Question

An industrial organization has bought a specialized machine for $120,000 which will save $20,000 each year for 10 years. Straight Line (SL) basis depreciation should be taken into consideration with a depreciable life of 10 years. After tax MARR is 10% per year. Effective income tax rate is 40%. After 10 years, the machine will have zero salvage value. a) Draw a table showing Before Tax Cash Flow (BTCF) and After Tax Cash Flow (ATCF). b) Calculate the after tax PW and IRR. (Use interpolation method to find IRR). Is it feasible?

Answer 1

a. Before Tax Cash Flow (BTCF) and After Tax Cash Flow (ATCF):

Before Tax Cash Flow(BTCF) = Annual savings of $20,000 per year from year 1 to 10

After Tax Cash Flow(ATCF) = $16,800 per year from year 1 to 10

Notes:

1. Annual savings is the only cash flow item. Depreciation is a non cash item. Hence Before Tax Cash Flow will equal the annual savings of $20,000

2. Tax given at 40%. Hence on annual savings = $20,000*40% = $8,000

3. After tax annual savings = $20,000-$8,000 = $12,000

4. Depreciation per year = (Cost of the machine - salvage value at the end of the life) / Total life of the machine

= ($120,000-$0)/10 = $12,000

While depreciation is a non-cash item, depreciation is a tax deductible expense and hence the tax benefit on depreciation is a cash-in flow item.

Tax benefit on depreciation = $12,000* tax rate of 40% = $4,800

5. After tax Cash Flow = $12,000+$4,800 = $16,800

b. After tax PW and IRR

After Tax Present Worth (Net Present Value/NPV) = - Initial Investment + Present Value of Future Cash Flows

Inital Investment = $120,000

Present value of future cash flows = After tax Cash Flow from year 1 to 10 * Cumulative discount factor for 10 years for 10%

= $16,800 * (((1-(1+10%)^-10))/10% = $16,800*6.144567 = $103,228.73

After Tax Present Worth = -$120,000+$103,228.73 = -$16,771.27

IRR

IRR or Internal rate of return is the rate at which the Present Worth will be zero.

At the discount rate of 10%, PW is negative at $16,771.27. Hence, for PW to be zero, discount rate needs to be lower. Hence, lets find the Present worth at a lower discount rate of 6%.

After Tax Present Worth (Net Present Value/NPV) using 6% discount rate= - Initial Investment + Present Value of Future Cash Flows

Inital Investment = $120,000

Present value of future cash flows = After tax Cash Flow from year 1 to 10 * Cumulative discount factor for 10 years for 6%

= $16,800 * (((1-(1+6%)^-10))/6% = $16,800*7.360087= $123,649.46

After Tax Present Worth = -$120,000+$123,649.46 = $3,649.46

IRR using interpolation method = Start rate + (PW at start rate / (PW at start rate - PW at end rate))*(End rate - start rate)

Start Rate = 6%

End Rate = 10%

PW at start rate = $3,649.46

PW at end rate = -$16,771.27

IRR = 6% + (($3,649.46/($3,649.46-(-$16,771.27))*(10%-6%)) = 6%+ 0.71% = 6.7%

(Pls note that IRR as per interpolation method will be approximation and NPV need not be exactly zero. To find accurate IRR, excel funciton =IRR can be used as per which IRR is 6.64%).

Thus,

After tax PW = - $16,771.27

IRR = 6.7%

Recommendation:

Since the after tax PW is negative and IRR is less than MARR of 10%, it is not feasible to invest in the machine.