Arnold Company is acquiring a new machine with a life of 5 years for use on its production line. The following data relate to this purchase: $\begin{array}{lr}\text { Cost of new machine }&\$100,000\
\text { Annual cost savings in cash expenses }&45,000\
\text { Terminal value } & 8,000 \
\text { Maintenance required in the 4th year } & 5,000 \
\text { Book value of the old machine } & 20,000
\end{array}$ The new machine would replace an old fully-amortized machine. The old machine can be sold for $15,000 at the time the new equipment is acquired. The income tax rate is 30%, and the discount rate is 12%. Arnold uses the straight-line method for amortization on all machines (ignore the half-year convention). Note: some amounts are rounded.
The present value of the maintenance cost in year 4 is:
A) $2,226
B) $3,180
C) $954
D) $420

Question

Quizplus · Accepted Answer

To calculate the present value of the maintenance cost in year 4, you use the formula for present value: $$PV = \frac{FV}{(1 + r)^n}$$ where $FV$ is the future value ($5,000), $r$ is the discount rate (0.12), and $n$ is the number of years (4). Plugging in the values: $$PV = \frac{5,000}{(1 + 0.12)^4} = \frac{5,000}{1.5748} = 3,177.62$$ which rounds to approximately $3,180.

Arnold Company Is Acquiring a New Machine with a Life