Question

Exercise 12-6 (Video)

BSU Inc. wants to purchase a new machine for $39,840, excluding $1,400 of installation costs. The old machine was bought five years ago and had an expected economic life of 10 years without salvage value. This old machine now has a book value of $2,000, and BSU Inc. expects to sell it for that amount. The new machine would decrease operating costs by $9,000 each year of its economic life. The straight-line depreciation method would be used for the new machine, for a six-year period with no salvage value.

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(a)

Determine the cash payback period. (Round cash payback period to 2 decimal places, e.g. 10.53.)

Cash payback period

years

(b)

Determine the approximate internal rate of return. (Round answer to 0 decimal places, e.g. 13%. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

Internal rate of return

%

(c)

Assuming the company has a required rate of return of 9%, determine whether the new machine should be purchased.

The investment shouldshould not be accepted.

Answer 1

Annual cash savings = $ 9,000

Initial cost = Purchasing cost + Installation – Market price of old machine

                = $ 39,840 + $ 1,400 - $ 2,000 = $ 39,240

a)

Payback period = A + B/C

A = Last period number with a negative cumulative cash flow

B = Absolute value of cumulative cash flow at the end of period A

C = Total cash flow during the period following period A.

Year	Cash Flow	‘Cumulative Cash Flow
0	-$ 39,240	-$39,240
1	$ 9,000	-$30,240
2	$ 9,000	-$21,240
3	$ 9,000	-$12,240
4	$ 9,000	-$3,240
5	$ 9,000	$5,760
6	$ 9,000	$14,760

Payback period = 4 + $ 3,240/$ 9,000 = 4 + 0.36 = 4.36 years

Payback period for the replacement is 4.36 years.

b)

Let’s compute IRR using trial and error method.

NPV at discount rate of 9 %:

NPV1 = PV of cash inflows – Initial investment

       = $ 9,000 x PVIFA (9 %, 6) – $ 39,240

      = $ 9,000 x 4.48592 – $ 39,240

       = $ 40,373.28 – $ 39,240

       = $ 1,133.28

As the NPV is positive, let’s compute NPV at a discount rate of 10 %.

NPV2 = $ 9,000 x PVIFA (10 %, 6) – $ 39,240

      = $ 9,000 x 4.35526 – $ 39,240

       = $ 39,197.34 – $ 39,240

       = - $ 42.66

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

     = 9 % + [$1,133.28 x (10 % - 9 %)]/ [$1,133.28 – (-$42.66)]

     = 9 % + ($1,133.28 x 1 %)/ ($1,133.28 + $42.66)

     = 9 % + ($11.3328 / $1,175.94)

      = 9 % + 0.009637226

      = 9 % + 0.9637226 %

      = 9.9637226 % or 10 %

Internal rate of return for the replacement is 10 %.

c)

NPV = PV of cash inflows – Initial investment

       = $ 9,000 x PVIFA (9 %, 6) – $ 39,240

      = $ 9,000 x 4.48592 – $ 39,240

       = $ 40,373.28 – $ 39,240

       = $ 1,133.28

NPV of the replacement at discount rate of 9 % is $ 1,133.28

The investment should be accepted as NPV is positive and IRR is higher than company’s required rate.