Chapter 14 Demonstration Problem Solutions Page 1

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1 Chapter 14 Demonstration Problem Solutions Page 1 Demo 14-1 ANSWER a. First, we need to calculate the tax bill: Year (A) (B) (CA-B) (D.4C) Cash Flow Depreciation Taxable Inc Tx Rate Taxes 1 $ 100,000 - $94,000 $6,000 x.4 $2, , ,400 49,600 x.4 19, ,000-90, ,760 x.4 63, ,000-54,144 95,856 x.4 38, ,000-54,144 45,856 x.4 18, ,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, ,160 Year 3 250,000 63, ,096 Year 4 150,000 38, ,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, $88,727 Year 2 180, ,893 Year 3 186, ,816 Year 4 111, ,263 Year 5 81, ,703 Year 6 70, ,981 Year 6 (Salvage) 30, ,935 Present Value of After Tax Cash Flow: $561,317 Investment: -$470,000 NPV: $91,317

2 Chapter 14 Demonstration Problem Solutions Page 2 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, , ,240 Year 3 186, ,856 6,144 Year 4 111, ,514 Year 5 Year 6

3 Chapter 14 Demonstration Problem Solutions Page 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_ Fourth Year Cash $111, You need.055 of the fourth year. The Payback Period is years. d. Simple Rate of Return? Depreciation Expense: ($470,000 - $50,000)/6 $70,000 Yr. (A) (B) (CA-B) BeforeTax Income (D.4C) Taxes (40%) (EC-D) Net Income Cash Flow Deprec. 1 $ 100,000 - $70,000 $30,000 - $12,000 $18, ,000 - $70, ,000-52,000 78, ,000 - $70, ,000-72, , ,000 - $70,000 80,000-32,000 48, ,000 - $70,000 30,000-12,000 18, ,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 %

4 Chapter 14 Demonstration Problem Solutions Page 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 or Payback Period Original Investment / Annual Cash Flow 50,000/20, years Year Annual Cash Flow Cumulative Cash Flow 1 20,000 20, ,000 40, ,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 All Cash Produced in Final Year 20,000.5 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 Chapter 14 Demonstration Problem Solutions Page 5 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, $25,000 Finally, we calculated the Accounting Rate of Return: Average Net Income 17,000 Average Investment 25, 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 )/ The Present Value of a dollar a year for 10 years: (1-(1/(1+d) n )/d (1-(1/(1.12) 10 )/ 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: Second Method: The Present Value of a four year annuity is: (1-(1/(1+d) n )/d (1-(1/(1.12) 4 )/ You will not receive this value until the end of the sixth year. (1/(1+d) n (1/(1.12) x

6 Chapter 14 Demonstration Problem Solutions Page 6 The Present Value of the Cash Flow: Demo 14-3 ANSWER a. Years 1-6: 20,000 x $82,220 Years 7-10: 25,000 x ,475 Present Value of Cash Flows: $120,695 Original Investment: -50,000 $70,695 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, , ,300 Payback occurs in the third year: Needed Cash 150, ,900 29,100 Cash in Third Year 38,400 38, The Payback Period is years.

7 Chapter 14 Demonstration Problem Solutions Page 7 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%): 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, ,900+8,400+7,000)/4 $76,300/4 $19,075 Simple Rate of Return: 19,075/150, %

8 Chapter 14 Demonstration Problem Solutions Page 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, years b. Simple Rate of Return: c. Average Investment (400, )/2 $200,000 Average Net Income / Original Investment 48,000/400,000 12% Net Present Value (15%): PVIF annuity (1-(1/(1+d) n )/d (1-(1/(1.15) 10 )/ Present Value of Cash Flow ( x 88,000) : $441,650 Original Investment: -400,000 Net Present Value $ 41,650

9 Chapter 14 Demonstration Problem Solutions Page 9 d. Net Present Value (20%): PVIF annuity (1-(1/(1+d) n )/d (1-(1/(1.20) 10 )/ Present Value of Cash Flow ( x 88,000) : $368,938 Original Investment: -400,000 Net Present Value -$ 31,062