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Nov 24, 2024
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To determine which of the two alternatives (purchase or lease) Dunn should
adopt, we need to calculate the present value of the net cash flows for each
alternative and then compare them. We'll use factor tables to perform the
calculations.
Purchase Alternative
:
1.
Initial Down Payment: $400,000
2.
Annual Payments (including interest) for 5 years: $350,000
3.
Salvage Value after 12 years: $500,000
4.
Annual Occupancy Expenses: $56,000
Using the present value of an ordinary annuity table, we'll calculate the
present value of the annual payments for 5 years and then the present value
of the salvage value at the end of year 12. The occupancy expenses don't
need discounting because they are paid at the end of each year.
Present Value of Annual Payments (PMT = $350,000, r = 10%, n = 5):
PV_Annual_Payments = $350,000 × 3.79079 = $1,326,276.50
Present Value of Salvage Value (FV = $500,000, r = 10%, n = 12):
PV_Salvage_Value = $500,000 × 0.322 = $161,000
Total Present Value for Purchase Alternative: PV_Purchase = Initial
Down Payment + PV_Annual_Payments + PV_Salvage_Value + Annual
Occupancy Expenses for 12 years PV_Purchase = $400,000 +
$1,326,276.50 + $161,000 + ($56,000 × 12) = $2,412,276.50
Lease Alternative
:
1.
Annual Lease Payments: $270,000
2.
Deposit: $100,000
Using the present value of an ordinary annuity table, we'll calculate the
present value of the annual lease payments for 12 years, and we'll discount
the deposit for 12 years.
Present Value of Annual Lease Payments (PMT = $270,000, r = 10%, n
= 12): PV_Lease_Payments = $270,000 × 7.53626 = $2,034,321.20
Present Value of Deposit (FV = $100,000, r = 10%, n = 12): PV_Deposit
= $100,000 × 0.322 = $32,200
Total Present Value for Lease Alternative: PV_Lease =
PV_Lease_Payments - PV_Deposit = $2,034,321.20 - $32,200 =
$2,002,121.20
Now, let's compare the total present values for both alternatives:
PV_Purchase = $2,412,276.50
PV_Lease = $2,002,121.20
Dunn should adopt the
Lease Alternative
because it has a lower total
present value, making it a more cost-effective option in terms of cash
outflows.
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