Alden Trucking Company is replacing part of its fleet of trucks by purchasing them under a note agreement with Kenworthy on January 1, 2016. Alden financed $37,908,000, and the note agreement will require $10 million in annual payments starting on December 31, 2016 and continuing for a total of four more years (final payment December 31, 2020). Kenworthy will charge Alden Trucking Company the market interest rate of 10% compounded annually. After the first payment was made, the note payable liability on December 31, 2016 is closest to:
A)$32,908,000.
B)$31,698,800.
C)$40,000,000.
D)$27,908,000.

Question

Quizplus · Accepted Answer

To calculate the note payable liability on December 31, 2016, we need to find the present value of the remaining payments at the market interest rate of 10%. 
Using the present value annuity formula: 
PV = PMT x [(1 - (1 / (1 + r)^n)) / r]
Where: 
PMT = $10,000,000 
r = 10% 
n = 4 (remaining years of payments) 
PV = $10,000,000 x [(1 - (1 / (1 + 0.10)^4)) / 0.10] 
PV = $10,000,000 x [(1 - (1 / 1.4641)) / 0.10] 
PV = $10,000,000 x (0.3170) / 0.10 
PV = $31,698,800

Therefore, the note payable liability on December 31, 2016 is $31,698,800, which is closest to choice B: $31,698,800.

Alden Trucking Company Is Replacing Part of Its Fleet of Trucks