Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual payments at the end of the next three years of $1,000,000 each.The bank has offered to allow Taggart Transcontinental to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years.If the interest rate on the loan is 6%,then the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to:
A)$2,673,000.
B)$3,000,000.
C)$3,184,000.
D)$3,375,000.

Question

Quizplus · Accepted Answer

To find the final payment that would make Taggart Transcontinental indifferent between the two payment options, we need to find the present value of both payment options and then equate them.

Option 1: Make three annual payments of $1,000,000 each
- Present value of three annual payments at 6% interest rate:
PV = $1,000,000 / (1 + 0.06)^1 + $1,000,000 / (1 + 0.06)^2 + $1,000,000 / (1 + 0.06)^3
PV = $2,723,599.28

Option 2: Skip two annual payments and make one large payment at the end of the loan's term
- Present value of one large payment at 6% interest rate:
PV = X / (1 + 0.06)^3
PV = X / 1.191016

To equate the present values of the two options, we set them equal to each other:
$2,723,599.28 = X / 1.191016
X = $3,238,544.90

Therefore, the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to $3,184,000 (choice C).

Taggart Transcontinental Currently Has a Bank Loan Outstanding That Requires