Question

A company is considering investing $10,000 in a heat exchanger. The heat exchanger will last 5 years, at which time it will be sold for $2,000. The maintenance cost at the end of the first year is estimated to be $1,000. Maintenance costs for the exchanger are estimated to increase by $500 per year over its life. As an alternative, the company may lease the equipment for $X per year, including maintenance. (a) Draw a cash flow diagram of both alternatives. (b) For what value of X should the company lease the heat exchanger? The company expects to earn 8% on its investments. Assume end-of-year lease payments.

Answer 1

Answer:

Initai Cost C=10000

Year	Maintenance Cost Mi
1	1000
2	1500
3	2000
4	2500
5	3000

A)

10000 25000 3000 2000 1500 1000 Maintenance Cost Salvage 2000

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B)

rate =8%

Number of Years N=5

Salvage Value S= 2000

When NPV of Lease is less than or equal to NPV of Purchase then he should buy lease

NPV of Lease = X*(1-(1+r)^-N)/r

NPV of Lease = X*(1-(1+8%)^-5)/8% =3.99X

NPV of Purchase = ∑Mi/(1+r)^i +S/(1+r)^N-C

Year	Maintenance Cost Mi	PV of Mi
1	1000	925.93
2	1500	1286.01
3	2000	1587.66
4	2500	1837.57
5	3000	2041.75
	∑Mi/(1+r)^i	7678.92

NPV of Purchase = 7678.92 -2000/(1+8%)^5+10000= 16317.76

SInce NPV of Lease <=NPV of Purchase

3.99X <=16317.76

X<=4086.89