Question

PAYBACK, ACCOUNTING RATE OF RETURN, NET PRESENT VALUE, INTERNAL RATE OF RETURN

Ripit Company wants to buy a numerically controlled (NC) machine to be used in producing specially machined parts for manufacturers of tractors The outlay required is $480,000. The NC equipment will last five years with no expected salvage value. The expected after-tax cash flows associated with the project follow:

Year                Cash Revenues       Cash Expenses

1                      $780,000                   $600,000

2                      780,000                   600,000

3                      780,000                   600,000

4                      780,000                   600,000

5                      780,000                   600,000

Required:

1.    Compute the payback period for the NC equipment.

2.    Compute the NC equipment's ARR.

3.    Compute the investment's NPV, assuming a required rate of return of 10 percent.

4.    Compute the investment's IRR.

Answer 1

1.

Year	Cash Revenues	Cash Expenses	Net Cash Inflow [Revenue - Expenses]
1	780000	600000	180000
2	780000	600000	180000
3	780000	600000	180000
4	780000	600000	180000
5	780000	600000	180000

Initial Cash outlay = 480,000

Payback during first 2 years = 180000+180000 = 360000

Balance will be recovered in 3rd year = 480000-360000 = 120000

Recovery of 120000 = 120000/180000 = 0.667

Payback period = 2+0.667 = 2.667 years

2. Accounting Rate of Return = Average Income/ Initial Outlay

= 180000/480000

= 37.5%

3.

Year	Cash Revenues	Cash Expenses	Net Cash Inflow [Revenue - Expenses] (A)	PVAF @10% (B)	Present Value of Future Cash inflow (A*B)
1	780000	600000	180000	0.9091	163636.3636
2	780000	600000	180000	0.8264	148760.3306
3	780000	600000	180000	0.7513	135236.6642
4	780000	600000	180000	0.6830	122942.422
5	780000	600000	180000	0.6209	111765.8382
Total					682341.6185

NPV = 682341.6185 - 480000 = 202341.6185

4. Finding out IRR by trial and error method.

Assuming that the IRR lies between 10% and 14%

Year	Cash Revenues	Cash Expenses	Net Cash Inflow [Revenue - Expenses] (A)	PVAF @10% (B)	Present Value of Future Cash inflow @10%	PVAF @14%	Present Value of Future Cash inflow @14%
1	780000	600000	180000	0.9091	163636.3636	0.8772	157894.7368
2	780000	600000	180000	0.8264	148760.3306	0.7695	138504.1551
3	780000	600000	180000	0.7513	135236.6642	0.6750	121494.8729
4	780000	600000	180000	0.6830	122942.422	0.5921	106574.4499
5	780000	600000	180000	0.6209	111765.8382	0.5194	93486.35958
Total					682341.6185		617954.5744
NPV (Present Value -480000)					202341.6185		137954.5744

IRR = 10% + [202341.6185 / (202341.6185 - 137954.5744) *4%]

= 22.57%