Question

Matt is investigating the possibility of installing a new client management system for his business. The cost of purchasing the system would be S300,000. After one year, staff would have to undergo training costing the company an additional S100,000 At the end of 5 years, system upgrades costing the company an additional $200,000 would be incurred. The estimated cost savings of the company during each of the first 5 years after the system is installed is $100,000. The estimated cost savings in years six through ten is $50,000. After ten years, the new system is not estimated to provide any additional value. Assume that the company's required rate of return on the new system is 5% per year 1. Calculate the present value of the total cost of the new system. (20 pts) 2. Calculate the present value of the total cost savings of the new system. (20 pts) 3. Should the company invest in the new system? Justify your answer. (20 pts)

Answer 1

1. P. V. Of total cost of new machine = Initial cost + Year 1 end additional cost * (1/(1+rate)^n) + Year 5 end additional cost * (1/(1+rate)^n)

P. V. Of total cost of new machine = $3,00,000 + $1,00,000 * (1/(1+0.05)^1) + $2,00,000 * (1/(1+0.05)^5)

P. V. Of total cost of new machine = $3,00,000 + ($1,00,000 * 0.9524) + ( $2,00,000 * 0.7835)

P. V. Of total cost of new machine = $3,00,000 + $95,240 + $1,56,700 = $5,51,940

2. P. V. Of total savings = Annual saving from 1 - 5 years * ((1 - (1/(1+rate)^5)) / 0.05) + Annual savings from 5 - 10 years * ((1 - (1/(1+rate)^n)) / 0.05) - ((1 - (1/(1+rate)^n)) / 0.05)

P. V. Of total savings = $1,00,000 * ((1 - (1/(1+0.05)^5)) / 0.05) + $50,000 * ((1 - (1/1+0.05)^10)) / 0.05) - ((1 - (1/(1+0.05)^5)) / 0.05)

P. V. Of total savings = ( $1,00,000 * 4.3295) + ($50,000 * (7.7217 - 4.3295)) = $4,32,950 + $169,610 = $6,02,560

3. Decision : Company should invest in this new machine as it is having higher savings than its cost.

Net benefit = $6,02,560 - $5,51,940 = $50,620

4. Net benefit is nothing but an NPV $50,620.

5. If company sells it's new machine after 6 year end $1,25,000

P. V. Of savings for 6 years = P. V. Of savings for 5 years + P. V. Of savings for next 1 year + P. V. Of sales value

P. V. Of saving for 6 years = $4,32,950 + ($50,000 + $1,25,000) * (1/(1+0.05)^6) = $4,32,950 + ($1,75,000 * 0.7462)

P. V. Of savings for 6 years = $4,32,950 + $1,30,585 = $5,63,535

P. V. Of total cost (as per 1) = $5,51,950

As saving is still higher in this case than it's cost. Hence they can do this.