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A manufacturer can lease a machine for 6 years at $2,680 per quarter, payable at the beginning of each quarter. Alternatively, they can purchase the machine for $60,000 and sell it for $5,900 in 6 years. The cost of capital is 7.3% compounded annually. What is the present value of the cost:

i) of the lease option?
ii) of the purchase option?

1 Answer

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Answer:

We can use the present value formula to calculate the present value of the cost of each option, where PV = FV/(1+r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

i) Lease Option:

The lease is for 6 years, with payments made quarterly. So, there are 24 payments in total (6 years x 4 quarters per year). The payment amount is $2,680.

Using the formula for the present value of an annuity due:

PV = Pmt x [(1 - (1 + r)^-n)/r] x (1+r)

where Pmt is the payment amount, r is the interest rate, and n is the number of payments.

PV = 2680 x [(1 - (1+0.073/4)^-24)/(0.073/4)] x (1+0.073/4)

PV = $51,517.59

Therefore, the present value of the cost of the lease option is $51,517.59.

ii) Purchase Option:

The purchase price of the machine is $60,000 and the selling price after 6 years is $5,900. To calculate the present value of the cost of the purchase option, we need to find the present value of the difference between the purchase price and the selling price after 6 years.

PV = (FV - Selling Price)/(1+r)^n

where FV is the purchase price, Selling Price is the selling price after 6 years, r is the interest rate, and n is the number of years.

PV = (60000 - 5900)/(1+0.073)^6

PV = $44,188.23

Therefore, the present value of the cost of the purchase option is $44,188.23.

User Christos Michael
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