Question

1.Assume a tax rate of 35%. You are considering a new machine that will increase gross income by $120,000/year for 5 years. The machine costs $250K, and will be straight-line depreciated over 5 years (so $50K/y depreciation charge). What are the after tax cash flows (increase to income, and depreciation tax break) for Y1-Y5? (Answer: +78K, +17.5K, total of 95.5K)

2.What’s the NPV of the cash flows, at an 8% discount rate?

3.Assume a tax rate of 20% and re-do #1 & 2.

4.Assume a 35% tax rate, and assume the machine is depreciated over 2 years (straight-line, so $125K/y). What are the after-tax CF’s for 5y, and what’s the NPV at an 8% discount rate?

*Need help with the Bolded problems.

Answer 1

Answer 3

At tax rate 20%

Gross income after tax=(1-20%)*120000=120000*0.8=$96000

Depreciation tax break=20%*50000=$10000

Hence after tax cashflow=96000+10000=$106000

PV of after tax cashflow =A*(1-(1+r)^n)/r

=106000*(1-(1+8%)^-5)/8%

=106000*(1-1.08^-5)/0.08

=106000*(1-0.6806)/0.08

=106000*0.3194/0.08

=$423227.26

Hence NPV=423227.26-250000=$173227.26

Answer 4

Gross income after tax=(1-35%)*120000=0.65*120000=$78000

Depreciation tax break for 2 years =35%*125000=$43750

Hence after tax cashflow for first 2 years=78000+43750=$121750

After tax cashflow for last 3 years=$78000

PV of after tax cashflow for first 2 years =A*(1-(1+r)^n)/r

=121750*(1-(1+8%)^-2)/8%

=121750*(1-1.08^-2)/0.08

=121750*(1-0.8573)/0.08

=121750*0.1427/0.08

=$217112.48

PV of after tax cashflow at the end of year 2 for years 3 to 5 =A*(1-(1+r)^n)/r

=78000*(1-(1+8%)^-3)/8%

=78000*(1-1.08^-3)/0.08

=78000*(1-0.7938)/0.08

=78000*0.2062/0.08

=$201013.56

PV at the end of year 0 = 201013.56/(1+8%)^2=201013.56/1.08^2=201013.56*0.8573=$172336.73

NPV=217112.48+172336.73-250000=$139449.21