Suppose you have to decide whether selling an old machine or

Suppose you have to decide whether selling an old machine or keeping it with a major overhaul:

A) Selling the machine at time zero for $750,000 with zero book value and paying the tax of 40%.

B) Keeping the machine, which requires a major overhaul cost of $1,000,000 at time zero. The overhaul cost is depreciable from time 0 to year 5 (over six years) based on MACRS 5-year life depreciation with the half year convention (table A-1 at IRS (https://www.irs.gov/publications/p946)). In this case machine can produce and generate equal annual revenue for five years (year 1 to 5) and salvage value of the machine will be $250,000 with zero book value at the end of year 5. The operating cost of the machine will be $400,000 per year from year 1 to year 5.

Calculate the minimum annual revenue that machine has to generate to break-even the selling with NPV of keeping the machine. Consider 40% income tax rate and after-tax minimum ROR of 16%.

Solution

(A) Cash flow if machine sold in 0 year = $450000

(B) cash flow in case of overhaul

step 1 initial investment 1000000

step 2 depreciation.

yr. op block. depreciation

0. 1000000. 200000

1. 800000. 320000

2. 480000. 192000

3. 288000. 115200

4. 172800. 115200

\'5. 57600. 57600

step 3 :_ salvage value at 5th yr. = 250000*0.6 = 150000

step 4:- calculations of reoccurring cashflow here we need to do reverse calculations to find minimum annual revenue hence let\'s assume minimum annual revenue = x

part/yr 1. 2. 3. 4. 5

cash flow. x. x. x. x. x.

less

depn. 320000. 192000. 115200. 115200. 57600

exp. 400000. 400000. 400000. 400000. 400000

profit before tax. x-720000. x-592000. x-515200. . x-515200. x-457600

pofit after tax. 0.6x-432000. 0.6x-355200 0.6x-309120. 0.6x-309120. 0.6x-274560

?ADD

deprn. 320000. 192000. 115200. 115200. 57600

cash inflow. 0.6x-112000. 0.6x-163200. 0.6x-193920. 0.6x-193920. 0.6x-216960

step 5 Calculations of present value

yr cash inflow. pv fector. pv

0. -920000 (note 1) 1. -920000

1. -112000. 0.8621. - 96555

2. -163200. 0.7432. -121290

3. -193920. 0.6407. -124244

4. -193920. 0.5523. -107102

5. -66960. 0.4761. -31880

(216960-150000)

0.6x(note 2) 3.2743. 1.9646x

TOTAL. 1.9646x-1401071

there fore x = 1401071/1.9646 = 713158

there for annual revenue required to break even = 713158

note 1 cash inflow for yr 0

= depn for 0 yr = 200000 where tax saving = 80000 ( 200000*0.4)

therefore cash inflow = (-1000000+80000)=-920000

note 2 here 0.6 is available in all year hence taken as common and multiply with pvifa @ 16% for 5 yrs