Harding Company is in the process of purchasing several large pieces of equipment from Danning Machine Corporation. Several financing alternatives have been offered by Danning:
1.
Pay $950,000 in cash immediately.
2.
Pay $420,000 immediately and the remainder in 10 annual installments of $80,000, with the first installment due in one year.
3. Make 10 annual installments of $125,000 with the first payment due immediately.
4. Make one lump-sum payment of $1,580,000, 3 years from date of purchase.
Required:
Determine the best alternative for Harding, assuming that Harding can borrow funds at a(n) 4% interest rate.
Round all PV factors to 5 decimal places if you use the PV tables, and final answers to the nearest whole dollar.
Choose the best alternative by entering the option number in the answer box.
1 PV = $ ____________
2 PV = $420,000 +($ ____________ x ____________)= $ ____________
3 PV = $ ____________ x ____________ = $ ____________
4 PV = $ ____________ x ____________ = $ ____________
Harding should choose option ____________ .
1. 950000
To determine the best alternative for Harding Company, we need to calculate the present value (PV) for each financing option. We will use the formula for present value of annuity (PV) as follows:
PV = Payment x (1 - (1 + Interest Rate)^(-n)) / Interest Rate
where:
Payment = Annual payment amount
Interest Rate = Interest rate per period
n = Number of periods
Option 1:
PV = $950,000
Option 2:
PV = $420,000 + ($80,000 x [(1 - (1 + 0.04)^(-10)) / 0.04)]
PV = $420,000 + ($80,000 x [(1 - 1.41158883109) / 0.04)]
PV = $420,000 + ($80,000 x [0.58841116891 / 0.04])
PV = $420,000 + ($80,000 x 14.7102792228)
PV = $420,000 + $1,176,822.34
PV = $1,596,822.34
Option 3:
PV = $125,000 x [(1 - (1 + 0.04)^(-10)) / 0.04)]
PV = $125,000 x [0.48858616874 / 0.04]
PV = $125,000 x 12.2146542185
PV = $1,526,831.78
Option 4:
PV = $1,580,000 x (1 + 0.04)^(-3)
PV = $1,580,000 x 0.88573783943
PV = $1,397,281.72
Based on the calculated PV for each option, we can see that the best alternative for Harding Company is Option 1 (PV = $950,000).
To determine the best financing alternative for Harding Company, we need to calculate the present value (PV) of each option. The PV of an option is the value of all future cash flows discounted to their present value using the given interest rate of 4%.
Let's calculate the PV for each option:
1. Option 1: Pay $950,000 in cash immediately.
The PV of Option 1 is simply $950,000 since there are no future cash flows to discount.
PV = $950,000
2. Option 2: Pay $420,000 immediately and the remainder in 10 annual installments of $80,000, with the first installment due in one year.
To calculate the PV of Option 2, we need to discount each future cash flow and then sum them up.
First, we calculate the PV of the 10 installments of $80,000:
PV of installments = $80,000 x (1 - (1 + 0.04)^-10) / 0.04 = $537,428.66
Next, we add the immediate payment of $420,000 to get the total PV of Option 2:
PV = $420,000 + $537,428.66 = $957,428.66
3. Option 3: Make 10 annual installments of $125,000 with the first payment due immediately.
Similar to Option 2, we need to calculate the PV of the 10 installments and then add the present value of the immediate payment.
PV of installments = $125,000 x (1 -(1 + 0.04)^-10) / 0.04 = $829,622.17
PV = $829,622.17
4. Option 4: Make one lump-sum payment of $1,580,000, 3 years from the date of purchase.
To calculate the PV of Option 4, we need to discount the future lump-sum payment back to the present.
PV = $1,580,000 / (1 + 0.04)^3 = $1,421,578.69
Now we compare the PVs of each option to determine the best alternative. The option with the lowest PV is considered the best choice.
1 PV = $950,000
2 PV = $957,428.66
3 PV = $829,622.17
4 PV = $1,421,578.69
From the calculations, Option 3 has the lowest PV, making it the best choice for Harding Company.
Therefore, Harding should choose Option 3.
These were the present values I had obtained.
1. PV = 1,180,000
2. PV = 671476
3. PV = 1,087,033
4. PV = 1,204,627
4 is the one I had trusted myself least on.