Question

Masters Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $470,000 is estimated to result in $196,000 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of $72,000. The press also requires an initial investment in spare parts inventory of $37,000, along with an additional $3,950 in inventory for each succeeding year of the project. The shop’s tax rate is 22 percent and its discount rate is 11 percent. (MACRS schedule) Calculate the NPV of this project. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Should the company buy and install the machine press? No Yes

Answer 1

Answer:

Yes, the machine has a higher present value than their cost.

Explanation:

F0:

machine press:      470,000

spare part inventory 37,000

constant Annual cash flow:

cost savings :       196,000

adtional inventory: (3,950)

                              192050

tax rate of 22%:     (42,251)

net:                          149,799‬

MACRS depreciation for tax purposes: (tax shield)

1st   470,000 x 0.2 = 94,000 x 22% = 20,680

2nd 470,000 x 0.32 =150,400 x 22% =33,088

3rd  470,000 x 0.192 =  90,240 x 22% = 19,852.8

4th  470,000 x 0.1152 =   54,144 x 22% = 11,911.68

Present value of annual cash flow:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 149,799

time 4

rate 0.11

$149799 \times \frac{1-(1+0.11)^{-4} }{0.11} = PV$

PV $705,512.9941

Present value of the tax shield:

$\frac{20680}{(1 + 0.11)^{1} } = PV$  

PV   18,630.63

$\frac{33088}{(1 + 0.11)^{2} } = PV$  

PV   26,854.96

$\frac{19852.8}{(1 + 0.11)^{3} } = PV$  

PV   14,516.20

$\frac{11911.68}{(1 + 0.11)^{4} } = PV$  

PV   7,846.59

Present Value of the Savage value:

Book value at end of the project:

470,000 x (1 - .2 + .32 + .192 + .1152) = 81, 216

Expected salvage Value at disposal:  (72,000)

long-term capital loss                             (9,216)

As we are not gaining at disposal we do not recognize any income tax.

We just discount the salvage value:

$\frac{72000}{(1 + 0.11)^{4} } = PV$  

PV   47,428.63

Net Present value of  the mahcine press:

annual cash flow + depreciation tax shied + salvage value - investment

705,513 +  18,630.63 +26,854.96 + 14,516.20 + 7,846.59 + 47,428.63 - 470,000 - 37,000

NPV: 313.790,01‬

As it is positive we should prchase the machine.