Question

A firm is considering an investment in a new machine with a price of $18.06 million to replace its existing machine. The current machine has a book value of $6.06 million and a market value of $4.56 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.76 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $256,000 in net working capital. The required return on the investment is 11 percent and the tax rate is 35 percent.

What is the NPV of the decision to purchase a new machine? (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 1,234,567.89.)
  
NPV           $

What is the IRR of the decision to purchase a new machine? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
IRR            %

What is the NPV of the decision to purchase the old machine? (A negative answer should be indicated by a minus sign. Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 1,234,567.89.)
  
NPV           $
  
What is the IRR of the decision to purchase the old machine? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. A negative answer should be indicated by a minus sign.)
  
IRR            %

Answer 1

Part a)

The NPV of the new machine is calculated as below:

NPV = -Initial Outlay + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4

Initial Outlay = Purchase Price + Initial Working Capital = 18,060,000 + 256,000 = $18,316,000

Cash Flow Year 1 to Year 3 = (Savings in Operating Costs-Depreciation)*(1-Tax Rate) + Depreciation = (6,760,000 - 18,060,000/4)*(1-35%) + 18,060,000/4 = $5,974,250

Cash Flow Year 4 = 5,974,250 + Recovery of Working Capital = 5,974,250 + 256,000 = $6,230,250

Using these values in the above formula, we get,

NPV (New Machine) = -18,316,000 + 5,974,250/(1+11%)^1 + 5,974,250/(1+11%)^2 + 5,974,250/(1+11%)^3 + 6,230,250/(1+11%)^4 = $387,421.29

_____

Part b)

IRR is the minimum rate of return acceptable from a project. It can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic function/formula of IRR is given as below:

NPV = 0 = -Initial Outlay + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4

IRR is calculated with the use of EXCEL as follows:

where:

IRR (New Machine) = IRR(B2:B6) = 11.98%

_____

Part c)

The NPV of the old machine is calculated as below:

NPV = -Initial Outlay + Cash Flow Year 1/(1+Required Rate of Return)^1 + Cash Flow Year 2/(1+Required Rate of Return)^2 + Cash Flow Year 3/(1+Required Rate of Return)^3 + Cash Flow Year 4/(1+Required Rate of Return)^4

Initial Outlay = Market Value of Old Machine + Tax Rate*(Book Value - Market Value) = 4,560,000 + 35%*(6,060,000 - 4,560,000) = $5,085,000

Cash Flow Year 1 to Year 4 = -Depreciation*(1-Tax Rate) + Depreciation = -(6,060,000/4)*(1-35%) + 6,060,000/4 = $530,250

Using these values in the above formula, we get,

NPV (Old Machine) = -5,085,000 + 530,250/(1+11%)^1 + 530,250/(1+11%)^2 + 530,250/(1+11%)^3 + 530,250/(1+11%)^4 = -$3,439,928.17

_____

Part d)

IRR is the minimum rate of return acceptable from a project. It can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic function/formula of IRR is given as below:

NPV = 0 = -Initial Outlay + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4

IRR is calculated with the use of EXCEL as follows:

where:

IRR (Old Machine) = IRR(B2:B6) = -27.67%