On January 2, 2020, Zimbabwe Corp. purchases a new machine. The company makes a $ 3,000 cash down payment, and agrees to pay eight semi-annual instalments of $ 2,000 each, starting July 1, 2020, signing a non-interest-bearing note to this effect. The cash equivalent price of the machine is not known, but the appropriate interest rate for this type of transaction is 8% p.a. Rounding to the nearest dollar (if necessary), Zimbabwe should record the cost of the machine at
A) $ 15,413.
B) $ 16,465.
C) $ 16,000.
D) $ 19,000.

Question

Quizplus · Accepted Answer

To find the cost of the machine, we need to calculate the present value of the cash flows (the down payment and the semi-annual installments) using the appropriate interest rate. The down payment of $3,000 is already at present value since it's paid at the time of purchase. The semi-annual installments need to be discounted back to their present value as of the purchase date using the semi-annual interest rate (which is half of the annual rate, 4%). The formula for the present value of an annuity is used for the installments, and then we add the down payment to this value.The present value of the annuity (PVA) can be calculated using the formula: PVA = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods.For the installments: P = $2,000, r = 0.08/2 = 0.04 (since interest is compounded semi-annually), and n = 8.PVA = $2,000 * [(1 - (1 + 0.04)^-8) / 0.04] ≈ $13,465Adding the down payment: Total cost = $13,465 + $3,000 = $16,465.