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a)
To determine: The present value profit or loss of the deal.
Introduction:
Present value (PV):
It is the value that is in present form of money in contrast to some future amount. This is achieved when it is invested in compound interest.
The NPV is the measurement of profit that is calculated by subtracting the present values of
a)
Answer to Problem 39P
The present value profit or loss of the deal is $77,750.
Explanation of Solution
Given information:
Initial cost = $1,000,000
Salvage cost= $50,000
Interest rate = 10%
Yearly maintenance= $75,000
Yearly dues = $300,000
Number of members = 500
From the present value of $1 table,
PV annuity factor @ 10% for 0 year= 1.000
PV annuity factor @ 10% for 1 year= 0.909
PV annuity factor @ 10% for 2 year= 0.826
PV annuity factor @ 10% for 3 year= 0.751
PV annuity factor @ 10% for 4 year= 0.683
PV annuity factor @ 10% for 5 year= 0.621
Calculation of cost at year 0:
The cost at year 0 is calculated summing the initial investment and yearly maintenance and expenses.
Calculation revenue for year 5:
The revenue of year 5 is calculated by adding the yearly dues and the salvage cost.
The cost for year 1 to year 4 is $75,000. The revenue for year 1 to year 4 is $300,000.
Formula to calculate profit for each year:
Formula to calculate net present value (NPV) for each year:
Formula to calculate total profit:
Formula to calculate total net present value (NPV):
Calculation of profit for each year:
The profit is calculated by subtracting the yearly revenues with yearly cost.
Year 0 Profit:
Year 1 Profit:
Year 2 Profit:
Year 3 Profit:
Year 4 Profit:
Year 5 Profit:
Calculation of total profit:
The total profit is calculated by summing all the individual year profits.
Calculation of net present value (NPV):
The net present value for each year is calculated by multiplying the annuity factor with the respective profit.
Year 0 NPV:
Year 1 NPV:
Year 2 NPV:
Year 3 NPV:
Year 4 NPV:
Year 5 NPV:
Calculation of total net present value (NPV):
The total net present value (NPV) is calculated by summing all the individual NPV values.
Hence, the present value profit of the deal is $77,750.
b)
To determine: The special deal should be made or not made.
Introduction:
Present value (PV):
It is the value that is in present form of money in contrast to some future amount. This is achieved when it is invested in compound interest.
Net present value (NPV):
The NPV is the measurement of profit that is calculated by subtracting the present values of cash outflows and cash inflows. The NPV is used as a tool to measure the profitability of investing in a project.
b)
Answer to Problem 39P
The special deal should be made.
Explanation of Solution
Given information:
Initial cost = $0
Salvage cost= $0
Interest rate = 10%
Yearly maintenance= $0
Yearly dues = $600
From the present value of $1 table,
PV annuity factor @ 10% for 0 year= 1.000
PV annuity factor @ 10% for 1 year= 0.909
PV annuity factor @ 10% for 2 year= 0.826
PV annuity factor @ 10% for 3 year= 0.751
PV annuity factor @ 10% for 4 year= 0.683
PV annuity factor @ 10% for 5 year= 0.621
The cost for year 0 to year 5 is $0. The revenue for year 0 to year 5 is $600.
Formula to calculate profit for each year:
Formula to calculate net present value (NPV) for each year:
Formula to calculate total profit:
Formula to calculate total net present value (NPV):
Calculation of profit for each year:
The profit is calculated by subtracting the yearly revenues with yearly cost.
Year 0 Profit:
Year 1 Profit:
Year 2 Profit:
Year 3 Profit:
Year 4 Profit:
Year 5 Profit:
Calculation of total profit:
The total profit is calculated by summing all the individual year profits.
Calculation of net present value (NPV):
The net present value for each year is calculated by multiplying the annuity factor with the respective profit.
Year 0 NPV:
Year 1 NPV:
Year 2 NPV:
Year 3 NPV:
Year 4 NPV:
Year 5 NPV:
Calculation of total net present value (NPV):
The total net present value (NPV) is calculated by summing all the individual NPV values.
The present value profit of the deal is $2,274. The PV profit is less than $3,000. This deal is more worth than the health club deal.
Hence, the special must be made.
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