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.

Answer 1

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.