1. Faced with the task of making optimal investment decisions, given the following investment information, compute the Accounting Rate of Return. Depreciation is straight line.

* Cost of installations: 2,850,000
* Expected project life span: 5years
* Annual cash inflow: N300,000, N500,000, N750,000, N780,000, N570,000.
* Salvage value: N500,000
* Tax : 25%
* Discount rate : 16%

2. If you had used profitability index to appraise the above project, would your previous decision have changed?

Note: You have yourself a better job if you answer right. It's on first correct answers first serve basis.
Show all workings.
Submission expires 21st March at exactly 12 noon.
Good-luck.

saintruky:
1. Faced with the task of making optimal investment decisions, given the following investment information, compute the Accounting Rate of Return. Depreciation is straight line.

* Cost of installations: 2,850,000
* Expected project life span: 5years
* Annual cash inflow: N300,000, N500,000, N750,000, N780,000, N570,000.
* Salvage value: N500,000
* Tax : 25%
* Discount rate : 16%

2. If you had used profitability index to appraise the above project, would your previous decision have changed?

Note: You have yourself a better job if you answer right. It's on first correct answers first serve basis.
Show all workings.
Submission expires 21st March at exactly 12 noon.
Good-luck.

cost=2850000 less 16‰ disc rate =2,394,000.
depreciation = 2,394,000-500,000/5=378,800

year 1, cash flow 300,000- depr 378,800= loss bf tax (78,800).
year 2, cashflow 500,000- depr 378,800= inc bf tax 121,200 less loss b/f (78,800)= 42,400 less tax@25% =31,800
year 3, cash flow 750,000- depr 378,800 = inc bf tax 371200 less tax@25%= 278,400
year 4, cashflow 780,000- depr 378,800= inc bf tax 401,200 less tax@25% = 300,900
year 5, cashflow 570,000- depr 378,800= inc bf tax 191,200 less tax@25%= 143,400


av profit ={78,800)+31,800+278,400+300,900+143,400= 675,700/5= 135,140

av investment= 2,394,000+500,000/2= 1.447,000

av profit/av investment = 135,140/1447000= 9.3%

an investment that generates 9.3% income yearly .

therefore, my decision would have been negative because the project incures a loss in its first year before having a steady rise of profit for the next 3 years then a decline in profit in the 5th year


2. profitability index less than 1 ..workings coming up later

1) Using d method that involves depreciation

Accounting rate of return (ARR)= average annual profit/initial investment

Depreciation =initial value-salvage value/lifespan of asset

=2850000-500000/5 = #470000

ARR calculation

Average annual profit = profit - depreciation

300000 + 500000 + 750000 + 780000 + 570000 - 470000
= #2430000

ARR = 2430000/2850000 = 85%

(2) Using profitability index (PI) to appraise the project

PI = 1 + NPV/initial investment
NPV-net present value

NPV= - 2850000+162162.16+146198.83+118483.41+66609.74+26303.65 = -2330242.21
The profitability index will be less dan one(1) because d NPV value is negative,this makes this project not to be profitable.
The first method show d profitability of d investment but this profitability index method hv shown dat d project is not profitable hence it should nt be implemented.

1. There are many different definitions for average
accounting return. The most commonly used one is the
average net income to average investment.

Since OP didn't specify the definition he wants, I'm using;
AAR = Average net income/Average Investment

Annual depreciation= cost of installation - salvage value
(2850000-500000)÷5yrs
=N470000/yr

Figures in the table below are '000s;
Year. 1 2 3 4 5 5(salvage)
Cash.
inflow 300 500 750 780 570 500
Dep. 470 470 470 470 470 -
EBIT. (170) 30. 280 310 100 500
Tax
(25%) nil. 7.5 70 77.5 25 125
Net
income (170) 22.5 210 232.5 75 375 = 745

Total income = N745000

Where EBIT = earnings before interest and tax

Average net income = N745000 ÷ 5
= N149000

Estimate average book value (i.e. for straight-line
depreciation, average book value is [historical value –
salvage value]/2)

= (2850000-500000)÷2
= N1175000

ARR = (149000 ÷ 1175000) x 100%
=12.68%

Decision rule: reject the project because its AAR of 12.68% is less than 16%.

2. Profitability index =
Present value future of cash flows ÷ initial investment

Year Cashflow(N) DCF @ 16% PV
1. 300000 0.862 258600
2. 500000 0.743 371500
3. 750000 0.641 480750
4. 780000 0.552 430560
5. 570000 0.476 271320
5. 500000 0.476 238000
Pv of future cash flow. 2050730

PI = 2050730 ÷ 2850000
PI = 0.72

Since PI is less than 1, based on this, the project is still to be rejected.
My decision remains for the project to be rejected because a PI less than 1 would also have a negative net present value of cash flows.