One division of the Marvin Educational Enterprises has depreciable assets costing $4,000,000. The cash flows from these assets for the past three years have been:
$$\begin{array} { c l l }
\text { Year } & { \text { Cash flows } } \
1 & \mathbf { \$ } 1,200,000 \
2 & \$ 1,400,000 \
3 & \$ 1,620,000
\end{array}$$
The current (i.e., replacement) costs of these assets were expected to increase 25% each year.
-Marvin used the straight-line depreciation method and the estimated useful life is 10-years with no salvage value. For return on investment (ROI) calculations, Marvin uses end-of-year balances.
What is the residual income for each year, assuming the cost of capital is 15% and Marvin uses historical costs and gross book values to compute residual income?
$\begin{array} { l l l l l l l }
& { \text { Year } 1 } & { \text { Year 2 } } & { \text { Year 3 } } \\end{array}$
A.$\begin{array} { l c c c } & \$ & 200,000 & \$ & 400,000 & \$ & 620,000 \\end{array}$
B.$\begin{array} { l c c c } & \$ & 200,000 & \$ & 200,000 & \$ & 200,000 \\end{array}$
C.$\begin{array} { l c c c } & \$ & 250,000 & \$ & 200,000 & \$ & 450,000 \\end{array}$
D.$\begin{array} { l c c c } & \$ & 250,000 & \$ & 400,000 & \$ & 375,000
\end{array}$

Question

One division of the Marvin Educational Enterprises has depreciable assets costing $4,000,000. The cash flows from these assets for the past three years have been:
$$\begin{array} { c l l } 
\text { Year } & { \text { Cash flows } } \
1 & \mathbf { \$ } 1,200,000 \
2 & \$ 1,400,000 \
3 & \$ 1,620,000
\end{array}$$
The current (i.e., replacement) costs of these assets were expected to increase 25% each year. 
-Marvin used the straight-line depreciation method and the estimated useful life is 10-years with no salvage value. For return on investment (ROI) calculations, Marvin uses end-of-year balances.
What is the residual income for each year, assuming the cost of capital is 15% and Marvin uses historical costs and gross book values to compute residual income?
$\begin{array} { l l l l l l l } 
& { \text { Year } 1 } &  { \text { Year 2 } } &  { \text { Year 3 } } \\end{array}$
A.$\begin{array} { l c c c }  & \$ & 200,000 & \$ & 400,000 & \$ & 620,000 \\end{array}$
B.$\begin{array} { l c c c } & \$ & 200,000 & \$ & 200,000 & \$ & 200,000 \\end{array}$
C.$\begin{array} { l c c c } & \$ & 250,000 & \$ & 200,000 & \$ & 450,000 \\end{array}$
D.$\begin{array} { l c c c } & \$ & 250,000 & \$ & 400,000 & \$ & 375,000
\end{array}$

Quizplus · Accepted Answer

The correct answer is A because the residual income is calculated as the difference between the actual cash flows and the expected cash flows, which are based on the cost of capital and the gross book value of the assets. The gross book value of the assets is the original cost of the assets minus the accumulated depreciation. The accumulated depreciation is calculated as the straight-line depreciation method, which is the cost of the assets divided by the estimated useful life. The estimated useful life is 10 years, so the annual depreciation expense is $4,000,000 / 10 = $400,000. The gross book value of the assets at the end of each year is the original cost of the assets minus the accumulated depreciation. The original cost of the assets is $4,000,000, so the gross book value of the assets at the end of each year is:Year 1: $4,000,000 - $400,000 = $3,600,000Year 2: $3,600,000 - $400,000 = $3,200,000Year 3: $3,200,000 - $400,000 = $2,800,000The expected cash flows are calculated as the cost of capital multiplied by the gross book value of the assets. The cost of capital is 15%, so the expected cash flows are:Year 1: $3,600,000 x 15% = $540,000Year 2: $3,200,000 x 15% = $480,000Year 3: $2,800,000 x 15% = $420,000The residual income is calculated as the difference between the actual cash flows and the expected cash flows. The actual cash flows are given in the question, and the expected cash flows are calculated above. The residual income is:Year 1: $1,200,000 - $540,000 = $660,000Year 2: $1,400,000 - $480,000 = $920,000Year 3: $1,620,000 - $420,000 = $1,200,000

One Division of the Marvin Educational Enterprises Has Depreciable Assets