Question

1) Cooper and Morton​, LLP, a law​ firm, is considering the replacement of its old accounting system with new software that should save $19,000 per year in net cash operating costs. The old system has zero disposal​ value, but it could be used for the next 12 years. The estimated useful life of the new software is 12 years with zero salvage​ value, and it will cost $190,000. The required rate of return is 14​%.

Requirements:

1.	What is the payback​ period?
2.	Compute the NPV.
3.	Management is unsure about the useful life. What would be the NPV if the useful life were
	(a) 5 years instead of 12 or​ (b) 20 years instead of 12​?
4.	Suppose the life will be 12 years, but the savings will be $15,000 per year instead of $19,000. What would be the​ NPV?
5.	Suppose the annual savings will be $16,000 for 8 years. What would be the​ NPV?

Answer 1

Part 1

Payback period = initial investment / annual cash savings = 190000/19000 = 10 years

Part 2

NPV = present value of cash inflows – present value of cash outflows = ((19000/(1.14^1))+ (19000/(1.14^2))+ (19000/(1.14^3))+ (19000/(1.14^4))+ (19000/(1.14^5))+ (19000/(1.14^6))+ (19000/(1.14^7))+ (19000/(1.14^8))+ (19000/(1.14^9))+ (19000/(1.14^10))+ (19000/(1.14^11))+ (19000/(1.14^12)))-190000 = -$82454.45

Part 3

In case of 5 years

NPV = (19000/(1.14^2))+ (19000/(1.14^3))+ (19000/(1.14^4))+ (19000/(1.14^5)))-190000 = -141438.13

In case of 20 years

NPV =((19000/(1.14^1))+ (19000/(1.14^2))+ (19000/(1.14^3))+ (19000/(1.14^4))+ (19000/(1.14^5))+ (19000/(1.14^6))+ (19000/(1.14^7))+ (19000/(1.14^8))+ (19000/(1.14^9))+ (19000/(1.14^10))+ (19000/(1.14^11))+ (19000/(1.14^12))+((19000/(1.14^13))+ (19000/(1.14^14))+ (19000/(1.14^15))+ (19000/(1.14^16))+ (19000/(1.14^17))+ (19000/(1.14^18))+ (19000/(1.14^19))+ (19000/(1.14^20)))-190000 = -64160.52

Part 4

NPV = present value of cash inflows – present value of cash outflows = ((15000/(1.14^1))+ (15000/(1.14^2))+ (15000/(1.14^3))+ (15000/(1.14^4))+ (15000/(1.14^5))+ (15000/(1.14^6))+ (15000/(1.14^7))+ (15000/(1.14^8))+ (15000/(1.14^9))+ (15000/(1.14^10))+ (15000/(1.14^11))+ (15000/(1.14^12)))-190000 = -$105095.62

Part 5

NPV = present value of cash inflows – present value of cash outflows = ((16000/(1.14^1))+ (16000/(1.14^2))+ (16000/(1.14^3))+ (16000/(1.14^4))+ (16000/(1.14^5))+ (16000/(1.14^6))+ (16000/(1.14^7))+ (16000/(1.14^8)))-190000 = -$115778.18