Question

A piece of labor-saving equipment has just come onto the market that Mitsui Electronics, Ltd., could use to reduce costs in one of its plants in Japan. Relevant data relating to the equipment follow: Purchase cost of the equipment $ 640,500 Annual cost savings that will be provided by the equipment $ 105,000 Life of the equipment 10 years Required: 1a. Compute the payback period for the equipment. 1b. If the company requires a payback period of four years or less, would the equipment be purchased? 2a. Compute the simple rate of return on the equipment. Use straight-line depreciation based on the equipment’s useful life. 2b. Would the equipment be purchased if the company’s required rate of return is 13%?

Answer 1

Answer:

1 a. The payback period=15.64 years or 16 full years

1 b. No, the equipment would not be purchased since the payback period is 16 years.

2 a. Simple rate of return=-56.41%

2 b. No, since the current value would need to be higher $723,765 in order to get a required rate of return of 13%

Explanation:

1 a. Payback period

The payback period is the time required to recover the cost of an equipment. Its the time it takes to break-even. This can be expressed as;

Total costs=total gain

where;

total costs=purchase cost+annual depreciable cost×number of years

purchase cost=$ 640,500

depreciable cost=acquisition cost-salvage value

acquisition cost=$ 640,500

assume salvage value=0

depreciable cost=640,500-0=640,500

annual depreciable cost=depreciable cost/useful life=640,500/10=64,050

number of years=n

replacing;

total cost=640,500+(64,050×n)=64,050 n+640,500

total gain=annual cost savings×number of years

where;

annual cost savings=$ 105,000

number of years=n

replacing;

total gain=105,000×n=105,000 n

replacing in the original expression;

64,050 n+640,500=105,000 n

105,000 n-64,050 n=640,500

40,950 n=640,500

n=640,500/40,950=15.64

n=15.64 years

The payback period=15.64 years or 16 full years

1 b. No, the equipment would not be purchased since the payback period is 16 years.

  2 a. The simple rate of return can be computed using the formula;

simple rate of return={(Current value-initial value)/initial value}×100

Current value=salvage value+(annual cost savings×useful life)-depreciable cost

where;

salvage value=0

annual cost savings=$ 105,000

useful life=10 years

depreciable cost=$ 640,500

replacing;

Current value=0+(105,000×10)-640,500=$409,500

Initial value=$ 640,500

required rate of return={(409,500-640,500)/409,500}×100

required rate of return=(231,000/409,500)×100=-56.41%

simple rate of return=-56.41%

2 b. Determine the initial value required when the required rate of return=13%

current value=C

initial value=$ 640,500

13%={(C-640,500)/640,500}×100

0.13×640,500=C-640,500

83,265+640,500=C

C=$723,765

No, since the current value would need to be higher $723,765 in order to get a required rate of return of 13%