Chapter 10, Problem 1P

To determine

Calculate the time period.

Explanation of Solution

The recovery rate under the General Depreciation System for five year is given in the below table:

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.

$\begin{array}{c}\text{TG}=\left(\text{Salvage value}-\left(\text{Investment}-\text{Investment}\left({\text{RR}}_1+{\text{RR}}_2+\mathrm{...}+{\text{RR}}_{\text{n}}\right)\right)\right)\text{TR}\\ =\left(\text{0}-\left(\text{65,000}-65,000\left(0.2+0.32+0.192+0.1152+0.1152+0.0576\right)\right)\right)\left(0.4\right)\\ =0\end{array}$

Taxable gain is $0.

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	-65,000	-	-	-	-55,000	-65,000
1	23,000	13,000	10,000	4,000	19,000	16,522
2	23,000	20,800	2,200	880	22,120	16,726
3	23,000	12,480	10,520	4,208	18,792	12,356
4	23,000	7,488	15,512	6,205	16,795	9,603
5	23,000	7,488	15,512	6,205	16,795	8,350
6	23,000	3,744	19,256	7,702	15,298	6,614
7						5,170

The net present worth is $5,170. Since the present wroth is positive the project is acceptable.