Chapter 12, Problem 1P

(a):

To determine

Calculate the net cash flow.

Explanation of Solution

The recovery rate (RR) under the General Depreciation System for five year is given in Table-1.

                    Table-1

Year	RR
1	0.2
2	0.32
3	0.192
4	0.1152
5	0.1152
6	0.0576

Taxable gain (TG) can be calculated as follows.

$\begin{array}{c}\text{TG}=\left(\text{Salvage value}-\left(\text{Investment}-\left({\text{D}}_1+{\text{D}}_2+\mathrm{...}+{\text{D}}_{\text{n}}\right)\right)\right)\text{TR}\\ =\left(\text{30,000}-\left(\text{100,000}-\left(20,000+32,000+9,600\right)\right)\right)\left(0.4\right)\\ =-3,360\end{array}$

Taxable gain is -$3,360.

Table 2 shows the after tax cash flow. Column 2 is equal to net annual revenue. Column 3 is obtained by multiplying the RR value with the investment. When the investment is retired before its life time, then half of the depreciation is captured in the last year. Column 4 is obtained by subtracting the column 3 from column 2. Column 5 is obtained by multiplying the tax rate with column 4. Column 6 is obtained by subtracting the column 5 from column 2. Last year net cash flow is added with salvage value and subtract the taxable gain from it. Present worth (PW) can be obtained by multiplying the $\left(\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\right)$ with respective ATCF.

Table-2

1	2	3	4	5	6	7
Year	BTCF	D	TI	TAX	ATCF	PW
0	-100,000				-100,000	-100,000
1	45,000	20,000	25,000	10,000	35,000	30,435
2	45,000	32,000	13,000	5,200	39,800	30,095
3	45,000	19,200	25,800	10,320	64,200	42,213
4						2,742

Present wroth is $2,741. Since the project has positive present worth, it is acceptable.

(b):

To determine

Calculate the new net cash flow.

Explanation of Solution

The required investment is become $110,000. Labor saving should be $50,744 so that the project present worth would become $0 with the MARR 15%. This could be verified by using the same procedure done in part ‘a’.