Palm Cay, Inc, plans to purchase a new metal stamping machine for use in its manufacturing process. After contacting the appropriate vendors, the purchasing department received differing terms and options from each vendor. The engineering department has determined that each vendor's stamping machine is substantially identical and each has a useful life of 30 years. In addition, engineering has estimated that required year-end maintenance costs will be $3,000 per year for the first 10 years, $5,000 per year for the next 10 years, and $12,000 per year for the last 10 years. Vendor A: $40,000 cash at the time of delivery and 5 year end payments of $50,000 each. Vendor A offers all its customers the right to purchase at the time of sale a separate 30-year maintenance service contract, under which Vendor A will perform all year-end maintenance at a one-time initial cost of $47,000. Vendor B: Forty- semi-annual payments of $14,000 each, with the first installment due upon delivery. Vendor B will perform all year-end maintenance for the next 30 years at no extra charge. Vendor C: Full cash price of $225,000 will be due upon delivery. Instructions: Assuming that both Vendors A and B will be able to perform the required year-end maintenance, and that Palm Cay's cost of funds is 8%, and the machine will be purchased on January 1, from which Vendor should they purchase the machine from

Since the $50,000 will be paid at the end of each year, the present value of 5 years annual payment can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

Present value of 5 years annual payment = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

P = Monthly payment = $50,000

r = cost of funds = 8%, or 0.08

n = number of years = 5

Substitute the values into equation (1), we have:

Present value of 5 years annual payment = 50,000 * ((1 - (1 / (1 + 0.08))^5) / 0.08) = $199,635.50

Total cost of buying from Vendor A = Amount paid at the time of delivery + Present value of 5 years annual payment = $40,000 + $199,635.50 = $249,635.50

Step 2: Calculation of total cost of buying from Vendor B

Since the first $14,000 installment is due upon delivery, the present value of Forty- semi-annual payments can be calculated using the formula for calculating the present value of annuity due as follows:

Present value of Forty- semi-annual payments = P * ((1 - (1 / (1+r))^n) / r) * (1+r) .................................. (2)

Where ;

P = Semi-annual payment = $14,000

r = semi-annual cost of funds = Cost of funds / 2 = 8% / 2 = 4%, or 0.04

n = number of semiannuals = 40

Substituting the values into equation (2) above, we have:

Present value of Forty- semi-annual payments = $14,000 * ((1 - (1 / (1+0.04))^40) / 0.04) * (1+0.04) = $288,182.79

Therefre, we have:

Total cost of buying from Vendor B = Present value of Forty- semi-annual payments = $288,182.79

Step 3: Calculation of total cost of buying from Vendor C

Note: See the attached excel file for the calculation of the total present value of the required year-end maintenance costs (in bold red color).

Full cash price = $225,000

Total present value of the required year-end maintenance costs = $52,946.21

Total cost of buying from Vendor C = Full cash price + Total present value of the required year-end maintenance costs = $225,000 + $52,946.21 = $277,946.21

Step 4: Decision

Total cost of buying from Vendor A = $249,635.50

Total cost of buying from Vendor B = $288,182.79

Total cost of buying from Vendor C = $277,946.21

Since the Total cost of buying from Vendor A which is $249,635.50 is the lowest, they purchase the machine from Vendor A.