Julio Company is considering the purchase of a new bubble packaging machine. If the machine will provide $20,000 annual savings for 10 years and can be sold for $50,000 at the end of the period, what is the present value of the machine investment at a 9% interest rate with savings realized at year end?
Present value of the machine is the sum of the present values of the annual savings of $20000 and terminal cash flow (by sale of machine) of $50000 at the end of the period.
Annual savings will be same every year, so it is an annuity. Terminal cash inflow at the end of the period is a one time payment.
Now,
First we will calculate the present value of annual savings:
For calculating the present value, we will use the following formula:
PVA = P * (1 - (1 + r)-n / r)
where, PVA = Present value of annuity, P is the periodical amount = $20000, r is the rate of interest = 9% and n is the time period = 10
Now, putting these values in the above formula, we get,
PVA = $20000 * (1 - (1 + 9%)-10 / 9%)
PVA = $20000 * (1 - ( 1+ 0.09)-10 / 0.09)
PVA = $20000 * (1 - ( 1.09)-10 / 0.09)
PVA = $20000 * ((1 - 0.42241080689) / 0.09)
PVA = $20000 * (0.5775891931 / 0.09)
PVA = $20000 * 6.41765770116
PVA = $128353.15
Next, we will calculate the present value of terminal cash flow:
For calculating present value, we will use the following formula:
FV = PV * (1 + r%)n
where, FV = Future value = $50000, PV = Present value, r = rate of interest = 9%, n= time period = 10
now, putting theses values in the above equation, we get,
$50000 = PV * (1 + 9%)10
$50000 = PV * (1 + 0.09)10
$50000 = PV * (1.09)10
$50000 = PV * 2.36736367459
PV = $50000 / 2.36736367459
PV = $21120.54
Now,
Present value of the machine investment = Present value of annual savings+ Present value of terminal cash flow
Present value of the machine investment = $128353.15 + $21120.54 = $149473.69
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