Chapter 10, Problem 22PSB

a.

To determine

Ascertain the net present value and the present value index of the investment, assuming that

Company W uses straight-line depreciation for financial and income tax reporting.

Explanation of Solution

Net present value method:

Net present value method is the method which is used to compare the initial cash outflow of investment with the present value of its cash inflows. In the net present value, the interest rate is desired by the business based on the net income from the investment, and it is also called as the discounted cash flow method.

Ascertain the net present value of the investment under straight line method as follows:

Particulars	Amount ($) (a)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Present value of net cash inflows (1)	$67,500	3.790787	$ 255,878
Add: Present value of Salvage value	50,000	0.620921	31,046
Less: Initial investment			(200,000)
Net present value			$ 86,924

Table (1)

Note:

• The Present value of an ordinary annuity of $1 for 5 years at 10% is 3.790787 (refer table 2 in appendix).
•  The present value of $1 for 5th year at 10% is 0.620921 (refer table 1 in appendix).

Working notes:

Calculate the amount of cash flow under straight line for each year:

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Revenue	80,000	80,000	80,000	80,000	80,000
Less: Depreciation (3)	30,000	30,000	30,000	30,000	30,000
Income before tax	50,000	50,000	50,000	50,000	50,000
Less: Income  tax (2)	12,500	12,500	12,500	12,500	12,500
Net Income	37,500	37,500	37,500	37,500	37,500
Add: Depreciation	30,000	30,000	30,000	30,000	30,000
Cash flow	67,500	67,500	67,500	67,500	67,500

Table (2)

...... (1)

Calculate the amount of income tax expense:

$\begin{array}{c}\text{Income tax expense}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{25}{100}\times \$50,000\\ =\$12,500\end{array}$

…… (2)

Ascertain the depreciation expenses under straight line as follows:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$200,000}-\text{\$50,000}}{\text{5 years}}\\ =\$30,000\end{array}$

…… (3)

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (5)}}\\ =\frac{\text{\$334,309}\text{.01}}{\text{\$247,384}\text{.84}}\\ =1.35\end{array}$

Working notes:

Calculate the present value of cash inflows:

Particulars	Amount ($) (a)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Present value of cash inflows	$80,000	3.790787	$303,262.96
Add: Present value of Salvage value	50,000	0.620921	$31,046.05
Total PV of cash inflows			$334,309.01

Table (3)

 …… (4)

Note:

• The Present value of an ordinary annuity of $1 for 5 years at 10% is 3.790787 (refer table 2 in appendix).
•  The present value of $1 for 5th year at 10% is 0.620921 (refer table 1 in appendix).

Calculate the present value of cash outflows:

Particulars	Amount ($) (a)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Present value of tax payments (2)	$12,500	3.790787	$$47,384.84
Add: Initial investment			200,000
Total PV of cash outflows			$247,384.84

Table (4)

 …… (5)

Note:

• The Present value of an ordinary annuity of $1 for 5 years at 10% is 3.790787 (refer table 2 in appendix).

b.

To determine

Ascertain the net present value and the present value index of the investment, assuming that

Company W uses double-declining-balance depreciation for financial and income tax reporting.

Explanation of Solution

Ascertain the net present value of the investment under double declining balance method as follows:

Particulars	Amount ($) (a) (6)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Present value of net cash inflows:
Year 1	$80,000	0.909091	$72,727
Year 2	72,000	0.826446	59,504
Year 3	65,500	0.751315	49,211
Year 4	60,000	0.683013	40,981
Year 5	60,000	0.620921	37,255
Salvage value	50,000	0.620921	31,046
Less: Present value of cash outflows			200,000
Net present value			$90,724

Table (5)

Note:

• For the present value factors refer table 1 in appendix.

Working notes:

Calculate the amount of cash flow under double declining method for each year:

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Revenue	80,000	80,000	80,000	80,000	80,000
Less: Depreciation (7)	80,000	48,000	22,000	-	-
Income before tax (8)	-	32,000	58,000	80,000	80,000
Less: Income  tax	-	8,000	14,500	20,000	20,000
Net Income	-	24,000	43,500	60,000	60,000
Add: Depreciation	80,000	48,000	22,000	-	-
Cash flow	80,000	72,000	65,500	60,000	60,000

Table (6)

…… (6)

Compute the depreciation expenses under double declining method for each year:

Year	Depreciation expenses
Year 1	$\begin{array}{l}=\left(\$200,000\times \frac{40}{100}\right)\\ =\$80,000\end{array}$
Year 2	$\begin{array}{l}=\left(\$200,000-\$80,000\right)\times \frac{40}{100}\\ =\$48,000\end{array}$
Year 3	$\begin{array}{l}=\left(\$200,000-\$80,000-\$48,000\right)\times \frac{40}{100}\\ =\$28,800\end{array}$

Table (7)

…... (7)

Note:

Since the book value of asset $\left(\$200,000-\$80,000-\$48,000-\$28,800\right)$ at the 4^th year is less than the salvage value ($50,000). Hence the salvage value should be deducted with the 4^th year book value of asset $\left(\$50,000-\$43,200=6,800\right)$ and this amount should be deducted from the depreciation expenses of 3^rd year $\left(\$28,800-\$6,800=\$22,000\right)$.

Compute the depreciation rate applied each year:

Useful life = 5 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{5 Years}}\times 2\\ =40\%\end{array}$

Note: Use 100% to represent depreciation in percentage. Multiply the depreciation rate with 2 as it is a double-declining method.

Compute the income tax expenses under double declining method for each year:

Year	Income tax expenses
Year 2	$\begin{array}{l}=\left(\$32,000\times \frac{25}{100}\right)\\ =\$8,000\end{array}$
Year 3	$\begin{array}{l}=\left(\$58,000\times \frac{25}{100}\right)\\ =\$14,500\end{array}$
Year 4	$\begin{array}{l}=\left(\$80,000\times \frac{25}{100}\right)\\ =\$20,000\end{array}$
Year 5	$\begin{array}{l}=\left(\$80,000\times \frac{25}{100}\right)\\ =\$20,000\end{array}$

Table (8)

…... (8)

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (9)}}\\ =\frac{\text{\$334,309}\text{.01}}{\text{\$243,584}\text{.32}}\\ =1.37\end{array}$

Working notes:

Calculate the present value of cash outflows:

Particulars	Amount ($) (a)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Year 1 income tax payment	0	0.909091	$0
Year 2 income tax payment (7)	8,000	0.826446	6,611.568
Year 3 income tax payment (7)	14,500	0.751315	108,94.0675
Year 4 income tax payment (7)	20,000	0.683013	13,660.26
Year 5 income tax payment (7)	20,000	0.620921	12,418.42
Add: Initial investment			200,000
Total PV of cash outflows			$243,584.32

Table (9)

 …… (9)

Note:

• For the value of Present value factor refer table 1 in appendix.

c.

To determine

Explain the reason for the difference in the net present values computed.

Explanation of Solution

In this case, the net present value and the present value index under double-declining-balance depreciation are higher because the accelerated depreciation delays the cash payment of taxes.

d.

To determine

Ascertain the payback period and unadjusted rate of return (use average investment), assuming that Company W uses straight-line depreciation.

Explanation of Solution

The annual rate of return method:

The annual rate of return is the amount of income which is earned over the life of the investment. It is used to measure the annual income as a percent of the annual investment of the business, and it is also known as the accounting rate of return.

Payback period:

Payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the proposal of long-term investment (fixed assets) of the business.

Ascertain the payback period under straight line method as follows:

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$200,000}{\$67,500}\\ =2.96\text{ years}\end{array}$

Ascertain the unadjusted rate of return under straight line method as follows:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$37,500(1)}{\left(\frac{\$200,000}{2}\right)}\times 100\\ =37.50\%\end{array}$

e.

To determine

Determine the payback period and unadjusted rate of return (use average investment), assuming that Company W uses double-declining-balance depreciation.

Explanation of Solution

The annual rate of return method:

The annual rate of return is the amount of income which is earned over the life of the investment. It is used to measure the annual income as a percent of the annual investment of the business, and it is also known as the accounting rate of return.

Payback period:

Payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the proposal of long-term investment (fixed assets) of the business.

Ascertain the payback period under double declining method as follows:

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Total Cash flows }}\\ =\frac{\$200,000}{\frac{\left[\begin{array}{l}\$80,000+\$72,000+\$65,500\\ +\$60,000+\$60,000\end{array}\right]}{5}}\\ =2.96\text{ years}\end{array}$

Ascertain the unadjusted rate of return under double declining method as follows:

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\frac{\left[\begin{array}{l}\$0+\$24,000+\$43,500\\ +\$60,000+\$60,000\end{array}\right]}{5}}{\left(\frac{\$150,000}{2}\right)}\times 100\\ =37.50\%\end{array}$

f.

To determine

Explain the reason why there are no differences in the payback periods or unadjusted rates of return computed in Requirements d and e.

Explanation of Solution

Explain the reason why there are no differences in the payback periods or unadjusted rates of return computed in Requirements d and e as follows:

In this case, there are no differences in the payback period or in the unadjusted rates of return under both straight-line and double-declining-balance depreciation methods, because under both methods the overall cash flow and net income remains same.