LCM assignment 2
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Assignment 2
Solution 1) a) To calculate the total revenue and profit over a 5-year period, we need to consider the 10% annual increase in sales. We'll start with the initial monthly sales of $6,800 and calculate the sales for each year.
Year 1: $6,800 x 12 = $81,600
Year 2: $81,600 x 1.10 = $89,760
Year 3: $89,760 x 1.10 = $98,736
Year 4: $98,736 x 1.10 = $108,609.60
Year 5: $108,609.60 x 1.10 = $119,470.56
We sum up the sales for each year to get the total revenue over 5 years:
$81,600 + $89,760 + $98,736 + $108,609.60 + $119,470.56 = $498,176.16
We need to subtract the initial investment ($500,000) from the total revenue to calculate total profit:
$498,176.16 - $500,000 = -$1,823.84
The car-wash franchise wouldn't generate a profit over the 5-year period, resulting in a negative return on investment.
b) To determine the break-even point in terms of years, we need to find the year where the cumulative profit reaches zero. A constant discount rate of 8%, we calculate the present value of the monthly profits
and find the year where the cumulative present value equals the initial investment.
Using the formula for present value, we can calculate the present value of the monthly profit of $3,800 over a year:
PV = CF / (1 + r)^n
PV = $3,800 / (1 + 0.08)^1 = $3,518.52
To find the break-even point, we divide the initial investment by the present value of the monthly profit:
$500,000 / $3,518.52 ≈ 142.10 months
We round up to the nearest whole year as the answer cannot be in decimal point:
Break-even point = 143 years
Hence, it would take approximately 143 years for the franchise operation to reach the break-even point.
Solution 2) From the given data, we know that the projected cost in 2020 is $31,083. To find the annual cost for each
year, we use the 5% annual inflation rate.
Year 1: $31,083
Year 2: $31,083 x 1.05 = $32,637.15
Year 3: $32,637.15 x 1.05 = $34,269.01
Year 4: $34,269.01 x 1.05 = $35,982.46
Now, let's calculate the total cost over the 4-year period:
Total cost = Year 1 + Year 2 + Year 3 + Year 4
Total cost = $31,083 + $32,637.15 + $34,269.01 + $35,982.46
Total cost = $133,971.62
Since the student plans to cover 40% of the costs through part-time work, they would need to save or loan for the remaining 60% of the costs.
Total amount to save or loan = 60% of Total cost
Total amount to save or loan = 0.6 x $133,971.62
Total amount to save or loan = $80,382.97
Therefore, the student would need to save or loan $80,382.97 to cover the remainder of the costs over the 4-year period.
Solution 3) a) To calculate the present value of the total cost of owning and operating the solar panel system over its 25-year lifespan, we need to consider the installation cost, maintenance costs, energy savings, and salvage value. From the given data:
1. Installation cost: $100,000 (initial cost)
2. Maintenance costs: $2,000 every 5 years, so a total of $2,000 x (25/5) = $10,000 over 25 years.
3. Energy savings: $12,000 per year, discounted at a rate of 6% over 25 years.
4. Salvage value: 20% of the initial cost, which is 0.2 x $100,000 = $20,000 after 25 years.
To calculate the present value, we need to discount the future cash flows. The formula for present value is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
Now we calculate the present value for each component and then sum them up to get the total:
1. Installation cost: $100,000 / (1 + 0.06)^25 = $29,740.26
2. Maintenance costs: $10,000 / (1 + 0.06)^25 = $2,974.03
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3. Energy savings: $12,000 x [(1 - (1 + 0.06)^-25) / 0.06] = $151,669.18
4. Salvage value: $20,000 / (1 + 0.06)^25 = $5,948.80
Total present value = $29,740.26 + $2,974.03 + $151,669.18 + $5,948.80 = $190,332.27
Therefore, the present value of the total cost of owning and operating the solar panel system over its 25-
year lifespan is approximately $190,332.27.
b) To calculate the equivalent annual cost of the solar panel system, we'll divide the total present value by the annuity factor. The annuity factor can be calculated using the formula:
Annuity factor = (1 - (1 + r)^-n) / r
Where r is the discount rate and n is the number of years.
We already calculated the total present value as $190,332.27. Now, we need to divide this by the annuity
factor to find the equivalent annual cost.
The discount rate is 6% and the number of years is 25.
Let’s calculate the annuity factor:
Annuity factor = (1 – (1 + 0.06)^-25) / 0.06 = 13.5904
Now, we divide the total present value by the annuity factor:
Equivalent annual cost = $190,332.27 / 13.5904 = $14,011.80
Therefore, the equivalent annual cost of the solar panel system over its lifespan is approximately $14,011.80.
For the viability of the investment, it depends on the company’s specific financial goals and considerations. However, it’s important to note that the equivalent annual cost is lower than the annual energy savings of $12,000. This suggests that the investment could be financially viable, as it has the potential to generate positive cash flows over its lifespan.
Solution 4) a) Calculating the present value of the total cost of the manufacturing plant upgrade over its 15-year lifespan.
1. Initial Upgrade Cost: $500,000 (current dollars)
2. Overhaul Cost after 10 years: To estimate the overhaul cost in 10 years, we use the formula:
Overhaul Cost in 10 years = $200,000 * (1 + 0.04)^10 = $291,047.07
3. Maintenance Costs: To calculate the present value of the maintenance costs over 15 years, considering
the inflation rate of 3% per year, we can use the formula for the present value of an annuity:
Maintenance Costs Present Value = $20,000 * [(1 - (1 + 0.03)^-15) / 0.03] = $225,822.61
4. Operational Savings: To calculate the present value of the operational savings over 15 years, considering the discount rate of 5%, we can use the formula for the present value of an annuity:
Operational Savings Present Value = $40,000 * [(1 - (1 + 0.05)^-15) / 0.05] = $408,146.89
5. Insurance Premium Savings: To calculate the present value of the insurance premium savings over 15 years, considering the discount rate of 5%, we can use the formula for the present value of an annuity:
Insurance Premium Savings Present Value = $10,000 * [(1 - (1 + 0.05)^-15) / 0.05] = $102,036.41
Now, we sum up all these values to get the Present Value of the Total Cost:
Total Cost Present Value = Initial Upgrade Cost + Overhaul Cost in 10 years + Maintenance Costs Present Value - Operational Savings Present Value - Insurance Premium Savings Present Value
Total Cost Present Value = $500,000 + $291,047.07 + $225,822.61 - $408,146.89 - $102,036.41
Total Cost Present Value = $506,687.38
b) To estimate the overhaul cost of the new machinery 10 years from now in current dollars, we can use the formula: Overhaul Cost in 10 years = $200,000 * (1 + 0.04)^10 The estimated overhaul cost of the new machinery 10 years from now in current dollars is $296,048.85
c) The current cost of the overhaul is $200,000. We’ll factor in the annual cost growth rate for the overhaul, which is 4%, over the next 10 years.
To calculate the future cost, we use the formula:
Future Cost = Current Cost * (1 + Annual Cost Growth Rate)^Number of Years
Future Cost = $200,000 * (1 + 0.04)^10
Calculating that, we get:
Future Cost = $200,000 * 1.48886417
Therefore, the future cost of the machinery overhaul 10 years from now is $297,772.83.
Solution 5) a) To calculate the Present Worth of the Total Savings in Electricity Costs over 16 years, we need to calculate the annual savings for each year. The current annual electricity cost for cooling is $50,000. The new system is expected to reduce these costs by 20% annually, but the electricity costs are anticipated to increase by 5% annually.
So, the savings for each year would be:
Year 1: $50,000 * (1 - 0.20) = $40,000
Year 2: $40,000 * (1 - 0.20) = $32,000
Year 3: $32,000 * (1 - 0.20) = $25,600
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Year 4: $25,600 * (1 - 0.20) = $20,480
Year 5: $20,480 * (1 - 0.20) = $16,384
Year 6: $16,384 * (1 - 0.20) = $13,107.20
Year 7: $13,107.20 * (1 - 0.20) = $10,485.76
Year 8: $10,485.76 * (1 - 0.20) = $8,388.61
Year 9: $8,388.61 * (1 - 0.20) = $6,710.89
Year 10: $6,710.89 * (1 - 0.20) = $5,368.71
Year 11: $5,368.71 * (1 - 0.20) = $4,294.97
Year 12: $4,294.97 * (1 - 0.20) = $3,435.98
Year 13: $3,435.98 * (1 - 0.20) = $2,748.78
Year 14: $2,748.78 * (1 - 0.20) = $2,199.02
Year 15: $2,199.02 * (1 - 0.20) = $1,759.22
Year 16: $1,759.22 * (1 - 0.20) = $1,407.38
Now, we calculate the Present Worth of the Total Savings
Using a discount rate of 8% per year, we’ll calculate the present value factor for each year and multiply it by the corresponding savings amount. Then, we sum up all the present values
Year 1: $40,000 * (1 / (1 + 0.08)^1) = $37,037.04
Year 2: $32,000 * (1 / (1 + 0.08)^2) = $27,777.78
Year 3: $25,600 * (1 / (1 + 0.08)^3) = $21,333.33
…
Year 16: $1,407.38 * (1 / (1 + 0.08)^16) = $501.69
After suming up all the present values, we get:
$37,037.04 + $27,777.78 + $21,333.33 + … + $501.69 = $305,679.43
So, the Present Worth of the Total Savings is $305,679.43
b) Future cost of system upgrade:
FV = 200,000×(1+0.03)8
=266, 011.08
Therefore, the future cost of the system upgrade in current dollars is approximately $266,011.08
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