Chapter 14 Demonstration Problem Solutions Page 1

(1)

Please send comments and corrections to me at [email protected]

Demo 14-1 ANSWER

a.

First, we need to calculate the tax bill:

Year (A) (B) (C=A-B) (D=.4C)

Cash Flow Depreciation Taxable Inc Tx Rate Taxes

1 $ 100,000 - $94,000 = $6,000 x.4= $2,400

2 200,000 - 150,400 = 49,600 x.4= 19,840

3 250,000 - 90,240 = 159,760 x.4= 63,904

4 150,000 - 54,144 = 95,856 x.4= 38,342

5 100,000 - 54,144 = 45,856 x.4= 18,342

6 100,000 - 27,072 = 72,928 x.4= 29,171

6(Salvage) 50,000 - = 50,000 x.4= 20,000

Next, you subtract the tax bill from the cash flow from the investment:

Cash Flow Less Taxes After Tx Cash

Year 1 $ 100,000 $2,400 $97,600

Year 2 200,000 19,840 180,160

Year 3 250,000 63,904 186,096

Year 4 150,000 38,342 111,658

Year 5 100,000 18,342 81,658

Year 6 100,000 29,171 70,829

Year 6 (Salvage) 50,000 20,000 30,000

$ 950,000 $758,000

Now you need to get the present value of the after tax cash flow:

After Tx Cash PVIF PV

Year 1 $97,600 0.9091 $88,727

Year 2 180,160 0.8265 148,893

Year 3 186,096 0.7513 139,816

Year 4 111,658 0.6830 76,263

Year 5 81,658 0.6209 50,703

Year 6 70,829 0.5645 39,981

Year 6 (Salvage) 30,000 0.5645 16,935 Present Value of After Tax Cash Flow: $561,317 Investment: -$470,000 NPV: $91,317

(2)

Please send comments and corrections to me at [email protected] Using Excel:

b.

IRR:

c.

Payback Period

After Tx Cash

Cumulative After Tax Cash Flow

Needed Cash Flow Until Investment Is Recouped

Year 1 $97,600 $97,600 $372,400

Year 2 180,160 277,760 192,240

Year 3 186,096 463,856 6,144

Year 4 111,658 575,514

Year 5 Year 6

(3)

You only need part of the fourth year in order to recoup the remaining balance of our

$470,000 investment.

Portion of Year Needed To

Recoup Your Investment = _____Cash______

= _$6,144_

= .0550 Fourth Year Cash $111,658

You need .055 of the fourth year. The Payback Period is 3.055 years.

d.

Simple Rate of Return?

Depreciation Expense: ($470,000 - $50,000)/6 = $70,000 Yr.

(A) Cash Flow

(B) Deprec.

(C=A-B) BeforeTax Income

(D=.4C) Taxes

(40%)

(E=C-D) Net Income 1 $ 100,000 - $70,000 = $30,000 - $12,000 = $18,000 2 200,000 - $70,000 = 130,000 - 52,000 = 78,000 3 250,000 - $70,000 = 180,000 - 72,000 = 108,000 4 150,000 - $70,000 = 80,000 - 32,000 = 48,000 5 100,000 - $70,000 = 30,000 - 12,000 = 18,000 6 100,000 - $70,000 = 30,000 - 12,000 = 18,000

50,000 - =

$288,000

Average Annual Net Income = $288,000 / 6

(There are only 6 years, the Salvage sale and Year 6 payoff happened in the same year.)

Average Annual Net Income = $48,000

Accounting Rate of Return = Average Net Income / Average Investment Accounting Rate of Return = $48,000/$470,000

Accounting Rate of Return = 10.212765957%

(4)

Demo 14-2 ANSWER

a.

Payback Period:

What is the investment? 20x(2500) = 50,000

What is the annual after tax cash flow in the early years? 20,000

Payback Period = Original Investment / Annual Cash Flow

= 50,000/20,000

= 2.5 years or

Year Annual Cash Flow Cumulative Cash Flow

1 20,000 20,000

2 20,000 40,000

3 20,000 60,000

We know that the payback period ends in the third year. We need $10,000 from the third year in order to recoup our investment. The whole third year produces $20,000 of cash. So we need the following portion of the third year:

Needed Cash to Recoup

= 10,000

= .5 All Cash Produced in Final Year 20,000

b.

Accounting Rate of Return:

First, we need to calculate the average Net Income. The Net Income for each of the first six years is:

Annual After-Tax Cash Flow - Depreciation Exp.= 20,000 - 5,000 = 15,000 The annual Net Income for the last four years is:

Annual After-Tax Cash Flow - Depreciation Exp.= 25,000 - 5,000 = 20,000

(5)

Please send comments and corrections to me at [email protected] 6 x 15,000 = $ 90,000

4 x 20,000 = 80,000

Total Net Income: $170,000 Divide By No. Of Years: ÷10 Average Net Income: $17,000 Next, we have to calculate the Average Investment:

Original Investment + Salvage Value

= 50,000 + 0

= $25,000

2 2

Finally, we calculated the Accounting Rate of Return:

Average Net Income

= 17,000

= .68 Average Investment 25,000

c.

Net Present Value:

You could do it year by year, but let's use the annuity formula. The problem here is that the cash flow changes in the seventh year. Getting the Present Value of the annuity for the first six years is easy, but getting the Present Value of the annuity for the final four years is tricky. There are two ways to get the Present Value this annuity:

First Method:

The Present Value of a dollar a year for 6 years:

(1-(1/(1+d)ⁿ)/d = (1-(1/(1.12)⁶)/.12 = 4.1114 The Present Value of a dollar a year for 10 years:

(1-(1/(1+d)ⁿ)/d = (1-(1/(1.12)¹⁰)/.12 = 5.6502

If you subtract the six-year annuity from the ten-year annuity, then you have the Present Value of the annuity in the final four years:

5.6502-4.1114 = 1.5388 Second Method:

The Present Value of a four year annuity is:

(1-(1/(1+d)ⁿ)/d = (1-(1/(1.12)⁴)/.12 = 3.037349347 You will not receive this value until the end of the sixth year.

(1/(1+d)ⁿ = (1/(1.12)⁶= .506631121 x 3.037349347 = 1.5388

(6)

Please send comments and corrections to me at [email protected] The Present Value of the Cash Flow:

Years 1-6: 20,000 x 4.111 = $82,220 Years 7-10: 25,000 x 1.539 = 38,475 Present Value of Cash Flows: $120,695

Original Investment: -50,000

$70,695

Demo 14-3 ANSWER

a.

Depreciation Expense: ($150,000 - $30,000)/4 = $30,000 Payback Period.

Tax Expense:

Year 1 Year 2 Year 3 Year 4 Before-Tax Cash Flow: $60,000 $87,000 $42,000 $40,000 Less Depreciation: -30,000 -30,000 -30,000 -30,000 Taxable Income: $30,000 $57,000 $ 12,000 $10,000

x.3 x.3 x.3 x.3

Taxes (30%): $ 9,000 $17,100 $ 3,600 3,000 After-Tax Cash Flow:

Year 1 Year 2 Year 3 Before-Tax Cash Flow: $60,000 $87,000 $42,000 Less Taxes (30%): $ 9,000 $17,100 $ 3,600 Net Cash Flow: $51,000 $69,900 $38,400 Cumulative Cash Flow: $51,000 120,900 159,300 Payback occurs in the third year:

___Needed Cash __

= 150,000-120,900

= 29,100

= .7578125

Cash in Third Year 38,400 38,400

The Payback Period is 2.7578125 years.

(7)

Please send comments and corrections to me at [email protected] b.

Net Present Value:

Cash Flow:

Year 1 Year 2 Year 3 Year 4 Salvage Total Before-Tax Cash Flow: $60,000 $87,000 $42,000 $40,000

Less Taxes (30%) 9,000 17,100 3,600 3,000

Net Cash Flow: $51,000 $69,900 $38,400 $37,000 $30,000 x PVIF(15%): .86956 .75614 .65752 .57175 .57175

PV $44,348 $52,854 $25,249 $21,155 $17,153 $160,759

Less Investment: -150,000

NPV: $ 10,759

c.

Simple Rate of Return.

Net Income:

Year 1 Year 2 Year 3 Year 4 Before-Tax Cash Flow: $60,000 $87,000 $42,000 $40,000 Less Depreciation Expense: 30,000 30,000 30,000 30,000 Before-Tax Net Income: $30,000 $57,000 $ 12,000 $10,000 Tax Expense (30%): -9,000 -17,100 -3,600 -3,000 Net Income: $21,000 $39,900 $ 8,400 $7,000 Average Net Income: (21,000 + 39,900+8,400+7,000)/4 = $76,300/4= $19,075 Simple Rate of Return: 19,075/150,000 = 12.716666666%

(8)

Demo 14-4 ANSWER

a.

Payback Period:

First we need to calculate our After-Tax Cash Flow. We can calculate it by adding back the Depreciation Expense:

After-Tax Cash Flow = Net Income + Non-Cash Expenses (Depreciation)

= 48,000 + $40,000

= $88,000

Alternately, you could redo the income statement on a cash basis. If you do this, however, remember to leave the tax expense alone, because depreciation is a deduction for tax purposes:

Increase in annual cash revenue $200,000 Less: Cash operating expenses -80,000 Less: Income tax expense (40%): -32,000 After-Tax Cash Flow: $ 88,000 Payback Period = $400,000/88,000 = 4.5454545 years

b.

Simple Rate of Return:

Average Investment = (400,000 + 0)/2 = $200,000

Average Net Income / Original Investment = 48,000/400,000 = 12%

c.

Net Present Value (15%):

PVIFannuity = (1-(1/(1+d)ⁿ)/d = (1-(1/(1.15)¹⁰)/.15 = 5.0187686

Present Value of Cash Flow (5.0187586 x 88,000) : $441,650

Net Present Value $ 41,650

(9)

Please send comments and corrections to me at [email protected] d.

Net Present Value (20%):

PVIFannuity = (1-(1/(1+d)ⁿ)/d = (1-(1/(1.20)¹⁰)/.20 = 4.192472

Present Value of Cash Flow (4.192472 x 88,000) : $368,938

Net Present Value -$ 31,062