If the investment is desirable or not.
Answer to Problem 22P
The investment is not desirable.
Explanation of Solution
Concept used:
Write the expression to calculate the
d1=2N(BVt−1) ....... (I)
Here, the depreciation is d1, the total number of year is N and the book value of previous year is BVt−1.
Write the expression to calculate cumulative depreciation.
CD=dt+dt−1 ....... (II)
Here, the cumulative depreciation is CD, the depreciation of the current year is dt and the depreciation o the previous year is dt−1.
Write the expression to calculate the book value.
BVt=BV0−CDt ....... (III)
Here, the book value of the current year is BVt, the book value at 0 year is BV0 and the depreciation for current year is Dt.
Write the expression to calculate the depreciation by straight line method.
dt=BV−SN ....... (IV)
Here, the depreciation is dt, the book value is BV, the salvage value is S and the total number of year is N.
Write the expression to calculate the depreciation recaparture.
DC=SV−BV ....... (V)
Here, the depreciation recapture is DC, the book value is BV and the salvage value is SV.
Calculations:
All values are taken in ($1000).
Calculate the depreciation for year 1.
Substitute $12000 for BVt−1 and 6 for N in Equation (I).
d1=26($12000)d1=$4000
Calculate the cumulative depreciation for year 1.
Substitute $4000 for dt and $0 for CDt−1 in Equation (II).
CD1=$4000+$0CD1=$4000
Calculate the book value for year 1.
Substitute $12000 for BV0 and $4000 for CD1.
BV1=$12000−$4000=$8000
Calculate the depreciation for year 2.
Substitute $8000 for BVt−1 and 6 for N in Equation (I).
d2=26($8000)d2=$2667
Calculate the cumulative depreciation for year 2.
Substitute $2667 for dt and $4000 for CDt−1 in Equation (II).
CD2=$4000+$2667CD2=$6667
Calculate the book value for year 2.
Substitute $12000 for BV0 and $6667 for CD2.
BV2=$12000−$6667=$5333
Calculate the depreciation for year 3.
Substitute $5333 for BVt−1 and 6 for N in Equation (I).
d3=26($5333)d3=$1778
Calculate the cumulative depreciation for year 3.
Substitute $1778 for dt and $6667 for CDt−1 in Equation (II).
CD3=$6667+$1778CD3=$8445
Calculate the book value for year 3.
Substitute $12000 for BV0 and $8445 for CD3
BV3=$12000−$8445=$3555
Calculate the depreciation for year 4.
Substitute $3555 for BVt−1 and 6 for N in Equation (I)
d4=26($3555)d4=$1185
Calculate the cumulative depreciation for year 4.
Substitute $1185 for dt and $8445 for CDt−1 in Equation (II).
CD4=$1185+$8445CD4=$9630
Calculate the book value for year 4.
Substitute $12000 for BV0 and $9630 for BV4=$12000−$9630=$2370
The depreciation for year 5 and 6 has to be calculated by straight line method.
Calculate the depreciation for year 5.
Substitute $2370 for BV, $700 for S and 2 for N in Equation (IV).
d5=$2370−$7002=$835
Calculate the cumulative depreciation for year 5.
Substitute $835 for dt and $9630 for CDt−1 in Equation (II).
CD5=$9630+$835CD5=$10465
Calculate the book value for year 5.
Substitute $12000 for BV0 and $10465 for CD5
BVt=$12000−$10465=$1535
Substitute $2370 for BV, $700 for S and 2 for N in Equation (IV).
d6=$2370−$7002=$835
Calculate the cumulative depreciation for year 6.
Substitute $835 for dt and $10465 for CDt−1 in Equation (III).
CD6=$10465+$835CD6=$11300
Calculate the book value for year 6.
Substitute $12000 for BV0 and $11300 for CD6.
CD1=$12000−$11300=$700
Tabulate the obtained above values.
Year | Deprecation | Cumulative Depreciation | Book Value |
1 | $4000 | $4000 | $8000 |
2 | $2667 | $6667 | $5333 |
3 | $1778 | $8445 | $3555 |
4 | $1185 | $9360 | $2370 |
5 | $835 | $10465 | $1535 |
6 | $835 | $11300 | $700 |
The book value obtained after the end of 6 years is $700 while the salvage value is $1000. This results into depreciation recaparture.
Substitute $1000 for SV and $700 for BV in Equation (V).
DC=$1000−$700=$300
Tabulate the values for before tax and after cash flows.
Year | Before taxCash flow (a) | Depreciation (b) | Taxable income c=(a−b) | Income taxes d=−(c×0.34) | After taxCash flow e=(a+d) |
0 | −$12000 | −$12000 | |||
1 | $1727 | $4000 | −$2273 | $773 | $2500 |
2 | $2414 | $2667 | −$253 | $86 | $2500 |
3 | $2872 | $1778 | $1094 | −$372 | $2500 |
4 | $3177 | $1185 | $1992 | −$677 | $2500 |
5 | $3358 | 835 | $2523 | −$858 | $2500 |
6 | $1997 | $835 | $1162 | −$395 | $1602 |
6 | $1000 | $300 | −$102 | $898 |
Now calculate the after tax return.
Write the expression to calculate the rate when A and P given.
P=A((1+i)n−1i(1+i)) ....... (V)
Here the present value is P, the annual investment is A, the number of years is n and the rate of return is i.
Substitute $12000 for P, 6 for n and $2500 for A in Equation (V).
12000=2500((1+i)6−1i(1+i)6)4.8i(1+i)6−(1+i)6+1=0 ........ (VI)
Solve Equation (VI) for the value of i.
i=0.0677i=(0.0677×100)%i=6.77%.
Conclusion:
The after tax rate of return is less than expected rate of return.
Hence the investment is not desirable.
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Chapter 12 Solutions
ENGINEERING ECO ALANYSIS W/STUDY GUIDE
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