Question

You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 100 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. Ignore the half-year rule for accounting for depreciation.   

(ii) Profitability Index (PI)                                                                                  (1 mark)

(iii) Payback period (in years)                                                                            (1 mark)

(iv) Discounted payback period (in years)                                                          (1 mark)

(v) Internal Rate of Return (IRR in %)                                                              (1 mark)

(vi) Average Accounting Return (AAR in %)                                                  

      Hint: Net Income = {[(Price – variable cost)*Quantity Sold] – Fixed Costs – Depreciation} * (1 – Tax rate)

Answer 1

Net income :-

Depreciation = Cost of the machine / life of machine in years = $ 680,000 / 4 = $ 170,000 per year

Particulars	Year 1	year2	year 3	Year4
Price per unit	19,000	19,000	19,000	19,000
Variable cost per unit	14,000	14,000	14,000	14,000
Contribution	5,000	5,000	5,000	5,000
Quantity sold	100 units	100 units	100 units	100 units
Contribution margin	500000	500000	500000	500000
Less- Fixed cost	150000	150000	150000	150000
less-Depreciation	170000	170000	170000	170000
EBT	180000	180000	180000	180000
Less-Tax@35%	63000	63000	63000	63000
Net Income	117000	117000	117000	117000
Add-Depreciation	170000	170000	170000	170000
Operating cash flows	287000	287000	287000	287000

ii) Profitability index :-

Present value of cash inflows :-

Year	Cash inflows	PVF@15%	PV of CF
1	287000	0.869565	249565.217
2	287000	0.756144	217013.233
3	287000	0.657516	188707.159
4	287000	0.571753	164093.181
PV of Cash inflows	819378.790

PI = Present value of cash inflows / initial investment = $ 819,378.79 / 680,000 = 1.20497

iii) Calculation of the Payback period :-

Year	Cash inflows	Cumulative CF
0	-680,000	-680,000
1	287000	-393,000
2(x)	287000	-106,000(y)
3	287000(z)	181,000
4	287000	468,000

Payback period = X + Y/Z

· In this calculation:                                            

· X = is the last time period where the cumulative cash flow (CCF) was negative

· Y = is the absolute value of the CCF at the end of that period X

· Z = is the value of the CF in the next period after X

Payback period = 2 years + 106,000 / 287,000 = 2 + 0.369 = 2.369 years

iv) Discounted payback period :-

Year	Cash inflows	PVF@15%	DCF	Cumulative DCF
0	-680,000	1.00	-680,000	-680,000
1	287000	0.8695652	249565.217	-430434.783
2	287000	0.7561437	217013.233	-213421.550
3(X)	287000	0.6575162	188707.159	-24714.391(y)
4	287000	0.5717532	164093.181(Z)	139378.790

Discounted payback period = X + Y /Z

· In this calculation:                                            

· X = is the last time period where the cumulative discounted cash flow (CCF) was negative

· Y = is the absolute value of the CCF at the end of that period X

· Z = is the value of the DCF in the next period after X

Discounted payback period = 3 years + 24,714.391 / 164,093.181 = 3 + 0.15061 = 3.15061 years

V) Calculation of the IRR :-

Vi)Average Accouting Return :-

Accounting return =Average Net income / Average investment

Average Income = $ 117000 +117000 +117000 +117000 / 4 = 117,000

Accounting return = $ 117,000 / 680,000 = 17.206%