# Vol. 2, Chapter 4 Capital Budgeting

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1 Vol. 2, Chapter 4 Capital Budgeting Problem 1: Solution Answers found using Excel formulas: 1. Amount invested = \$10,000 \$21, Compounding period = annually Number of years = 10 Annual interest rate = 8% Effective interest rate = 8% # of periods compounded = Amount invested = \$5,000 \$8, Compounding period = semi-annually Number of years = 5 Annual interest rate = 10% Effective interest rate = 5% = 10% / 2 # of periods compounded = 10 = 5 years * 2 3. Amount invested = \$8,000; PV of \$8,000 = \$7, Compounding period = quarterly Number of years = 4 \$12, Annual interest rate = 12% Effective interest rate = 3% = 12% / 4 # of periods compounded = 16 = 4 years * 4 Answers found using time value of money tables: 1. Amount invested = \$10,000 =\$10,000 FVF(.08,10) Compounding period = annually =\$10, Number of years = Annual interest rate = 10 8% =\$21, Effective interest rate = 8% # of periods compounded = Amount invested = \$5,000 =\$5,000 FVF(.05,10) Compounding period = semi-annually =\$5, Number of years = 5 =\$8, Annual interest rate = 10% Effective interest rate = 5% = 10% / 2 # of periods compounded = 10 = 5 years * 2 3. Amount invested = \$8,000 =8,000 FVF(.03,16) Compounding period = quarterly =8, Number of years = 4 =\$12, Annual interest rate = 12% Effective interest rate= 3% =12% / 4 # of periods compounded= 16 = 4 years 4 Capital Budgeting 1

2 Problem 2: Solution Answers found using Excel formulas: 1. Amount required = \$100,000 Compounding periods = annually Annual interest rate = 10% Effective interest rate = 10% Number of compounding periods = 5 Amount to invest = \$62, Amount required = \$100,000 Compounding periods = semi-annually Annual interest rate = 10% Effective interest rate = 5% = 10% / 2 Number of compounding periods = 10 = 5 years 2 Amount to invest = \$61, Amount required = \$100,000 Compounding periods = quarterly Annual interest rate = 8% Effective interest rate = 2% = 8% / 4 Number of compounding periods = 20 = 5 years 4 Amount to invest = \$67, Answers found using time value of money tables: 1. Amount required = \$100,000 =\$100,000 PVF(.10,5) Compounding periods = annually =\$100, Annual interest rate = 10% Effective interest rate = 10% Number of compounding periods =5 Amount to invest = \$62, Amount required = \$100,000 =\$100,000 PVF(.05,10) Compounding periods = semi-annual =\$100, Annual interest rate = 10% Effective interest rate = 5% = 10% / 2 Number of compounding periods= 10 = 5 years 2 Amount to invest = \$61, Amount required = \$100,000 =\$100,000 PVF(.02, 20) Compounding periods = quarterly =\$100, Annual interest rate = 8% Effective interest rate = 2% = 8% / 4 Number of compounding periods= 20 =5 years 4 Amount to invest = \$67,300 Capital Budgeting 2

3 Problem 3: Solution Answers found using time value of money tables: Amount at age 29 Amount at age 65 =\$10,000 FVFA(.10,10) =\$10, =\$159,374 =\$159,374 (1+.10)^36 =\$4,478, Note: Exhibit 1 does not contain a line for 36 years so the formula (1+k)^n is used. Problem 4: Solution 1. Invest \$8,000 annually starting in one year for 10 and then let the investment grow. Age Calculation Solution \$8, \$127, \$127, ( ) \$2,224, Note: is from the future value factors for an annuity table 10%, 10 years. 2. Wait until age 36 to invest \$10,000 per year for 30 years. Age Calculation Solution \$10, \$1,644, Problem 5: Solution Answer found using Excel formula: \$1,060, Answer found using time value of money table: = \$100,000 PVFA(.08,20) (1+k) = \$100, (1+.08) = \$1,060,355 Problem 6: Solution 1. \$10,000 1 = \$10,000 \$10, = 53,282 \$63, \$100, = \$32, \$10, = \$56, \$12,000 1 = \$12, \$12, = 36, \$8, * = 18, Total \$66, *Sum of present value factors for the end of years 5-9 (or the beginning of years 6-10) from Chapter 13, Exhibit 2. Capital Budgeting 3

4 1. ARR Problem 7: Solution 1. Amount = \$25,000 ) = \$1, Amount needed after 10 years = \$27, = \$24, Amount to be invested each year for ten years: Amount = \$24, ) = \$1, Note: The investment is to be made at the end of each year for ten years. Amounts needed at the end of ten years for each year in college: Year Amount 1 \$ 25, \$27, , \$29, , \$31, , \$33, , \$123, Amount to be invested each year = \$123, ) = \$8, Problem 8: Solution 1. ARR = Average Annual Income Average Investment = \$5,731,070 \$5,000, = 22.92% 2. No, since computed ARR at 22.92% is less than 35%. Problem 9: Solution ARR = Average Annual Project Income = \$7, % Average Investment \$7,500 Avg. Annual Income = Revenue - Cash Expenses - Depreciation Avg. Annual Income = \$80,000 - \$70,000 - \$3,000 = \$7,000 Avg. Investment = Project Cost - Salvage = \$15,000-0 = \$7, Capital Budgeting 4

5 Problem 9: Solution (continued) 2. Payback Yearly Cash Flow = Incremental revenues - incremental cash expenses Yearly Cash Flow = \$80,000 - \$70,000 Yearly Cash Flow = \$10,000 Cost of Equipment Payback Period = Annual Cash Flow Payback Period = \$15,000 =1.5 years \$10, NPV 4. IRR NPV = Cost + CF Annuity Factor NPV = \$(15,000) + \$10, NPV = \$24,927 Annual Cash Flows 10,000 Discount Factor ,000 Cost of Equipment (15,000) NPV 0 Note: The discount rate of approximately 60.3% results in an NPV of \$0.00. Therefore this is the IRR. Problem 10: Solution 1. Project cost = \$23,500 Year Cost savings = \$5, , , , ,000 5 Payback is 5.0 years, so Ms. Rollins should not invest in the oven. Capital Budgeting 5

6 Problem 10: Solution (continued) 2. Cost savings = \$4,500 each year Payback = \$23,500 \$4,500 = 5.22 years Since 5.22 years is greater than the required payback period, Ms. Rollins should not invest in the oven. Problem 11: Solution Present value of income stream Increase in park revenue \$ 300,000 Increase in costs 70,000 Annual profit increase 230,000 Annuity factor: 15%/10 yrs ,154,324 Less: Cost 1,500,000 Negative NPV \$ (345,676) No, the equipment should not be purchased. Problem 12: Solution Annual pizza sales \$50,000 Less: food costs 35% -17,500 Less: labor costs 30% -15,000 17,500 Annuity factor 15% / 7 years ,807 Present value of salvage value \$2, ,559 Less: Cost -20,000 NPV \$53,559 The machine should be purchased. Problem 13: Solution 1. Payback period Cash revenues: \$50,000 Cash expenses: \$20,000 Net cash flow: \$30,000 Payback period: Investment = \$100,000 = 3.3 years Annual Cash Flow \$30, PV of annual cash flows: \$30, = \$108,144 Cost of equipment \$100,000 NPV \$ 8,144 Capital Budgeting 6

7 Problem 14: Solution 1. Payback Analysis Years Hence Additional Rooms Food Service Operation 0 \$ 500,000 \$500, , , , , , , , , ,000 6 \$0 / \$130,000 = 0 \$120,000 / \$140,000 =.86 Payback Period 5.0 years 5.86 years 2. NPV Additional Rooms Present Value of Years Hence Cash Flow P.V. Factor Cash Flow 0 \$(500,000) \$ (500,000.00) 1 80, , , , , , , , , , , , , , , , , , , , Capital Budgeting 7 NPV \$220, Food Service Operation Years Hence Cash Flow P.V. Factor Present Value of Cash Flow 0 \$(500,000) \$(500,000.00) 1 20, , , , , , , , , , , , , , , , , , , , NPV \$185,427.71

8 Problem 15: Solution 1. Increased green fees \$20,000 Increased food sales net of related costs 2,000 Increased miscellaneous sales 8,000 Increased related expenses (4,000) 4,000 Increased annual cash flow 26,000 Annuity factor Present value of cash flows 50,000 Initial construction cost 50,000 Net present value \$0.00 Internal rate of return = % 2. Increased green fees \$20,000 Increased food sales net of related costs 2,000 Increased miscellaneous sales 8,000 Increased related expenses (4,000) 4,000 Increased annual cash flow 26,000 Annuity factor Present value of cash flows 146,905 Initial construction cost Net present value 50,000 \$96, Problem 16: Solution Present value of cash outflows: keeping present machine Annual Cash Expenditures \$16, Less: Tax Savings 30% -4, Annual Cash Outflow Net of Tax 11, Annuity Factor 12%/5 years Present Value of Cash Flows \$40, Purchasing new machine Annual Cash Expenditures \$12, Less: Tax Savings 30% -3, Annual Cash Flow Net of Tax 9, Annuity Factor 12%/5 years Present Value of Annual Cash Flows 32, Plus: Cost of Machine 15, Less: Salvage Value of Old Machine Less Taxes at 30% -2, Less: Salvage Value of New Machine Less Taxes at 30% at the End of 5 Years (3, ) -1, Present Value \$43, No, the present value of cash flows are less at \$40, with the present equipment than with the proposed purchase. Capital Budgeting 8

9 Problem 17: Solution Part 1 Pre-Depr. Depr. Depr. Pretax Income Net Year Income Equip. Build. Income Taxes Income 1 (\$500,000) \$800,000 \$300,000 (\$1,600,000) \$0 (\$1,600,000) 2 (100,000) 640, ,000 (1,040,000) 0 (1,040,000) 3 400, , ,000 (412,000) 0 (412,000) 4 1,000, , , , , ,000, , ,000 2,372, ,372, ,000, , ,000 4,437, ,457 4,316, ,000, , ,000 4,490,285 1,347,086 3,143, ,000, , ,000 4,532,228 1,359,668 3,172, ,000, , ,000 4,565,782 1,369,735 3,196, ,000, , ,000 4,592,626 1,377,788 3,214,838 Net Add Cash Year Income Depr. Flow 1 (\$1,600,000) \$1,100,000 (\$500,000) 2 (1,040,000) 940,000 (100,000) 3 (412,000) 812, , , ,600 1,000, ,372, ,680 3,000, ,316, ,144 4,878, ,143, ,715 3,652, ,172, ,772 3,640, ,196, ,218 3,630, ,214, ,374 3,622,212 Interest Rate 0.12 Present value of cash flows \$10,166,012 Sale of Hotel: Cost \$20,000,000 Accumulated Depr. 6,570,503 Net book 13,429,497 Proceeds 15,000,000 Gain on sale 1,570,503 Taxes 471,151 Cash flow \$14,528,849 Present value of cash flow from sale 4,677,901 Original cost (20,000,000) Net present value(\$ 5,156,088) Capital Budgeting 9

10 Problem 17: Solution (continued) Part 2 Internal Rate of Return: Cash Flows Present Value Cost \$20,000,000 (\$20,000,000) Cash flows year 1 (500,000) (479,079) 2 (100,000) (91,807) 3 400, , ,000, , ,000,000 2,422, ,878,543 3,774, ,652,915 2,708, ,640,332 2,586, ,630,265 2,470, ,300,113 5,413,174 Net present value -3 IRR = Note: Determining an IRR to this degree of accuracy is only practical when using a computer. Part 3 The Fairview Hotel should not be purchased if the desired return is 12% since the NPV is negative and the IRR is only 4.367%. Capital Budgeting 10

11 Problem 18: Solution Keep: 20X1 20X2 20X3 20X4 20X5 EBDIPIT \$121,000 \$125,000 \$131,000 \$133,000 \$135,000 Depreciation 10,000 8,000 6,000 4,000 2,000 Interest 1, Prop. taxes 3,000 3,200 3,400 3,600 3,800 Insurance 3,000 3,000 3,000 3,000 3,000 Pretax Income 104, , , , ,000 Taxes 34,320 36,300 38,940 40,260 41,580 Net Income \$ 69,680 \$ 73,700 \$ 79,060 \$ 81,740 \$ 84,420 Cash Flow: Net Income \$ 69,680 \$ 73,700 \$ 79,060 \$ 81,740 \$ 84,420 Add: Depr. 10,000 8,000 6,000 4,000 2,000 Less: Debt Red. 2,000 2,000 2,000 2,000 2,000 Cash Flow \$ 77,680 \$ 79,700 \$ 83,060 \$ 83,740 \$ 84,420 Present Value \$ 69,357 \$ 63,536 \$ 59,120 \$ 53,218 \$ 47,902 Total of present value of above cash flows \$293,134 Sales price of building \$20,000 Net book value 0 Gain on sale Taxes 20,000 5,000 Net cash flow from sale \$15,000 Present value of cash flow from sale of building 8,511 Total \$301,646 Capital Budgeting 11

12 Problem 18: Solution (continued) Sale and Leaseback: 20X1 20X2 20X3 20X4 20X5 EBDIPIT \$121,000 \$125,000 \$131,000 \$133,000 \$135,000 Lease expense 12,000 12,000 12,000 12,000 12,000 Pretax income 109, , , , ,000 Income tax 35,970 37,290 39,270 39,930 40,590 Net income \$ 73,030 \$ 75,710 \$ 79,730 \$ 81,070 \$ 82,410 Present value \$ 65,205 \$ 60,356 \$ 56,750 \$ 51,521 \$ 46,762 Total present value \$280,594 Sale of Restaurant: Income Cash Flow Selling price \$ 50,000 \$ 50,000 Net book 30,000 Gain \$20,000 Taxes 5,000 Payment of mortgage (10,000) Cash flow from sale \$ 35,000 35,000 Total present value of this option \$315,594 Since the present value of the cash flows is greater with the sale and leaseback option, the Holt Company should pursue this alternative. Capital Budgeting 12

13 Problem 19: Solution Year Cash Savings/Expenses: Labor Cost Savings \$ 30,000 \$30,000 \$30,000 \$ 30,000 \$30,000 Annual cash expenses (10,000) (10,000) (10,000) (10,000) (10,000) Net cost reduction 20,000 20,000 20,000 20,000 20,000 Tax savings (costs) 9,800 3,080 (952) (4,928) (7,000) Total Annual Cash Flow 29,800 23,080 19,048 15,072 13,000 PV Factors PV of Cash Flows 27,091 19,073 14,311 10,294 8,072 Total PV of Cash Flows 78,841 PV of Salvage Value 20, = 12,418 Total 91,259 Less: Cost of Copier 120,000 NPV \$ (28,741) Recommendation: No the copier should not be purchased! Year Tax Savings (Costs) Calculations: Net cash cost reductions \$20,000 \$20,000 \$20,000 \$20,000 \$20,000 Less: Depreciation* 48,000 28,800 17,280 5,920 - Reduction in Taxable Income 28,000 8,800 (2,720) (14,080) (20,000) Marginal tax rate Tax Savings (Costs) 9,800 3,080 (952) (4,928) (7,000) * Double Declining Balance = Undepreciated Cost * (2/n) Annual Depreciation Year 1 \$120,000 * (0.4) = \$48,000 Year 2 \$72,000 * (0.4) = \$28,800 Year 3 \$43,200 * (0.4) = \$17,280 Year 4 \$25,920 - \$20,000 = \$5,920 Year 5 0 Note: Depreciation was limited to the cost - salvage value of \$100,000. Capital Budgeting 13

14 Problem 20: Solution Part 1 Investment Project #1: Cash flows: years 1-20 \$200,000 Present value factor ,493,880 Cost 1,000,000 Net present value \$ 493,880 Investment Project #2: Year Cash Flow 1 (200,000) 2 (50,000) 3 200, , ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100, ,100,000 Present value of above cash flows 5,180,539 Discount rate 0.12 Purchase cost 4,000,000 Net present value \$1,180,539 Based on the NPV model, select Investment Project #2. Capital Budgeting 14

15 Problem 20: Solution (continued) Part 2 Investment Project #1: IRR = Year Cash Flow Present Value 1 \$200,000 \$167, , , , , ,000 98, ,000 82, ,000 68, ,000 57, ,000 48, ,000 40, ,000 33, ,000 28, ,000 23, ,000 19, ,000 16, ,000 13, ,000 11, ,000 9, ,000 8, ,000 6, ,000 5,742 Total 1,000,000 Cost 1,000,000 Net present value (0) Investment Project #2: IRR = Year Cash Flow Present Value 1 (200,000) (173,878) 2 (50,000) (37,792) 3 200, , , , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100, , ,100,000 88, ,100,000 76, ,100,000 66,941 Capital Budgeting 15

16 Problem 20: Solution (continued) Total 4,000,000 Cost 4,000,000 Net present value (0) Based on the IRR model, select Investment Project #1. Note that this example shows clearly why it is preferable to follow the NPV model when the NPV and IRR models disagree. Although the IRR is higher for Project #1, Project #2 provides much more money. Capital Budgeting 16

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### Numbers 101: Taxes, Investment, and Depreciation The Anderson School at UCLA POL 2000-20 Numbers 101: Taxes, Investment, and Depreciation Copyright 2002 by Richard P. Rumelt. In the Note on Cost and Value over Time (POL 2000-09), we introduced the basic

### Chapter 7: Net Present Value and Capital Budgeting Chapter 7: Net Present Value and Capital Budgeting 7.1 a. Yes, the reduction in the sales of the company s other products, referred to as erosion, should be treated as an incremental cash flow. These lost

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### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### CHAPTER 7 MAKING CAPITAL INVESTMENT DECISIONS CHAPTER 7 MAKING CAPITAL INVESTMENT DECISIONS Answers to Concepts Review and Critical Thinking Questions 1. In this context, an opportunity cost refers to the value of an asset or other input that will

### Cash Flow, Taxes, and Project Evaluation. Remember Income versus Cashflow Cash Flow, Taxes, and Project Evaluation Of the four steps in calculating NPV, the most difficult is the first: Forecasting cash flows. We now focus on this problem, with special attention to What is cash

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### Continue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not. Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two

### Capital Budgeting: Decision. Example. Net Present Value (NPV) FINC 3630 Yost Capital Budgeting: Decision Criteria Example Consider a firm with two projects, A and B, each with the following cash flows and a 10 percent cost of capital: Project A Project B Year Cash Flows Cash Flows

### Practice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4. PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor

### The Time Value of Money C H A P T E R N I N E The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 \$1,000 present value \$ 10% interest \$1,464.10 future value 0 1 2 3 4 Number of periods Figure

### 9-17a Tutorial 9 Practice Review Assignment 9-17a Tutorial 9 Practice Review Assignment Data File needed for the Review Assignments: Restaurant.xlsx Sylvia has some new figures for the business plan for Jerel's. She has received slightly better

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### Solutions to Chapter 8. Net Present Value and Other Investment Criteria Solutions to Chapter 8 Net Present Value and Other Investment Criteria. NPV A = \$00 + [\$80 annuity factor (%, periods)] = \$00 \$80 \$8. 0 0. 0. (.) NPV B = \$00 + [\$00 annuity factor (%, periods)] = \$00 \$00

### Will the future benefits of this project be large enough to justify the investment given the risk involved? Chapter 1 The Overall Process Capital Expenditures Whenever we make an expenditure that generates a cash flow benefit for more than one year, this is a capital expenditure. Examples include the purchase

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### Main TVM functions of a BAII Plus Financial Calculator Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

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### CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project

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### 5. Time value of money 1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

### Net Present Value and Other Investment Criteria Net Present Value and Other Investment Criteria Topics Covered Net Present Value Other Investment Criteria Mutually Exclusive Projects Capital Rationing Net Present Value Net Present Value - Present value

### E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

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### Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1 Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

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### Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

### ] (3.3) ] (1 + r)t (3.4) Present value = future value after t periods (3.1) (1 + r) t PV of perpetuity = C = cash payment (3.2) r interest rate Present value of t-year annuity = C [ 1 1 ] (3.3) r r(1 + r) t Future value of annuity

### 1. What are the three types of business organizations? Define them Written Exam Ticket 1 1. What is Finance? What do financial managers try to maximize, and what is their second objective? 2. How do you compare cash flows at different points in time? 3. Write the formulas

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### Review Solutions FV = 4000*(1+.08/4) 5 = \$4416.32 Review Solutions 1. Planning to use the money to finish your last year in school, you deposit \$4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen

### Chapter 14 Notes Page 1 Chapter 14 Notes Page 1 Capital Budgeting This chapter examines various tools used to evaluate potential projects or investments. Accountants advocate the use of the Simple Rate of Return, which is based Chapter 20 Lease Financing ANSWERS TO END-OF-CHAPTER QUESTIONS 20-1 a. The lessee is the party leasing the property. The party receiving the payments from the lease (that is, the owner of the property) CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of