Question

A company is analyzing whether to replace an existing 5-year old machine with a more updated model. Original cost of old machine is $25K and it has a current book value of $12.5K (with a remaining life of 5 years). It can be sold for $15K. New machine will cost $40K. It has five-year life and is depreciated on a straight line basis to a book value of $20K. Revenue will increase $5K while lowering operating costs by $3K for the existing level of output. New machine can be sold at its book value at the end of five years. What is the NPV for this replacement based on a discount rate of 10% and tax rate of 40%? What would the company do?

A. Switch to the new machine because the replacement has a NPV of 6.89K.

B. Switch to the new machine because the replacement has a NPV of 2.76K.

C. Switch to the new machine because the replacement has a NPV of -3.58K.

D. Keep the old machine as the replacement has a NPV of -2.76K.

E. Keep the old machine as the replacement has a NPV of 3.68K.

Answer 1

Amount are in thousands (k)  
Sale value is   15
Book value of Old machine   12.5
Capital gain= (15-12.5)=   2.5
tax paid 40% =   1
  
Year 0 Cash flow  
Cost of machine.........   -40
Salvage of old machine..   15
Tax paid on Sale   -1
___________________________  
net Cash flow at year 0 is   -26
___________________________  
  
  
Cash flow from Year 1 to 5  
  
increase in sales   5.00
savings in costs   3.00
Add: saving in Depreciation of old machine   2.50
(12.5/5)  
less: Depreciation on new machine   -4
(40-20)/5  
  
______________________________________________  
Incremental profit.    6.50
less: tax @40%   -2.60
______________________________________________  
Profit after tax   3.90
add: Depreciation of new machine   4.00
less: Depreciation of old Machine   -2.50
______________________________________________  
Free cash flows   5.40
______________________________________________  
New machine is sold at Book value. so there will be no cpaital gain or loss at end of year.  
Terminal value in year 5, Salvage value=   20.00

Calcultion of NPV:  
Initial Cash outlay Present Value.....   -26

Year 1 to 5 have Annual cash flows of $5.40. So Present Value of Annuity formula will be used.  
Discount rate (i)= 10%  
Time (n)= 5  

Present value of Cash inflows = Annual amount * (1-(1/(1+r)^n) / r  
5.4*(1-(1/(1+10%)^5))/10%  
20.47024855  

Terminal Value Present Value = Terminal Value/(1+i)^n  
20/(1+10%)^5  
12.41842646  

NPV is Sum of present value of all cash flows  
-26 + 20.47024955+12.41842646  
6.89  
  
NPV of replacement is positive $6.89 k. So Switch to New machine  
  
Answer is A.