Survey Of Accounting
Survey Of Accounting
4th Edition
ISBN: 9780077862374
Author: Edmonds, Thomas P.
Publisher: Mcgraw-hill Education,
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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.

a.

Expert Solution
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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:

ParticularsAmount ($) (a)PV Factor (b)Present value (a×b)
Present value of net cash inflows (1)$83,5003.1698651$264,683
Add: Present value of Salvage value20,0000.6830132 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:

ParticularsYear 1Year 2Year 3Year 4
Revenue100,000100,000100,000100,000
Less: Depreciation (3)45,00045,00045,00045,000
Income before tax55,00055,00055,00055,000
Less: Income  tax (2)16,50016,50016,50016,500
Net Income38,50038,50038,50038,500
Add: Depreciation 45,00045,00045,00045,000
Cash flow83,50083,50083,50083,500

Table (2)

Working note (2):

Calculate the amount of income tax expense:

Income tax expense=Rate of tax×Income before tax=30100×$55,000=$16,500

Working note (3):

Ascertain the depreciation expenses under straight line as follows:

Depreciation expenses=Acquisition cost – Salvage valueUseful life =$200,000$20,0004 years=$45,000

Ascertain the present value index of the investment as follows:

Present value index=Present value of cash inflows (4)Present value of cash outflows (5)=$330,647$252,303=1.31

Working note (4):

Calculate the present value of cash inflows:

ParticularsAmount ($) (a)PV Factor (b)Present value (a×b)
Present value of cash inflows$100,0003.1698651$316,987
Add: Present value of Salvage value20,000 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:

ParticularsAmount ($) (a)PV Factor (b)Present value (a×b)
Present value of tax payments (4)$16,5003.1698651$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.

b.

Expert Solution
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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 (a×b)
Present value of net cash inflows:   
      Year 1100,0000.90909190,909
      Year 285,0000.82644670,248
      Year 377,5000.75131558,227
      Year 471,5000.68301348,835
Salvage value20,0000.68301313,660
Less: Present value of cash outflows200,000
Net present value81,879

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:

ParticularsYear 1Year 2Year 3Year 4
Revenue100,000100,000100,000100,000
Less: Depreciation (7)100,00050,00025,0005,000
Income before tax -50,00075,00095,000
Less: Income  tax (8)-15,00022,50028,500
Net Income-35,00052,50066,500
Add: Depreciation 100,00050,00025,0005,000
Cash flow100,000106,25077,50071,500

Table (6)

Working note (7):

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

YearDepreciation expenses
Year 1=($200,000×50100)=$100,000
Year 2=($200,000$100,000)×50100=$50,000
Year 3=($200,000$100,000$50,000)×50100=$25,000
Year 4=[($200,000$100,000$50,000$25,000)$20,000]=$5,000

Table (7)

Note: Compute the depreciation rate applied each year:

Useful life = 4 years

Depreciation rate=100%4 Years×2=50%

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:

YearIncome tax expenses
Year 2=($50,000×30100)=$15,000
Year 3=($75,000×30100)=$22,500
Year 4=($95,000×30100)=$28,500

Table (8)

Ascertain the present value index of the investment as follows:

Present value index=Present value of cash inflows (4)Present value of cash outflows (9)=$330,647$248,768=1.33

Working note (9):

Calculate the present value of cash outflows:

ParticularsAmount ($) (a)PV Factor (b)Present value (a×b)
Year 1 income tax payment00.9090911$0  
Year 2 income tax payment (8)15,0000.826446212,397
Year 3 income tax payment (8)22,5000.751315316,905
Year 4 income tax payment (8)28,5000.683013419,466
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.

c.

Expert Solution
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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.

d.

Expert Solution
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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:

Payback period=Cost of investmentCash flows per year (1)=$200,000$83,500=2.40 years

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

Unadjusted rate of return = Average increase in net incomeAverage cost of investment=$38,500$90,000(9)×100=38.50%

Working note (9):

Calculate the average cost of investment.

Average cost of investment=(Net cost of original investment2)=$180,0002=$90,000

e.

To determine

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

e.

Expert Solution
Check Mark

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:

Payback period=Cost of investmentTotal Cash flows =$200,000$88,500(10)=2.26 years

Working note (10):

Calculate the average cash inflows.

Average cash inflows = Annual cash inflowsNumber of years=$100,000+$85,000+$77,500+$91,5004=$88,500

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

Unadjusted rate of return = Average increase in net incomeAverage cost of investment=$38,500(11)$100,000(12)×100=38.50%

Working note (11):

Calculate the average annual income.

Average annual income = Annual incomeNumber of years=$0+$35,000+$52,500+$66,5004=$38,500

Working note (12):

Calculate the average cost of investment.

Average cost of investment=(Net cost of original investment2)=$200,0002=$100,000

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.

f.

Expert Solution
Check Mark

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.

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