Tax and Depreciation Answers

 

 

 

 

 

 

P1

a. SOYD = 1+2+3+4 =10
Depreciation
Year 1 (4/10)(8000 - 1000) = $2800
Year 2 (3/10)(8000 - 1000) = $2100
b. The book value will equal the estimated salvage.

P2

a. Year Depreciation
1 $3333 = (10000 - 0)/3
2 $2222 = (10000 - 3333)/3
b. Without switching, the BV has no relation to the estimated salvage value.
Final book value without switching
= 10000 - (3333+2222+1482+ 988+658+438) = 10000 - 9121 = 879
In this case the book value is below the estimated salvage value.

If we switched to straight line for the final year of depreciation, the depreciation in year 6 would be $317. The book value would then equal the salvage value.
c. In a before tax analysis, depreciation does not play a role. It is used in an after tax analysis to get the taxable income by subtracting it from the BTCF.

 

P3a

Before tax ROR
NPW = 0
- 10,000 + 5000(P/A,i,3) + 2000(P/A,i,2)(P/F,i,3) + 1000(P/F,i,5) = 0
Solve for i to get before tax ROR.
After tax ROR
NPW = 0
-10000 + 3500(P/F, i, 3) + 2000(P/A, i, 2)(P/F, i, 3) + 500(P/F, i, 5) = 0
Solve for i to get after tax ROR.

 

P3b

Before tax ROR Does not depend on depreciation method.

After tax ROR NPW= 0
-10,000 + 4166.67 (P/A, i, 3) + 333.34 (P/G, i, 3) + [1,666.67(P/A, i, 2) + 333.34(P/G, i, 2)](P/F, i, 3) + 500(P/F, i, 5) = 0
Solve for i to get after tax ROR.

P3c

Before tax ROR Does not depend on depreciation method.

After tax ROR: NPW= 0
-10,000 + 4500 (P/F, i, 1) + 3700 (P/F, i, 2) + 3220(P/F, i, 3) + 1432(P/F, i, 4) + 2148(P/F, i, 5) = 0
Solve for i to get after tax ROR.

P4

When the asset is sold the book value is 0. The entire resale receipts are taxable. The tax is 20% of $1000 or 200. The net from the resale is then $800. The complete cash flow at the end of year 5 is then $1500.

c. After tax ROR
Set NPW=0
-4500 + 1900(P/A, i, 5) - 300(P/G,i, 5) + 800(P/F, i, 5) = 0
i=20%: NPW = 32.62
i=25%: NPW= -389.94
Interpolating between 20% and 25% yields ROR = 24.11%.

 

P5a

Which option is best?
Option B is best.

Why?
The double declining balance method yields greater depreciation in early years. The after tax cash flows will then be greater in the early years and smaller in the later years for B rather than A. The ROR of the asset depreciated as in B will then be greater.

 

P5b

Which option is best?
Option A is best.

Why?
Although we will have to pay taxes on the gain when we sell the asset, the depreciation allows us to get a higher cash flow in the early years. Again the time value of money says that this is preferred.

 

P5c

Which option is best?
Option B.

Why?
Both options have the same investment and salvage. The taxable option has a tax of (240 - 200)*0.2 = $8 per year. The after tax return is $32 more than for option A.

 

P6

The cash flow due to income is BTCF - tax rate(BTCF - Depr)
Depr = 3000*2/5 = 1200
ATCF = 2000 - 0.3*(2000 - 1200) = 2000 - 240 = 1760

The cash flow due to sale of the truck is selling price - tax
The book value at the end of the year is 3000 - Depr = 1800
Tax = (Selling price - Book value)*(tax rate) = (600 - 1800)*0.3 = -1200*0.3 = -360
AT cash flow due to sale of truck = 600 + 360 = 960

Total ATCF = 1760 + 960 = 2720

 

P7

With the SOYD method, the remaining depreciation is X*(2/15 + 1/15), where X is the initial cost of the truck. Since this must exhaust the remaining book value we have:
3000 = X*(3/15) or X = $15,000.