Question

A company is considering purchasing a new second machine in order to expand their business. The information for the new machine is:

Cost= $100,000

Increase in contribution margin= $25,000

Life of the machine= 5 years

Required rate of return = 10%

Calculate the following:

a. Net present value (NPV) (Use factors to three decimal places, X.XXX, and use a minus sign or parentheses for a negative net present value. Enter the net present value of the investment rounded to the nearest whole dollar)

b. Payback period (Round your answer to two decimal places.)

c. Discounted payback period (Round interim calculations to the nearest whole dollar. Round the rate to two decimal places, X.XX%.)

d. Internal rate of return (Round the rate to two decimal places, X.XX%.)

e. Accrual accounting rate of return based on net initial investment (Round interim calculations to the nearest whole dollar. Round the rate to two decimal places, X.XX%.

Answer 1

a. NPV is $ (5,250)

Period	Amount	PV Factor	PV
		1/(1+10%)^Period	Amount X PV Factor
0	$ (1,00,000)	1.00	$                  (1,00,000)
1	$       25,000	0.91	$                        22,725
2	$       25,000	0.83	$                        20,650
3	$       25,000	0.75	$                        18,775
4	$       25,000	0.68	$                        17,075
5	$       25,000	0.62	$                        15,525
			$                        (5,250)

b. Payback Period = Initial Outflow / Annual Inflow = 100,000 / 25,000 = 4 years

c. Discounted Payback Period

As can be seen from a above, the sum of discounted cash inflows is $94,750, whereas that outflow is $100,000
The discounted payback period is more than 5 Years.

d. Internal Rate of return or IRR
IRR is the rate at which NPV = 0
or, PV of Cash Inflow - PV of Cash ouflow = 0
At 10% NPV = $ (5,250)

Period	Amount	PV Factor	PV
		1/(1+7%)^Period	Amount X PV Factor
0	$ (1,00,000)	1.00	$                  (1,00,000)
1	$       25,000	0.93	$                        23,250
2	$       25,000	0.87	$                        21,750
3	$       25,000	0.82	$                        20,500
4	$       25,000	0.76	$                        19,000
5	$       25,000	0.71	$                        17,750
			$                           2,250

At 7% NPV = $2,250

Using the above two, we find that the NPV = 0 at 8%. IRR = 8%

e. Accrual ARR

Depreciation = 100,000 / 5 = $20,000
Accounting Profit = 25,000 - 20,000 = $5,000
Investment = $100,000

ARR = 5000 / 100,000 = 5%