Question

Crockin Corporation is considering a machine that will save $9,000 a year in cash operating costs each year for the next six years. At the end of six years it would have no salvage value. If this machine costs $33,165 now, the machine's internal rate of return is closest to:_______.a. 16%.b. 17%.c. 18%.d. 19%.

Answer 1

IRR = 16.5%

Step-by-step explanation:

The IRR is the discount rate that equates the present value of cash inflows to that of cash outflows. At the IRR, the Net Present Value (NPV) of a project is equal to zero

If the IRR greater than the required rate of return , we accept the project for implementation

If the IRR is less than that the required rate , we reject the project for implementation

IRR = a% + ( NPVa/(NPVa + NPVb)× (b-a)%

NPV = PV of annual savings - initial cost

PV of annual savings = A× (1- (1+r)^(-n) )/r

A- annual savings in operating cost , r- rate of return, n- number of years

NPVa at 10% discount rate

PV of cash inflow = (9,000× 1-1.1^-6)/0.1 = 39,197.35

NPV = 65,328.91 - 33,165 = 6,032.35

NPVb at 20% discount rate

PV of cash inflow = (9,000× 1-1.2^-6)/0.2= (3,235.41)

NPV = 29,929.59 -33,165 = (3,235.41)

IRR = a% + ( NPVa/(NPVa + NPVb)× (b-a)%

IRR = 10% + ( (6,032.35/(6,032.35 +3,235.41) )× (20-10)%= 16.51%

IRR = 16.5%