Re: Cash Flow Analysis and Capital Rationing

We are considering the introduction of a new product. Currently we are in the 24 percent marginal tax bracket with a required rate of return or cost of capital of 17 percent. This project is expected to last 5 years and​ then, because this is somewhat of a fad​ product, be terminated. The new project information is here:

Cost of new plant and equipment: $7,900,000

Shipping and installation costs: $100,000

Unit Sales:

YEAR	UNITS SOLD
1	55,000
2	120,000
3	140,000
4	65,000
5	45,000

Sales price per unit: $320/unit in years 1 through 4, $280/unit in year 5

Variable cost per unit: $200/unit

Annual fixed costs: $200,000 per year in years 1 - 5

Working-capital requirements: There will be an initial​ working-capital requirement of ​$90,000 just to get production started. For each​ year, the total investment in net working capital will be equal to 20 percent of the dollar value of sales for that year.​ Thus, the investment in working capital will increase during years 1 and​ 2, then decrease in year 4.​ Finally, all working capital is liquidated at the termination of the project at the end of year 5.

Depreciation method: Bonus depreciation​ method, and as a result the bonus depreciation occurs in year​ 1, with no depreciation in any other years. If any losses​ occur, they would be offset by profits in other areas of the company.

e. What is the annual free cash flow associated with this project in year​ 1?

    What is the annual free cash flow associated with this project in year​ 2?

    What is the annual free cash flow associated with this project in year​ 3?

    What is the annual free cash flow associated with this project in year​ 4?

f. What is the terminal cash flow in year 5 ​(that is, what is the free cash flow in year 5 plus any additional cash flows associated with the termination of the​ project)?

g. Enter the amount of cash flow into the following diagram for this project. Enter a negative number for a net cash outflow and a positive number for a net cash inflow.

h. What is its net present​ value?

i. What is its internal rate of​ return?

Answer 1

Initial outlay for the company = cost of equipment + installation charges + working capital charges = $7,900,000 + $100,000 +$90,000 = $8,090,000

Earnings before tax = (unit sales * sales price) - (variable cost *unit sales) - fixed cost - depreciation

Tax= earnings before tax * tax rate

Earnings after tax = earnings before tax - tax

net cash flow for the year = earnings after tax + non-cash item (depreciation) - working capital expenditures

present value of the cash flow for the year = (net cash flow for the year) / (1 + discount rate or WACC)ⁿ, where n is the year in which the cash flow happens.

Bonus depreciation in year 1 = cost of equipment + installation cost = $7,900,000 + $100,000 = $8,000,000

Hence, earnings before tax for year 1 is (55,000 * $320) - (55,000 * $200) - $200,000 - $8,000,000

= $17,600,000 - $11,000,000 - $200,000 - $8,000,000

= -$1,600,000

Since any losses are absorbed by profits in other divisions, there is no incremental tax benefit of the tax

Hence, incremental earnings after tax for year 1 = -$1,600,000

net cash flow for year 1 =  -$1,600,000 + depreciation - working capital investment = -$1,600,000 + $8,000,000 - {20% (55,000*$320) = -$1,600,000 + $8,000,000 - $3,520,000 = $2,880,000. This is the annual free cash flow associated with this project in year​ 1

earnings before tax for year 2 = (120,000 * $320) - (120,000 * $200) - $200,000

= $38,400,000 - $24,000,000 - $200,000 (no depreciation) = $14,200,000

Tax = 0.24 * $14,200,000 = $3,408,000

Incremental earnings after tax for year 2 = $14,200,000 - $3,408,000 = $10,792,000

Incremental cash flow in year 2 = Incremental earnings after tax for year 2 - working capital investment ( which is 20% of sales)

= $10,792,000 - (0.20 *120,000 * $320) = $10,792,000 - $7,680,000 = $3,112,000.  This is the annual free cash flow associated with this project in year​ 2

earnings before tax for year 3 = (140,000 * $320) - (140,000 * $200) - $200,000

= $44,800,000 - $28,000,000 - $200,000 (no depreciation) = $16,600,000

Tax = 0.24 * $16,600,000 = $3,984,000

Incremental earnings after tax for year 2 = $16,600,000 - $3,984,000= $12,616,000

Incremental cash flow in year 3 = Incremental earnings after tax for year 3 - working capital investment ( which is 20% of sales)

= $12,616,000 - (0.20 *140,000 * $320) = $12,616,000 - $8,960,000 = $3,656,000.  This is the annual free cash flow associated with the project in year​ 3

earnings before tax for year 4 = (65,000 * $320) - (65,000 * $200) - $200,000

= $20,800,000 - $13,000,000 - $200,000 (no depreciation) = $7,600,000

Tax = 0.24 * $7,600,000 = $1,824,000

Incremental earnings after tax for year 2 = $7,600,000 - $1,824,000= $5,776,000

Incremental cash flow in year 4 = Incremental earnings after tax for year 4 - working capital investment ( which is 20% of sales)

= $5,776,000 - (0.20 *65,000 * $320) = $5,776,000 - $4,160,000 = $1,616,000.  This is the annual free cash flow associated with the project in year​ 4

earnings before tax for year 5 = (45,000 * $280) - (45,000 * $200) - $200,000

= $12,600,000 - $9,000,000 - $200,000 (no depreciation) = $3,400,000

Tax = 0.24 * $3,400,000 = $816,000

Incremental earnings after tax for year 5 = $3,400,000 - $816,000 = $2,584,000

Incremental cash flow in year 5 = Incremental earnings after tax for year 5 - working capital investment ( which is 20% of sales)

= $2,584,000 - (0.20 *45,000 * $280) = $2,584,000 - $2,520,000 = $64,000.  This is the annual free cash flow associated with the project in year​ 5

The terminal cash flow in year 5 = annual cash flow for year 5 that we just calculated + recapture of working capital throughout the five years

= $64,000 + $3,520,000 + $7,680,000 + $8,960,000 + $4,160,000 + $2,520,000 = $26,904,000

The diagram is attached below

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Net present value the sum of : (net cash flow for the year) / (1 + discount rate or WACC)ⁿ over the five year period minus the initial outlay.

Hence, NPV =  ($2,880,000/1.17) + ($3,112,000/(1.17²)) + ($3,656,000/(1.17³)) + ($1,616,000/(1.17⁴)) + ($26,904,000/(1.17⁵) - $8,090,000

= $2,461,538.46 + $2,273,358.17 + $2,282,698.75 + $862,378.48 + $12,271,214.44 - $8,090,000

NPV = $12,061,188.3

The internal rate of return can be calculated using the financial calculator

after inputting all the cash flow details in the calculator, IRR = 50.896%