Chapter 16, Problem 22P

Problem 10-22A Effects of straight-line versus accelerated depreciation on an investment decision

Harper Electronics is considering investing in manufacturing equipment expected to cost $250,000. The equipment has an estimated useful life of four years and a salvage value of $25,000. It is expected to produce incremental cash revenues of $125,000 per year. Harper has an effective income tax rate of 30 percent and a desired rate of return of 10 percent.

Required

Round your financial figures to the nearest dollar and all other figures to two decimal points.

1. a. Determine the net present value and the present value index of the investment, assuming that Harper uses straight-line depreciation for financial and income tax reporting.
2. b. Determine the net present value and the present value index of the investment, assuming that Harper uses double-declining-balance depreciation for financial and income tax reporting.
3. c. Why do the net present values computed in Requirements a and b differ?
4. d. Determine the payback period and unadjusted rate of return (use average investment), assuming that Harper uses straight-line depreciation.
5. e. Determine the payback period and unadjusted rate of return (use average investment), assuming that Harper uses double-declining-balance depreciation. (Note: Use average annual cash flow when computing the payback period and average annual income when determining the unadjusted rate of return.)
6. f. Why are there no differences in the payback periods or unadjusted rates of return computed in Requirements d and e?

To determine

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

Company H 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)	$104,375	3.1698651	$330,855
Add: Present value of Salvage value	25,000	0.6830132	17,075
Less: Initial investment			(250,000)
Net present value			$  97,930

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 notes:

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

Particulars	Year 1	Year 2	Year 3	Year 4
Revenue	125,000	125,000	125,000	125,000
Less: Depreciation (3)	56,250	56,250	56,250	56,250
Income before tax	68,750	68,750	68,750	68,750
Less: Income  tax (2)	20,625	20,625	20,625	20,625
Net Income	48,125	48,125	48,125	48,125
Add: Depreciation	56,250	56,250	56,250	56,250
Cash flow	104,375	104,375	104,375	104,375

Table (2)

(1)

Calculate the amount of income tax expense:

$\begin{array}{c}\text{Income tax expense}=\text{Rate of tax}\times \text{Income before tax}\\ =\frac{30}{100}\times \$68,750\\ =\$20,625\end{array}$

(2)

Ascertain the depreciation expenses under straight line as follows:

$\begin{array}{c}\text{Depreciation expenses}=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$250,000}-\text{\$25,000}}{\text{4 years}}\\ =\$56,250\end{array}$

(3)

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (5)}}\\ =\frac{\text{\$413,308}}{\text{\$315,378}}\\ =1.31\end{array}$

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	$125,000	3.1698651	$396,233
Add: Present value of Salvage value	25,000	0.6830132	17,075
Total PV of cash inflows			$413,308

Table (3)

(4)

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).

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)	$20,625	3.1698651	$65,378
Add: Initial investment			250,000
Total PV of cash outflows			$315,378

Table (4)

(5)

Note:

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

To determine

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

Company H 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)	PV Factor (b)	Present value $\left(\text{a}\times \text{b}\right)$
Present value of net cash inflows:
Year 1	125,000	0.909091	113,636
Year 2	106,250	0.826446	87,810
Year 3	96,875	0.751315	72,784
Year 4	89,375	0.683013	61,044
Salvage value	25,000	0.683013	17,075
Less: Present value of cash outflows			250,000
Net present value			102,349

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
Revenue	125,000	125,000	125,000	125,000
Less: Depreciation (6)	125,000	62,500	31,250	6,250
Income before tax (7)	-	62,500	93,750	118,750
Less: Income  tax	-	18,750	28,125	35,625
Net Income	-	43,750	65,625	83,125
Add: Depreciation	125,000	62,500	31,250	6,250
Cash flow	125,000	106,250	96,875	89,375

Table (6)

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

Year	Depreciation expenses
Year 1	$\begin{array}{l}=\left(\$250,000\times \frac{50}{100}\right)\\ =\$125,000\end{array}$
Year 2	$\begin{array}{l}=\left(\$250,000-\$125,000\right)\times \frac{50}{100}\\ =\$62,500\end{array}$
Year 3	$\begin{array}{l}=\left(\$250,000-\$125,000-\$62,500\right)\times \frac{50}{100}\\ =\$31,250\end{array}$
Year 4	$\begin{array}{l}=\left(\$250,000-\$125,000-\$62,500-\$31,250\right)\times \frac{50}{100}\\ =\$6,250\end{array}$

Table (7)

(6)

Compute the depreciation rate applied each year:

Useful life = 4 years

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

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	$\begin{array}{l}=\left(\$62,500\times \frac{30}{100}\right)\\ =\$18,750\end{array}$
Year 3	$\begin{array}{l}=\left(\$93,750\times \frac{30}{100}\right)\\ =\$28,125\end{array}$
Year 4	$\begin{array}{l}=\left(\$62,500\times \frac{30}{100}\right)\\ =\$35,625\end{array}$

Table (8)

(7)

Ascertain the present value index of the investment as follows:

$\begin{array}{c}\text{Present value index}=\frac{\text{Present value of cash inflows (4)}}{\text{Present value of cash outflows (8)}}\\ =\frac{\text{\$413,308}}{\text{\$310,959}}\\ =1.33\end{array}$

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	0.9090911	$0
Year 2 income tax payment (7)	18,750	0.8264462	15,496
Year 3 income tax payment (7)	28,125	0.7513153	21,131
Year 4 income tax payment (7)	35,625	0.6830134	24,332
Add: Initial investment			250,000
Total PV of cash outflows			$310,959

Table (9)

(8)

Note:

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

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.

To determine

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

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Cash flows per year (1)}}\\ =\frac{\$250,000}{\$104,375}\\ =2.40\text{ years}\end{array}$

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

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\$48,125(1)}{\left(\frac{\$250,000}{2}\right)}\times 100\\ =38.50\%\end{array}$

To determine

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

$\begin{array}{c}\text{Payback period}=\frac{\text{Cost of investment}}{\text{Total Cash flows }}\\ =\frac{\$250,000}{\frac{\left[\begin{array}{l}\$125,000+\$106,250\\ +\$96,875+\$89,375\end{array}\right]}{4}}\\ =2.40\text{ years}\end{array}$

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

$\begin{array}{c}\text{Unadjusted rate of return = }\frac{\text{Average increase in net income}}{\left(\frac{\text{Net cost of original investment}}{2}\right)}\\ =\frac{\frac{\left[\begin{array}{l}\$0+\$43,750+\\ \$65,625+83,125\end{array}\right]}{4}}{\left(\frac{\$250,000}{2}\right)}\times 100\\ =38.50\%\end{array}$

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.