Chapter 16, Problem 22P

a.

To determine

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

Company C 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)	$83,500	3.1698651	$264,683
Add: Present value of Salvage value	20,000	0.6830132	13,660
Less: Initial investment			(200,000)
Net present value			$  78,343

Table (1)

Note:

• • The Present value of an ordinary annuity of $1 for 4 years at 10% is 3.169865 (refer table 2 in appendix).
• • The present value of $1 for 4th year at 10% is 0. 0.683013 (refer table 1 in appendix).

Working note (1):

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

Particulars	Year 1	Year 2	Year 3	Year 4
Revenue	100,000	100,000	100,000	100,000
Less: Depreciation (3)	45,000	45,000	45,000	45,000
Income before tax	55,000	55,000	55,000	55,000
Less: Income  tax (2)	16,500	16,500	16,500	16,500
Net Income	38,500	38,500	38,500	38,500
Add: Depreciation	45,000	45,000	45,000	45,000
Cash flow	83,500	83,500	83,500	83,500

Table (2)

Working note (2):

Calculate the amount of income tax expense:

$\begin{array}{c}\text{Income tax expense}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{30}{100}\times \$55,000\\ =\$16,500\end{array}$

Working note (3):

Ascertain the depreciation expenses under straight line as follows:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$200,000}-\text{\$20,000}}{\text{4 years}}\\ =\$45,000\end{array}$

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (5)}}\\ =\frac{\text{\$330,647}}{\text{\$252,303}}\\ =1.31\end{array}$

Working note (4):

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	$100,000	3.1698651	$316,987
Add: Present value of Salvage value	20,000	0.6830132	13,660
Total PV of cash inflows			$330,647

Table (3)

Note:

• • The Present value of an ordinary annuity of $1 for 4 years at 10% is 3.169865 (refer table 2 in appendix).
• • The present value of $1 for 4th year at 10% is 0. 0.683013 (refer table 1 in appendix).

Working note (5):

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 (4)	$16,500	3.1698651	$52,303
Add: Initial investment			250,000
Total PV of cash outflows			$252,303

Table (4)

Note:

• • The Present value of an ordinary annuity of $1 for 4 years at 10% is 3.169865 (refer table 2 in appendix).

b.

To determine

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

Company C 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	100,000	0.909091	90,909
Year 2	85,000	0.826446	70,248
Year 3	77,500	0.751315	58,227
Year 4	71,500	0.683013	48,835
Salvage value	20,000	0.683013	13,660
Less: Present value of cash outflows			200,000
Net present value			81,879

Table (5)

Note:

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

Working note (6):

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

Particulars	Year 1	Year 2	Year 3	Year 4
Revenue	100,000	100,000	100,000	100,000
Less: Depreciation (7)	100,000	50,000	25,000	5,000
Income before tax	-	50,000	75,000	95,000
Less: Income  tax (8)	-	15,000	22,500	28,500
Net Income	-	35,000	52,500	66,500
Add: Depreciation	100,000	50,000	25,000	5,000
Cash flow	100,000	106,250	77,500	71,500

Table (6)

Working note (7):

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

Year	Depreciation expenses
Year 1	$\begin{array}{l}=\left(\$200,000\times \frac{50}{100}\right)\\ =\$100,000\end{array}$
Year 2	$\begin{array}{l}=\left(\$200,000-\$100,000\right)\times \frac{50}{100}\\ =\$50,000\end{array}$
Year 3	$\begin{array}{l}=\left(\$200,000-\$100,000-\$50,000\right)\times \frac{50}{100}\\ =\$25,000\end{array}$
Year 4	$\begin{array}{l}=\left[\begin{array}{l}\left(\$200,000-\$100,000-\$50,000-\$25,000\right)\\ -\$20,000\end{array}\right]\\ =\$5,000\end{array}$

Table (7)

Note: Compute the depreciation rate applied each year:

Useful life = 4 years

$\begin{array}{c}\text{Depreciation rate}=\frac{\text{100\%}}{\text{4 Years}}\times 2\\ =50\%\end{array}$

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

Working note (8):

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

Year	Income tax expenses
Year 2	$\begin{array}{l}=\left(\$50,000\times \frac{30}{100}\right)\\ =\$15,000\end{array}$
Year 3	$\begin{array}{l}=\left(\$75,000\times \frac{30}{100}\right)\\ =\$22,500\end{array}$
Year 4	$\begin{array}{l}=\left(\$95,000\times \frac{30}{100}\right)\\ =\$28,500\end{array}$

Table (8)

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (9)}}\\ =\frac{\text{\$330,647}}{\text{\$248,768}}\\ =1.33\end{array}$

Working note (9):

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	0.9090911	$0
Year 2 income tax payment (8)	15,000	0.8264462	12,397
Year 3 income tax payment (8)	22,500	0.7513153	16,905
Year 4 income tax payment (8)	28,500	0.6830134	19,466
Add: Initial investment			200,000
Total PV of cash outflows			$248,768

Table (9)

Note:

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

c.

To determine

State the reason for the difference in the computed net present values under straight line and double declining method.

Explanation of Solution

In this case, the present value index and the net present value 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 C 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:

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$200,000}{\$83,500}\\ =2.40\text{ years}\end{array}$

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

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\text{Average cost of investment}}\\ =\frac{\$38,500}{\$90,000(9)}\times 100\\ =38.50\%\end{array}$

Working note (9):

Calculate the average cost of investment.

$\begin{array}{c}\text{Average cost of investment}=\left(\frac{\text{Net cost of original investment}}{2}\right)\\ =\frac{\$180,000}{2}\\ =\$90,000\end{array}$

e.

To determine

Determine the payback period and unadjusted rate of return (use average investment), assuming that Company C 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:

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Total Cash flows }}\\ =\frac{\$200,000}{\$88,500(10)}\\ =2.26\text{ years}\end{array}$

Working note (10):

Calculate the average cash inflows.

$\begin{array}{c}\text{Average cash inflows = }\frac{\text{Annual cash inflows}}{\text{Number of years}}\\ =\frac{\$100,000+\$85,000+\$77,500+\$91,500}{4}\\ =\$88,500\end{array}$

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

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\text{Average cost of investment}}\\ =\frac{\$38,500(11)}{\$100,000(12)}\times 100\\ =38.50\%\end{array}$

Working note (11):

Calculate the average annual income.

$\begin{array}{c}\text{Average annual income = }\frac{\text{Annual income}}{\text{Number of years}}\\ =\frac{\$0+\$35,000+\$52,500+\$66,500}{4}\\ =\$38,500\end{array}$

Working note (12):

Calculate the average cost of investment.

$\begin{array}{c}\text{Average cost of investment}=\left(\frac{\text{Net cost of original investment}}{2}\right)\\ =\frac{\$200,000}{2}\\ =\$100,000\end{array}$

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

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.