Question

Companies invest in expansion projects with the expectation of increasing the earnings of its business Consider the case of Fox Co.: Fox Co. is considering an investment that will have the following sales, variable costs, and fixed operating costs: Year 1 Year 2 Year 3 Year 4 Unit sales Sales price Variable cost per unit Fixed operating costs except depreciation 4,200 $29.82 $12.15 $41,000 33% 4,100 $30.00 $13.45 $41,670 45% 4,300 $30.31 $14.02 $41,890 15% 4,400 $33.19 $14.55 $40,100 7% Accelerated depreciation rate This project will require an investment of $10,000 in new equipment. The equipment will have no salvage value at the end of the project's four-year life. Fox pays a constant tax rate of 40%, and it has a weighted average cost of capital (WACC) of 11%. Determine what the project's net present value (NPV) would be when using accelerated depreciation. Determine what the project's net present value (NPV) would be when using accelerated depreciation. (Note: Round your intermediate calculations to the nearest whole number.) $42,318 $47,608

Answer 1

Initial outlay = $10,000

Tax= earnings before tax * tax rate

Earnings before tax = (unit sales * sales price) - (variable cost *unit sales) - fixed cost - depreciation (which is depreciation rate* initial cost of equipment)

Earnings after tax = earnings before tax - tax

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

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.

Hence, earnings before tax for year 1 is (4,200 * $29.82) - (4,200* $12.15) - $41,000 - (33% of $10,000)

= $125,244 - $51,030 - $41,000 - $3,333.33 = $29,880.67

Tax = 0.40 * $29,880.67 = $11,952.268

Earnings after tax for year 1 = $29,880.67 -$11,952.268 = $17,928.40

net cash flow for year 1 =  $17,928.40 + depreciation = $17,928.40 + $3,333.33 = $21,261.73

earnings before tax for year 2 is (4,100 * $30.00) - (4,100* $13.45) - $41,670 - (45% of $10,000)

= $123,000 - $55,145 - $41,670 - $4,500 = $21,685

Tax = 0.40 * $21,685 = $8,674

Earnings after tax for year 2 = $21,685 -$8,674 = $13,011

net cash flow for year 2 =  $13,011+ depreciation = $13,011 + $4,500 = $17,511

earnings before tax for year 3 is (4,300 * $30.31) - (4,300* $14.02) - $41,890 - (15% of $10,000)

= $130,333 - $60,286 - $41,890 - $1,500 = $26,657

Tax = 0.40 * $26,657 = $10,662.8

Earnings after tax for year 3 = $26,657 - $10,662.8 = $15,994.2

net cash flow for year 3=  $15,994.2+ depreciation = $15,994.2 + $1,500 = $17,494.2

earnings before tax for year 4 is (4,400 * $33.19) - (4,400* $14.55) - $40,100 - (7% of $10,000)

= $146,036 - $64,020 - $40,100 - $700 = $41,216

Tax = 0.40 * $41,216 = $16,486.4

Earnings after tax for year 4 = $41,216 - $16,486.4 = $24,729.6

net cash flow for year 4=  $24,729.6+ depreciation = $24,729.6 + $700 = $25,429.6

As mentioned above, we now need to discount these cash flows using WACC using the following formula

(net cash flow for the year) / (1 + discount rate or WACC)ⁿ, where n is the year in which the cash flow happens, and then subtract the initial outlay to arrive at the NPV

NPV = ($21,261.73 / 1.11) + ($17,511/1.11²) + ($17,494.2/1.11³) + ($25,429.6/1.11⁴) - $10,000

= $19,154.71 + $14,212.32 + $12,791.61 + $16,751.13 - $10,000 = $52,909.91

Hence, the NPV in the first scenario = $52,909.91. The fourth option is the right answer after accounting for some rounding errors

Now we will find out the NPV if we used the straight line depreciation method. Since there is no salvage value at the end the depreciation charged in each of the four years will be $10,000/4 or $2,500

Hence, earnings before tax for year 1 is (4,200 * $29.82) - (4,200* $12.15) - $41,000 - $2,500

= $125,244 - $51,030 - $41,000 - $2,500 = $30,714

Tax = 0.40 * $30,714 = $12,285.6

Earnings after tax for year 1 = $30,714 - $12,285.6 = $18,428.4

net cash flow for year 1 =  $18,428.4 + depreciation = $18,428.4 + $2,500 = $20,928.4

earnings before tax for year 2 is (4,100 * $30.00) - (4,100* $13.45) - $41,670 - $2,500

= $123,000 - $55,145 - $41,670 - $2500 = $23,685

Tax = 0.40 * $23,685 = $9,474

Earnings after tax for year 2 = $23,685 - $9,474 = $14,211

net cash flow for year 2 =  $14,211+ depreciation = $14,211 + $2,500 = $16,711

earnings before tax for year 3 is (4,300 * $30.31) - (4,300* $14.02) - $41,890 - $2,500

= $130,333 - $60,286 - $41,890 - $2,500 = $25,657

Tax = 0.40 * $25,657 = $10,226.8

Earnings after tax for year 3 = $25,657 - $10,226.8 = $15,394.2

net cash flow for year 3=  $15,394.2 + depreciation = $15,394.2 + $2,500 = $17,894.2

earnings before tax for year 4 is (4,400 * $33.19) - (4,400* $14.55) - $40,100 - $2,500

= $146,036 - $64,020 - $40,100 - $2,500 = $39,416

Tax = 0.40 * $39,416 = $15,766.4

Earnings after tax for year 4 = $39,416 - $15,766.4 = $23,649.6

net cash flow for year 4=  $23,649.6+ depreciation = $23,649.6 + $2,500 = $26,149.6

As mentioned above, we now need to discount these cash flows using WACC using the following formula

(net cash flow for the year) / (1 + discount rate or WACC)ⁿ, where n is the year in which the cash flow happens, and then subtract the initial outlay to arrive at the NPV

NPV = ($20,928.4 / 1.11) + ($16,711/1.11²) + ($17,894.2/1.11³) + ($26,149.6/1.11⁴) - $10,000

= $18,854.41 + $13,563.02 + $13,084.08 + $17,225.55 - $10,000 = $52,727.06 Option 3 is the right answer

Hence, using the accelerated depreciation method will result in the highest NPV for the project

If the after tax cash flow of one division were to fall by $400 because of the project, we have to calculate the NPV by deducting $400 from each year's after-tax cash flow.

Hence, new NPV = (($21,261.73 - 400) / 1.11) + (($17,511- 400)/1.11²) + (($17,494.2-400)/1.11³) + (($25,429.6 - $400)/1.11⁴) - $10,000

= $18,793.69 + $13,887.67 + $12,499.13 + $16,487.77 - $10,000 = $51,668.26

Hence, the company has to reduce the NPV of the project by $52,909.91 - $51,668.26 = $1,241.65

The third option is the right answer