Time Value of Money

Accounting Rate of Return

What is the accounting rate of return for a project that is estimated to yield total income of $390,000 over three years and costs $920,000? _____________________________________________________________________________________________ SOLUTION: Accounting Rate of Return = Annual Net Income / Initial Investment                                                 = ($390,000 / 3 ) / $920,000                                                 = $130,000 / $920,000                                                 = 14.13%  

Payback Period

A project has estimated annual net cash flows of $80,000 and is estimated to cost $340,000. What is the payback period?                                                                                                                                                                          SOLUTION: Payback Period = Initial Investment / Annual Net Cash Flow                             = 340,000 / $80,000                             = 4.25 years

Rate of Return/Payback Period

Blue Marlin Company is considering the purchase of new equipment for its factory. It will cost $250,000 and have a $50,000 salvage value in five years. The annual net income from the equipment is expected to be $25,000, and depreciation is $40,000 per year. Calculate the accounting rate of return and payback period for the equipment:                                                                                                                                                                 Accounting Rate of Return = Annual Net Income / Initial Investment                                                  = $25,000 / $250,000                                                 = 10% Payback Period = Initial Investment / Annual Net Cash Flow                              = Initial Investment / (Net Income + Depreciation)                              =$250,000 / (25,000 + $40,000)                              = 3.85 years

Net Present Value

   Citrus Company is considering a project that has estimated annual net cash flows of $32,000 for six years and is estimated to cost $150,000. Citrus's cost of capital is 8%: Determine the net present value of the project:                                                                                                                                                                          SOLUTION: Year                   Annual Cash Flow                   PV Factor (8%)                  Present Value 0                        $(150,000)                                         ---                               $(150,000) 1-6                     $32,000                                         4.6229                           147,932.80 NPV                                                                                                                  $(2,067.20)                                                                                                                                                                         The negative NPV shows that the present value of the future cash inflows for the project is less than the original investment it requires. A negative NPV suggests the project is unacceptable.

Internal Rate of Return

Olive Company is considering a project that is estimated to cost $286,500 and provide annual net cash flows of $57,523 for the next five years. What is the internal rate of return for this project?                                                                                                                                                                 SOLUTION From Excel:  Year      Cash Flow 0            $(286,500) 1            $57,523 2            $57,523 3            $57,523 4            $57,523 5            $57,523                                                                                                                                                                    =IRR(B2:B7,0.1)*100 (10% is default)

Future Value of Savings

On January 1, 2018, you deposit $8,000 in a savings account. The account will earn 8% annual compound interest, which will be added to the fund balance at the end of the year.                                                                                                                                                                            What will the balance be in the savings account at the end of 10 years? $8,000 X 2.1589 = $17,271.20 (Future value of $1, 8%, 10 years)                                                                                                                                                                             What is the total interest for the 10 years? $17,271.20 - $8,000 = $9,271.20 (Time value of money, or interest)                                                                                                                                                                             How much interest revenue did the fund earn in 2018 and 2019? 2018: $8,000 X 8% = $640 (interest) 2019: ($8,000 + $640) X 8% = $691.20 (interest)

Future Value of a Deposit

You are saving for a Porsche Carrera Cabriolet, which currently sells for nearly half a million dollars. Your plan is to deposit $15,000 at the end of each year for the next 10 years. You expect to earn 8% per year. Determine how much you will have saved after 10 years: Future Value of Annuity of $1 (i=8%, n=10): 14.4866 $15,000 X 14.4866 = $217,299 (after 10 years)                                                                                                                                                                                      Determine the amount saved if you were able to deposit $17,500 each year: $17,500 X 14.4866 = $253,515.50 (after 10 years)                                                                                                                                                                                     Determine the amount saved if you deposit $15,000 each year, but with 10% interest: Future Value of Annuity of $1 (i=10%, n=10): 15.9374 $15,000 X 15.9374 = $239,061 (after 10 years)

Rate of Return/Payback Period/NPV

Balloons By Sunset (BBS) is considering the purchase of two new hot air balloons so that it can expand its desert sunset tours. Various information about the proposed investment follows: Initial Investment                               $420,000 Useful Life                                           10 years Salvage Value                                      $50,000 Annual Net Income Generated        $37,8000 BBS's Cost of Capital                          11%                                                                                                                                                                             Calculate the Accounting Rate of Return:    ARR = Annual Net Income / Initial Investment                        = $37,800 / $420,000                        = 9% Calculate the Payback Period:    PP = Initial Investment / Annual Net Cash Flow                      = Initial Investment / (Net Income + Depreciation)                      = $420,000 / ($37,800 + [($420,000 - $50,000) / 10]                      = $420,000 / 74,800                      = 5.61 years Calculate the Net Present Value: Year                  Annual Cash Flow                  PV Factor (11%)                  Present Value 0                        $(420,000)                                     ---                                    $(420,000) 1-10                        74,800                                 5.8892                                     440,512 10                           50,000                                 0.3522                                        17,610 NPV                            ---                                          ---                                      $(38,122) *Annual cash flow = $37,800 + [($420,000 - $50,000) / 10] = $74,800 Recalculate the Net Present Value assuming BBS's cost of capital is 15%:                                                                                                                          Present Value                                                                                                                            $(420,000)                                                                                                                                375,406                                                                                                                                  12,360                                                                                                                              $(32,234) *Annual cash flow = $37,800 + [($420,000 - $50,000) / 10] = $74,800

Time Value of Money, Cumulative

Hearne Company has a number of potential capital investments. Because these projects vary in nature, initial investment, and time horizon, management is finding it difficult to compare them. Assume the straight-line depreciation method is used. Project 1: Retooling This project would require an initial investment of $4,850,000. It would generate $865,000 in additional net cash flow each year. The new machinery has a useful life of eight years and a salvage value of $1,000,000. Project 2: Patent The patent would cost $3,400,000, which would be fully amortized over five years. Production of this product would generate $425,000 additional annual net income for Hearne. Project 3: Purchase Trucks Hearne could purchase 25 new delivery trucks at a cost of $115,000 each. The fleet would have a useful life of 10 years, and each truck would have a salvage value of $5,000. Purchasing the fleet would allow Hearne to expand its customer territory resulting in $200,000 additional net income per year.                                                                                                                                                                                Calculate Annual Net Income = Annual Cash Flow - Depreciation                                                        = [$865,000 - (($4,850,000 - 1,000,000)/8 years)]                                                        = $383,750 Project 1:          Accounting Rate of Return = Annual Net Income / Initial Investment                                                          = $383,750 / $4,850,000                                                          = 7.91% Project 2:          Accounting Rate of Return = Annual Net Income / Initial Investment                                                          = $425,000 / $3,400,000                                                          = 12.50% Project 3:          Accounting Rate of Return = Annual Net Income / Initial Investment                                                          = $200,000 / $2,875,000                                                          = 6.96% Based on the accounting rates of return, Project 2 is the best. Project 1 is the second best, while Project 3 gives the lowest accounting rate of return. Calculate the Payback Period: Project 1: Payback period = Initial Investment / Annual Net Cash Flow                                                             = $4,850,000 / $865,000                                                             = 5.61 years Project 2: Payback period = Initial Investment / Annual Net Cash Flow                                                            = Initial Investment / (Net Income + Depreciation)                                                            = $3,400,000 / [$425,000 + ($3,400,000 / 5)]                                                                   = $3,400,000 / $1,105,000                                                            = 3.08 years Project 3: Payback period = Initial Investment / Annual Net Cash Flow                                                            = Initial Investment / (Net Income + Depreciation)                                                            = $2,875,000 / ($200,000 + [($2,875,000 - $125,000) / 10])                                                            = $2,875,000 / $475,000                                                            = 6.05 years    Based on the payback period, Project 2 is preferred. Project 1 is the second preference, and project 3 has the longest payback period. Using a discount rate of 10%, calculate the net present value of each project: Project 1: Year         Annual Cash Flow         PV Factor (10%)         Present Value 0               $(4,850,000)                    1.0000                        $(4,850,000.00) 1-8                   865,000                     5.3349                           4,614,688.50 8                   1,000,000                     0.4665                              466,500.00 NPV                                                                                           $231,188.50 Project 2:  Year         Annual Cash Flow         PV Factor (10%)         Present Value 0               $(3,400,000)                    1.0000                        $(3,400,000.00) 1-5               1,105,000*                   3.7908                           4,188,834.00 5                                 0                          ---                                                    0 NPV                                                                                                  $788,834 *Annual Cash Flow = $425,000 + (3,400,000 / 5) Project 3: Year         Annual Cash Flow            PV Factor (10%)         Present Value 0                $(2,875,000)                     1.0000                        $(2,875,000) 1-10            475,000                           6.1446                           2,918,685 10               125,000                           0.3855                           48,187.50 NPV                                                                                         $91,872.50 *Annual Cash Flow = $200,00 + [($2,875,000 - $125,000) / 10] Determine the Profitability Index of each product and prioritize the projects for Hearne: Profitability Index = Present Value of Future Cash Flows / Initial Investment Project 1: Profitability Index = $5,081,188.50 / $4,850,000 = 1.0477 Project 2: Profitability Index = $4,188,834 / $3,400,000 = 1.2320 Project 3: Profitability Index = $2,966,872.50 / $2,875,000 = 1.0320 Prioritize Project 2, then Project 1, then Project 3.