Final answer:
The difference in present value of the offers from two suppliers is calculated by discounting the future payments using the risk-free interest rate. After discounting, we compare the present value costs from both suppliers to find that option c: $3,301.89 is the closest match to the difference, although the exact calculation gives $3,773.59, indicating a possible miscalculation in the provided answers.
Step-by-step explanation:
The question involves comparing two offers from suppliers using the concept of present value to determine the cost of purchasing keyboards today. To find the difference in present value terms, we need to discount the future payments back to today's dollars using the given risk-free interest rate of 6%.
For Supplier A, the payment is $100,000 today plus an additional payment of $10 per keyboard for 10,000 keyboards in one year, which amounts to $100,000 today and $100,000 in a year (10,000 keyboards × $10 per keyboard).
The present value of $100,000 in one year is calculated using the formula PV = FV / (1 + r)^n, where PV is present value, FV is future value, r is the interest rate, and n is the number of periods.
Thus, PV = $100,000 / (1 + 0.06)^1 = $94,339.62.
Adding the $100,000 paid today, the total present cost from Supplier A is $194,339.62.
For Supplier B, the cost is $21 per keyboard for 10,000 keyboards all payable in one year, which is $210,000.
The present value of this amount is PV = $210,000 / (1 + 0.06)^1 = $198,113.21.
To find the difference in costs today, we subtract the present value cost of Supplier B from that of Supplier A:
$198,113.21 - $194,339.62 = $3,773.59.
However, none of the options given exactly match this calculation. The closest option (and correct within the context of the possible answers provided) would be option c: $3,301.89, but it appears there has been a miscalculation.