Question

Two alternatives to investing in an e-commerce business with a five-year horizon are being considered. The first alternative (A) has an initial investment cost of 21,000 Euros and it is estimated that an additional investment cost of 10,000 Euros will be required in the third year (due to the necessary adjustment of the content in the online material). Benefits of around 12,000 Euros per year are expected and the entire investment will have a final value estimated at 15,000 Euros at the end of 5 years. The second alternative (B) includes respectively an initial investment of 25,000 Euros and an additional investment of 20,000 Euros at the end of the third year. The annual benefits are now expected to rise to 15,000 Euros while this investment will have estimated final value 20,000 Euros. For a minimum acceptable rate of return (MARR - ie opportunity cost) equal to 10%, answer the following questions: (a) Which alternative is the most advantageous? Use a cost-benefit ratio first (consider whichever definition you prefer) and confirm your decision with an internal degree of efficiency (if you want to make sure of the prevailing solution, you can use it quickly and at present value). (b) What is your decision, if there is also a 30% tax while there is an annual linear depreciation for the 5 years in which only the initial investment amount and the estimated final value should be calculated? Work now at present value.

Answer 1

Solution:

Showing cost benefit ratio

Discounting Rate=10%(i.e opportunity cost)

1.When there is no tax

Alternative (A)

a)Total cost

Initial Cost=21,000 Euros

Present value of additional investment=10,000 Euros*Present value factor @10 for 3rd year

=10,000Euros*0.751

=7510 Euros

Total cost=21,000 Euros+7510 Euros

=28,510 Euros

b)Total Benefits

Present value of Operating benefit=12,000 Euros*Present value of Annuity factor@10% for 5 years

=12,000 Euros*3.791

=45,492 Euros

Present value of Final value of investment= 15,000 Euros*Present value factor @10% for 5th year

=15,000 Euros*0.621

=9,315 Euros

Total benefit=45,492 Euros+9,315 Euros

=54,807 Euros

Benefit cost ratio=Benefit/cost

=54,807 Euros/28,510 Euros

=1.922

Alternative (B)

a)Total Cost

Initial Investment=25,000 Euros

Present value of additional investment=20,000 Euros*0.751

=15,020 Euros

Total Cost=25,000 Euros+15,020 Euros

=40,020 Euros

b)Total Benefit

Present value of operating benefit=15,000 Euros*3.791

=56,865 Euros

Present value of Final value of investment=20,000 Euros*0.621

=12,420Euros

Total Benefit=56,865 Euros+12,420Euros

=69,285 Euros

Benefit -Cost ratio=69,285 Euros/40,020 Euros

=1.731

On the basis of benefit-cost ratio,alternative (A) is more advantageous as it has higher benefit cost ratio of 1.922.

2.When there is tax of 30%

Annual Depreciation=(Initial Investment-Estimated final value)/Life

Alternative (A)

Annual depreciation=(21,000-15,000)/5

=1200 Euros

a)Total cost will be same as of in case 1 above,since tax benefit is not available in respect of additional investment.Therefore total cost is 28,510 Euros

b)Total Benefit

After tax annual operating benefit=[(Annual operating benefit-Depreciation)(1-tax rate)]+Depreciation

=[(12,000 Euros-1200 Euros)(1-0.30)]+1200 Euros

=8,760 Euros

Present value of After tax annual operating benefit=8,760 Euros*3.791

=33209.16 Euros

There will be no tax no final value of investment as the book value is equal to estimated final value.

Thus,Present value of Final value of investment=15,000 Euros*0.621

=9315 Euros

Total Benefit=33209.16 Euros+9315 Euros

=42,524.16 Euros

c)Benefit-Cost Ratio=42,524.16 Euros/28,510 Euros

=1.492

Alternative (B)

a)Total cost

Total cost will be same as of in case 1 above,since tax benefit is not available in respect of additional investment.Therefore total cost is 40,020 Euros

b)Total Benefit

Annual Depreciation=(25,000- 20,000)/5

=1000 Euros

After Tax annual operating benefit=[(15,000-1000)(1-0.30)]+1000

=10,800 Euros

Present value After Tax annual operating benefit=10,800 Euros*3.791

=40,942.80 Euros

There will be no tax no final value of investment as the book value is equal to estimated final value.

Thus,Present value of Final value of investment is

=20,000 Euros*0.621

=12,420 Euros

Total benefit=12,420 Euros+40,942.80 Euros

=53,362.80 Euros

c)Benefit-Cost ratio=53,362.80 Euros/40,020 Euros

=1.33

Even when threre is tax,Alternative (A) is more advantageous as it has higher benefit cost ratio of 1.492