Question

In: Economics

A used old model testing machine was donated to a University by a company one year...

A used old model testing machine was donated to a University by a company one year ago. It is expected that this machine will continue to serve its function for ten more years provided that a maintenance agreement is signed with another firm requiring 10 yearly payments of $9,000 each, with the first payment made now.

A new model can be leased for ten years.

The terms of lease include maintenance. For leasing the new model, a payment of $35,000 is due now and $40,000 will be due in 3 years.

Should the old model machine be replaced now, at MARR = 10%?

(i) Use present worth (PW) method.

(ii) Use incremental PW method.

(b) Use incremental IRR method.

Expert Solution

(i) In this part we will calculate the present value of cost in both the cases

The case, where present value of cost is less will be chosen.

Present value of a payment = Cash flow/(1+r)ⁿ

where r is MARR and n is period of cash flow

Present value of a stream of cash flows is sum of present values of all the payments

Present value of cost = C₀ + C₁/(1+r)¹ + C₂/(1+r)² + ..................... + C_n/(1+r)ⁿ

where C_n is cost in year n and r is MARR

For old testing machine

Initial payment is due now and there are total 10 payments

Therefore, first payment is now and next payment is beginning of next year and last payment will be in beginning of 10 years

Present value of cost in first case = 9000 + 9000/(1+0.1)¹ + 9000/(1+0.1)² + ............................ + 9000/(1+0.1)⁹

Payments are made in beginning of year, therefore we are considering last payment in end of year 9

Solving this we get, Present value of cost = $60,831.21

For new lease model

In second case, first payment of $35,000 is due now and another payment of $40,000 is due in 3 years

Present value of cost is the sum of present value of these two payments

Present value = 35000 + 40000/(1+0.1)³ = $65,052.6

So the present value of cost of new lease model is more than the present value of old testing machine, therefore, we should not replace the old machine.

(ii) In incremental present worth method, we subtract the cash flow in one scenario from another and then find the present value using the same MARR and decide which one to choose

So we are subtracting cost of old machine from the new lease model

Current due payment = 35000 - 9000 = 26000

Payment due in year 1, 2, 4, 5, 6, 7, 8, 9 = 0-9000 = -9000

Payment due in year 3 = 40000-9000 = 31000

No calculating the present value of this stream of cash flow

Present value = 26000 - 9000/(1+0.1)¹ - 9000/(1+0.1)² + 31000/(1+0.1)³ - 9000/(1+0.1)⁴ .....................- 9000/(1+0.1)⁹

Present value = $4,221.38

Present value is greater than zero which means cost of lease is more than maintenance payment of old machine, therefore we should not replace the old machine

(b) IRR is the rate that makes sum of present value of future cash flows equal to zero

Incremental IRR means we will subtract the cash flow in one scenario from another and then equate the present value of future cash flows with zero

Now,

Current due payment = 35000 - 9000 = 26000

Payment due in year 1, 2, 4, 5, 6, 7, 8, 9 = 0-9000 = -9000

Payment due in year 3 = 40000-9000 = 31000

Present value = 26000 - 9000/(1+r)¹ - 9000/(1+r)² + 31000/(1+r)³ - 9000/(1+r)⁴ .....................- 9000/(1+r)⁹

0 = 26000 - 9000/(1+r)¹ - 9000/(1+r)² + 31000/(1+r)³ - 9000/(1+r)⁴ .....................- 9000/(1+r)⁹

Solving this we get r is 6.99%

r is less than MARR which means replacing the machine would be costly, therefore, we should not replace the old machine

Rahul Sunny answered 2 years ago

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