Question

3Charles Company is considering the purchase of a new machine for $80,000. The machine would generate annual cash flow before depreciation and taxes of $28,778 for five years. At the end of five years, the machine would have no salvage value. The company's RRR for this investment is 12 percent. The company uses straight-line depreciation with no mid-year convention and has a 40 percent tax rate What is the internal rate of return for the machine rounded to the nearest percent?

Answer 1

Answer : Calculation of Internal rate of return for the machine :

Depriciation = Cost of new machine / Useful life

= $80,000 / 5 years = $16,000

Profit after dep. & tax = Profit before dep. & tax - Depriciation - Tax

= $28,778 - $16,000 - 40% of ($28,778 - $16,000)

= $12,778 - 5111.2

= $7,666.8

Annual Cash inflow = Profit after dep. & tax + Depriciation

= $7,666.8 + $16,000

= $23,666.8

Calculation of IRR :

Internal Rate of Return  =  R1  +	NPV1 x (R2 - R1)
(NPV1 - NPV2)

Where:

R1      =   Lower discount rate @14%

R2      =   Higher discount rate @16%

NPV1   =   Higher Net Present Value (derived from R1)

NPV2   =   Lower Net Present Value (derived from R2)

NPV1 @14% = Present value Annual Cash inflow - Initial cash outflow

= $23,666.8 X PVAF (14%, 5 years) - $80,000

= $23,666.8 X3.433 - $80,000

= $81,248 - $80,000

= $1,248

NPV1 @16% = Present value Annual Cash inflow - Initial cash outflow

= $23,666.8 X PVAF (16%, 5 years) - $80,000

= $23,666.8 X3.274 - $80,000

= $77,485 - $80,000

= ($2,515)

Internal Rate of Return  =  14% + [1248 (16% -14%)] / [$1,248 - ($2,515)]

= 14% + [1248 X 2] / $3,763

=   14% + 0.67

= 14.67%