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.
