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%
