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.