A company is considering an investment proposal to install new milling controls
ID: 2812676 • Letter: A
Question
A company is considering an investment proposal to install new milling controls at a cost of GHC 50,000. The facility has a life expectancy of 5 years and no salvage value. The tax rate is 35% . assume the firm uses straight line depreciation and the same is allowed for tax purposes. The estimated cash flows before depreciation and tax( CFBT) from the investment proposal are as follows:
Year
CFBT
1
GHC 10000
2
10692
3
12769
4
13462
5
20385
Compute the following:
Pay back period
Average rate of return
Internal rate of return
Net present value at 10% discount rate
Profitability index at 10% discount rate.
Year
CFBT
1
GHC 10000
2
10692
3
12769
4
13462
5
20385
Explanation / Answer
Computation of annual net cash flow:
Year
1
2
3
4
5
CFBTD
GHC 10,000
GHC 10,692
GHC 12,769
GHC 13,462
GHC 20,385
Less: Depreciation
10,000
10,000
10,000
10,000
10,000
CFBT
-
692.00
2,769.00
3,462.00
10,385.00
Less: Tax @ 35 %
-
242.20
969.15
1,211.70
3,634.75
Cash flow after tax
-
449.80
1,799.85
2,250.30
6,750.25
Add: Depreciation
10,000.00
10,000.00
10,000.00
10,000.00
10,000.00
Net cash flow
10,000.00
10,449.80
11,799.85
12,250.30
16,750.25
Computation of payback period:
Year
Cash Flow
‘Cum Cash Flow
0
GHC (50,000.00)
$ (50,000.00)
1
10,000.00
$ (40,000.00)
2
10,449.80
$ (29,550.20)
3
11,799.85
$ (17,750.35)
4
12,250.30
$ (5,500.05)
5
16,750.25
$ 11,250.20
Payback Period = A +B/C
Where,
A = Last period with a negative cumulative cash flow = 4
B = Absolute value of cumulative cash flow at the end of the period A = GHC 5,500.05
C = Total cash flow during the period after A = GHC 16,750.25
Payback Period = 4 +GHC (5,500.05) /GHC 35,000
= 4 + GHC 5,500.05 /GHC 30,000
= 4 + 0.328356293 = 4.328356293 or 4.33 years
Payback Period is 4.33 years.
Computation of average rate of return:
Average rate of return = Average annual return/Investment
= [(GHC 10,000 + 10,449.80 + 11,799.85 + 12,250.30 + 16,750.25)/2]/GHC 50,000
= (GHC 61,250.20/5)/ GHC 50,000
=GHC 12,250.04/ GHC 50,000 = 0.245001 or 24.50 %.
Average rate of return is 24.50 %
Computation of internal rate of return:
Year
Cash Flow
0
GHC (50,000.00)
1
10,000.00
2
10,449.80
3
11,799.85
4
12,250.30
5
16,750.25
IRR
6.58%
Excel formula for IRR is “=IRR(cell_: cell_)”
Internal rate of return is 6.58 %
Computation of Net present value @ 10 %:
Year
Cash Flow (C)
PV Factor Calculation
PV Factor @ 10 % (F)
PV (=F x C)
0
GHC (50,000.00)
1/(1+ 10%)^0
1
GHC (50,000.00)
1
10,000.00
1/(1+ 10%)^1
0.909090909
9,090.91
2
10,449.80
1/(1+ 10%)^2
0.826446281
8,636.20
3
11,799.85
1/(1+ 10%)^3
0.751314801
8,865.40
4
12,250.30
1/(1+ 10%)^4
0.683013455
8,367.12
5
16,750.25
1/(1+ 10%)^5
0.620921323
10,400.59
NPV
GHC (4,639.78)
Net present value of investment at 10 % discount rate is GHC (4,639.78).
Computation of Profitability index:
Profitability index = Initial investment + NPV/ Initial Investment
= GHC 50,000 + GHC (4,639.78)/ GHC 50,000
= GHC 45,360.22/ GHC 50,000 = 0.90720433 or 0.91
Profitability index at 10 % discount rate is 0.91.
Year
1
2
3
4
5
CFBTD
GHC 10,000
GHC 10,692
GHC 12,769
GHC 13,462
GHC 20,385
Less: Depreciation
10,000
10,000
10,000
10,000
10,000
CFBT
-
692.00
2,769.00
3,462.00
10,385.00
Less: Tax @ 35 %
-
242.20
969.15
1,211.70
3,634.75
Cash flow after tax
-
449.80
1,799.85
2,250.30
6,750.25
Add: Depreciation
10,000.00
10,000.00
10,000.00
10,000.00
10,000.00
Net cash flow
10,000.00
10,449.80
11,799.85
12,250.30
16,750.25
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