Answer:
They purchase the machine from Vendor A.
Explanation:
This can be determined using the following 4 steps:
Step 1: Calculation of total cost of buying from Vendor A
Amount paid at the time of delivery = $40,000
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.
