Question

4.12 A company is considering buying workstation computers to support its engi- neering staff. In today's dollars, it is estimated that the maintenance costs for the computers (paid at the end of each year) will be $20,000, $26,000, $34.000, $38,000, and $42,000 for years one through five, respectively. The general infla- tion rate (F) is estimated to be 10% per year, and the company will receive 16% per year on its invested funds during the inflationary period. The company wants to pay for maintenance expenses in equivalent equal payments (in actual dollars) at the end of each of the five years. Find the amount of the company's annual payment.

Answer 1

As per the question the company is buying workstation computers to support their engineering staff

Company is receiving on investment or Real MARR (i) = 16% = 0.16

Inflation rate (f) = 10% =0.1

Actual MARR(i) = i + f +(i)(f) = 0.16+ 0.1 + (0.16)(0.1) = 0.276 = 27.6%

The below table shows the annual expenses on maintenance and its present worth

Present worth factor (PVF) = (1+i)^-N

Where i=27.6% = 0.276

Years (N)	maintenance cost in $	[email protected]%	PV of Maintenance cost in $
1	20000	0.783699	15673.98
2	26000	0.614184	15968.79
3	34000	0.481336	16365.41
4	38000	0.377222	14334.45
5	42000	0.295629	12416.41
		NPV at 27.6%=	74759.03

The net present value (NPV) of the maintenance cost is =$74759.03

The annual equivalent maintenance expenses (A) =$74759.03(A/P,i,N)

Where i=0.276 and N=5 years

A =$74759.03[{i(1+i)^N}/{(1+i)^N-1}]

A = $74759.03 [{0.276(1+0.276)⁵}/{(1+0.276)⁵-1}]

A = $74759.03 [{0.276(1.276)⁵}/{(1.276)⁵-1}]

A = $74759.03 (0.93360346/2.38262124)

A = $74759.03 (0.39183880) =$29293.4886   or   Approx $29293.49

The annual equivalent maintenance expenses in actual dollar is $29293.49