Turtlelover05
26.03.2020 •
Business
1. A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for $20,000. Calculate the equivalent annual annuity to show the better option if the discount rate is 10%.
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Ответ:
The lease option is the better option.
Explanation:
We proceed as follows:
Step 1: Calculation of Lease Option NPV
Year = n Details CF ($) DF = 1/(1.1)^n PV ($)
1 Lease payment (30,000) 0.9091 (27,273)
2 Lease payment (30,000) 0.8264 (24,793)
3 Lease payment (30,000) 0.7513 (22,539)
4 Lease payment (30,000) 0.6830 (20,490)
Lease option NPV = (95,096)
Step 1: Calculation of Lease Option NPV Buy Option NPV
Year = n Details CF (CO) DF = 1/(1.1)^n PV
0 Purchase cost (80,000) 1.0000 (80,000)
1 Maintenance expenses (10,000) 0.9091 (9,091)
2 Maintenance expenses (10,000) 0.8264 (8,264)
3 Maintenance expenses (10,000) 0.7513 (7,513)
4 Maintenance expenses (10,000) 0.6830 (6,830)
4 Residual value 20,000 0.6830 13,660
Buy option NPV = (98,038)
Step 3: Calculation of equivalent annual annuity (EAA)
The equivalent annual annuity (EAA) for each option can be calculated as follows:
EAA = (r x NPV) / (1 - (1 + r)^-n )
Where:
EAA = equivalent annuity cash flow
NPV = net present value
r = discount rate per period
n = number of periods
Therefore, we have:
Lease option EAA = (0.1 × -95,096) / (1 - (1 + 0.1)^-4) = -30,000
Buy option EAA = (0.1 × 98,038) / (1 - (1 + 0.1)^-4) = -30,928
Since the lease option has a lower EAA of $30,000 in terms of cash outlay than the buy option of higher EAA of $30,928 in terms of cash outlay, the lease option is the better option.
Ответ:
Option 1 is preffered option because:
EAC of Instalment option = $30,000
EAC of Buying option = $37,660
Explanation:
The Equivalent Annual Cost would be calculated using the following formula:
Equivalent Annual Cost = Net Present Value of option / Annuity Factor
Now we will have to find the present value of the each option available.
Option 1
So present value of the installment option is given as under:
Present Value = Annual Cash flow * Annuity Factor
Here the annuity factor can be found from the following formula:
Annuity Factor = (1-(1+r)^-n ) / r
By putting the values we have:
Annuity Factor = (1 - (1.1)^-n) / 10% = 2.487
Present Value = $30000 * 2.487 = $74610
This implies
Equivalent Annual Cost = $74610 / 2.487 = $30000
Option 2
Present Value = $80000 Initial cash outflow +
$20000 cash inflow at Y4 / (1.1)^4 Discount factor at Year 4
Present Value = $80,000 + $20,000 / 1.4641
Present Value = $80,000 + $13,660 = $93,660
And
EAC = $93660 / 2.487 at 10% for 4 Years = $37,660
Decision Rule:
The cheapest option is the one with least value and in this case the cheapest option is option 1.
Ответ:
the correct answer for this question is option b