Ex 141 Net Present Value

1
Ex 14-1 Net Present Value

• Cost of Machine 25,000
• Annual Cost Savings
• provided by machine 4,000
• Life of Machine 10 years
• Required Rate of Return 12

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2
Ex 14-1 First lets look at cash flows of the
purchase without considering the time value of
money

• Total cash outflows (25,000)
• Total cash inflows (savings)
• 4,000 x 10 years 40,000
• Net cash flow of purchase 15,000

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3
Ex 14-1 Calculate Net Present Value

• Year Amount x PV Factor (12) PV ()
• 0 (25,000) 1.0000 (25,000)
• 1 4,000 .893 3,572
• 2 4,000 .797 3,188
• 3 4,000 .712 2,848
• 4 4,000 .636 2,544
• 5 4,000 .567 2,268
• 6 4,000 .507 2,028
• 7 4,000 .452 1,808
• 8 4,000 .404 1,616
• 9 4,000 .361 1,444
• 10 4,000 .322 1,288
• Net Present Value (NPV) (2,396)

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4
Ex 14-1 What is the NPV of the purchasing the
machine?

• Since the NPV is less than zero (negative) , the
  investment would not meet the required rate of
  return of 12.
• Therefore, the investment in the machine would
  not be made if based on the NPV.

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5
Since the cost savings is the same amount for
each of the ten years, we can use the annuity
factor (pg 620) to complete Ex 14-1 faster

• Year Amount x PV Factor PV ()
• 0 ( 25,000) 1.000 ( 25,000)
• 1- 10 4,000 5.650 22,600
• Net Present Value (NPV) (2,400)
• Note 5.650 is the sum of each individual PV
  factor from years 1 through 10 (the 4 difference
  in the answers is due to rounding)

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6
Ex 14-2 Internal Rate of Return

• Cost of Delivery Truck 45,000
• Annual Cost Savings
• provided by truck 5,400
• Additional Sales due to
• purchase of truck 1,800 pizzas
• Contribution Margin 2 per pizza
• Life of Truck 6 years

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7
Ex 14-2 - What are the total annual cash inflows
due to the purchase of the new truck?

• Savings on deliveries 5,400
• Profit on additional sales 3,600 (1,800
  units x 2 per unit)
• Total Annual Cash Flow 9,000

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8
Ex 14-2 - What is the approximate Internal Rate
of Return (IRR) of the purchasing the truck?

• IRR is where NPV of investment zero
• Year Amount x PV Factor PV ()
• 0 (45,000) 1.0000 (45,000)
• 1- 6 9,000 ??? 45,000
• Net Present Value (NPV) 0

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9
Ex 14-2 What is the approximate IRR of the
machine purchase?

• 9,000 x ??? 45,000
• 45,000 / 9,000 ???
• 45,000 / 9,000 5.00 (PV of annuity factor)
• Looking at table (pg 620), year 6, we find the PV
  of annuity factor of 5.00 is closest to the 5
  return column
• Therefore, IRR is approximately 5

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10
Ex 14-2 (3) Assume a salvage value of 13,000.
What rate of return makes the NPV closest to
zero?

• Year Amount x PV Factor (11) PV ()
• 0 (45,000) 1.000 (45,000)
• 1-6 9,000 4.231 38,079
• 6 13,000 .535 6,955
• Net Present Value (NPV) 34
• Since NPV is close to 0, where PV factor is 11,
  then IRR approximates 11.

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11
Ex 14-11- IRR and Net Present Value

• Cost of Machine 136,700
• Annual Increase to cash flow
• provided by machine 25,000
• Life of Machine 14 years
• Expected Salvage Value 0

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12
Ex 14-11, Part I Compute the Internal Rate of
Return

• Year Amount x PV Factor PV ()
• 0 (136,700) 1.0000 (136,700)
• 1-14 25,000 ??? 136,700
• Net Present Value (NPV) 0
• 136,700 / 25,000 5.468 PV Factor, therefore
  IRR 16

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13
Ex 14-11, Part II Net Present Value

• Year Amount x PV Factor (16) PV ()
• 0 (136,700) 1.000 (136,700)
• 1-14 25,000 5.468 136,700
• Net Present Value (NPV) -0-
• The reason for the zero present value is that 16
  represents the Internal Rate of Return (you
  calculated this in Part I of the problem)

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14
Ex 14-11, Part III Assume annual cash flows are
20,000. What is Internal Rate of Return?

• Year Amount x PV Factor PV ()
• 0 (136,700) 1.0000 (136,700)
• 1-14 20,000 ??? 136,700
• Net Present Value (NPV) 0
• 136,700 / 20,000 6.835 PV Factor, therefore
  IRR is between 11 and 12

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15
Ex 14-17, Part I Net Present Value

• Year Amount x PV Factor (15) PV ()
• 0 (40,350) 1.000 (40,350)
• 1-4 15,000 2.855 42,825
• Net Present Value (NPV) 2,475
• The machine is an acceptable investment. The net
  present value is positive, indicating that its
  rate of return exceeds the minimum requirement of
  15.

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16
Ex 14-17, Part II Internal Rate of Return

• Year Amount x PV Factor PV ()
• 0 (111,500) 1.0000 (111,500)
• 1- 15 20,000 ??? 111,500
• Net Present Value (NPV) 0
• 111,500 / 20,000 5.575 PV Factor, therefore
  IRR 16

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17
Ex 14-17, Part III Internal Rate of Return

• Year Amount x PV Factor PV ()
• 0 (14,125) 1.0000 (14,125)
• 1- 10 2,500 ??? 14,125
• Net Present Value (NPV) 0
• 14,125 / 2,500 5.65 PV Factor, therefore IRR
  12
• Not a good investment if required rate is 16

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