Question

Able Company has a possible project. It takes an initial investment of $600, and will produce two years of pretax, net cash flow of $1,000 each year. Taxes are assessed at 30 percent. The time value of money is 10 percent. We will compute the present value of the project under a variety of circumstances.

1. Suppose the $600 initial investment is money that we put aside for working capital. Working capital includes money we use in a cycle to pay vendors while we wait for collections from customers. At the end of the two years, we can recover the $600. The $600 is not deductible for tax purposes and not taxable when we recover it.

Find the present value of the project.

2. Suppose the $600 initial investment is investment in equipment that will be depreciated for tax purposes. The depreciation is taken straight line. That’s $300 of depreciation each year.

The net cash in is the $1,000 less taxes paid. Taxes paid are the tax rate x ($1,000 – depreciation).

Find the present value of the project.

3. Suppose the $600 initial investment is investment in equipment that will be depreciated for tax purposes. The depreciation is taken as accelerated depreciation of $400 in the first year and

$200 in the second year.

The net cash in is the $1,000 less taxes paid. Taxes paid are the tax rate x ($1,000 – depreciation).

Find the present value of the project.

4. Suppose the $600 initial investment is expensed off entirely in the first year for tax purposes.

The net cash in is the $1,000 less taxes paid. Taxes paid in the first year are tax rate x ($1,000-

$600). Taxes paid in the second year are tax rate x $1,000. Find the present value of the project.

5. Fill in the following schedule and comment on why the present value varies across the cells. I know that the difference in present value is small for conditions 2, 3, and 4. Despite the small difference, it illustrates the direction of the effect. Earlier tax deductions increase the present value. The effect would be greater for larger projects that cover more time periods.

	The initial investment is:
Setup	1. Working capital	2. Depreciated straight line	3. Depreciated accelerated	4. Tax deduction entirely in first year
Present value

Answer 1

Able Company:

We have given following information,

Initial investment in project = $600

Pretax cash flow each year = $1,000

Tax rate = 30%

Time value of money i.e. Present value discounting rate = 10%

Now, we need to calculate present value in different circumstances.

Present value factors are:

Formula is 1/(1+r)ⁿ where r is rate of time value of money i.e. 10% and n is no of years which are 2 years

Year zero - it is always 1 irrespective of rate of discount.

Year 1 = 1/(1+0.10)¹ = 0.9091

Year 2 = 1/(1+0.10)² = 0.8264

1) Situation 1:

In the first case, we have given that $600 initial investment is being treated as working capital and it will be recovered at the end of 2nd year. But, it will not have any tax effect.

So, we will take $600 as working capital requirement in year zero and this working capital will be recovered after 2 years which is cash inflow for project and will be taken as $600 recovery in year 2.

No depreciation and other information is given.

Now, we will calculate present value of project as follows:

Initial investment = requirement of working capital = $600

Calculation of operating cash flow:

Particulars	Year 1	Year 2
Pretax cash inflows given	$1,000	$1,000
Less: Tax @ 30% on above	($300)	($300)
After tax cash inflow i.e. operating after tax cash inflow	$700	$700

We have terminal cash flow as recovery of working capital in year 2 as $600

Calculation of present value of project:

Year	Particulars	Cash inflow	Discounting factor calculated	Present value of cash inflow = Cash flow * Respective year's discounting factor
0	Working capital requirement	($600)	1	($600)*1 = ($600)
1	Operating after tax cash inflow	$700	0.9091	$700*0.9091 = $636.37
2	Operating after tax cash inflow	$700	0.8264	$700*0.8264 = $578.48
2	Recovery of working capital	$600	0.8264	$600*0.8264 = $495.84
	Present value			-$600+$636.37+$578.48+$495.84 = $1110.69

Present value in first situation is $1110.69

2) Situation 2:

Initial investment of $600 is treated as investment in equipment for depreciation purpose.

Depreciation each year given as $300

Net pretax cash inflow is $1,000

Depreciation is a non cash item. Hence, depreciation is an expenditure and will be deducted for tax purposes only. And to arrive at operating cash inflows after tax, we need add it back again. It is given that the net cash in is $1,000 - tax paid and tax paid is calculated as tax rate * ($1,000 - Depreciation)

Calculation of tax amount:

Particulars	Year 1	Year 2
Pretax cash flow	$1,000	$1,000
Less: Depreciation	($300)	($300)
Value	$700	$700
Tax amount @ 30%	$210	$210

Now, net cash in is calculated as:

Year 1 = $1,000-$210 = $790

Year 2 =$1,000 -$210 = $790

There is no terminal cash flow in this

Calculation of Present value of project:

Year	Particulars	Cash inflow	Present value factor	Present value of cash flow= Cash inflow * Present value factor
0	Initial investment in equipment	($600)	1	($600) * 1 = ($600)
1	Operating cash inflow	$790	0.9091	$790*0.9091 = $718.189
2	Operating cash inflow	$790	0.8264	$790*0.8264 = $652.856
	Present value			-$600+$718.189+$652.856 = $771.045

Present value of project is $771.045

3) Situation 3:

Initial investment = $600

In this case, depreciation is different for both years. In year 1, it is $400 and in year 2, it is $200

The net cash in is the $1,000 less taxes paid. Taxes paid are the tax rate x ($1,000 – depreciation).

Calculation of taxed paid:

Particulars	Year 1	Year 2
Pretax cash flow	$1,000	$1,000
Less: Depreciation	($400)	($200)
Amount after depreciation	$600	$800
Tax @ 30% on above amount	$180	$240

Calculation of after tax cash flow:

Net cash in for year 1 = $1,000 - $180 = $820

Net cash in for year 2 = $1,000 - $240 = $760

Calculation of present value:

Year	Particulars	Cash inflow	Present value factor	Present value of cash flow
0	Initial investment	($600)	1	($600)*1 = ($600)
1	Cash inflow	$820	0.9091	$820*0.9091 = $745.462
2	Cash inflow	$760	0.8264	$760*0.8264 = $628.064
	Present value			-$600+$745.462+$628.064 = $773.526

Present value of project in situation 3 is $773.526

4) Situation 4:

It is given that initial investment is expensed off entirely in first year for tax purposes.

The net cash in is the $1,000 less taxes paid. Taxes paid in the first year are tax rate x ($1,000-

$600). Taxes paid in the second year are tax rate x $1,000. Find the present value of the project.

Calculations of taxes paid:

Year 1 = ($1,000-$600) * 30% as given in problem = $400*30% = $120

Year 2 = $1,000 *30% = $300

Calculations of cash inflow:

Year 1 = $1,000 - Taxes of $120 = $880

Year 2 = $1,000 - Taxes of $300 = $700

Calculation of present value:

Year	Particulars	Cash inflow	Present value factor	Present value of cash flow
0	Initial investment	($600)	1	($600)*1 = ($600)
1	Cash inflow	$880	0.9091	$880*0.9091 = $800.008
2	Cash inflow	$700	0.8264	$700*0.8264 = $578.48
	Present value			-$600+$800.008+$578.48 = $778.488

Present value in situation 4 is $778.488

Interpretation of problem:

Setup	Present value of project	Reasons why project value is different in all cases
Working capital	$1110.69	In this case, there were no depreciation to deduct and also working capital is being recovered in last year which is cash inflow and therefore, present value has been increased as compared to others as others don't have terminal cash inflow.
Depreciation straight line	$771.045	This present value is least of all above as depreciation is based on straight line which is same in all years. Hence, same amount is getting multiplied by time value of money factor which indicates present value in year 1 is less. Same tax amount is reflected in both years. Hence cash flows are same.
Depreciation accelerated	$773.526	In this, depreciation is accelerated.i.e. it is different in both the years and it compensate the time value of money factor in both years. Factor in year 1 is higher than in year 2. Simmilarly depreciation in year 1 is higher than in year 2 which both compensate each other. Because of this taxes are increasing in year 2. Hence cash inflow is decreasing in year 2.
Tax deduction entirely in first year	$778.488	In first year itself,600 amount is getting deducted which results in lower taxes in first year and taxes are increasing in second year which results in higher cash flow in year 2. Expenses are higher.