Question

In: Finance

A company is analyzing three external providers to subcontract the service of maintenance for their installations...

A company is analyzing three external providers to subcontract the service of maintenance for their installations and equipment. Provider A offers a service through subcontracts that renews every single year, with a cost of $200,000 at the beginning of each year.

Provider B offers a service with contracts that renew every two years, through four $150,000 payments. The first one is done today and the other remaining three in intervals of six months each.

Provider C offers a service with contracts that renew every three years, with a payment of $500,000 today and another of $200,000 in two years.

All three providers offer to renew their services under the same economic conditions.

We wish to analyze the alternatives considering the same length of the projects, using the least common multiple of their durations.

The interest rate is of an annual 18%, capitalizable every six months.

What is the net present value of each alternative?

Solutions

Expert Solution

Present Value(PV) of Cash Flow
(Cash Flow)/((1+i)^N)
i=discount rate=(18/2)%=0.09
N=Six monthly period of Cash flow
Duration:
Provider A=1 year
Provider B=2 years
ProviderC=3 year
Lowest Common Multiplier=1*2*3=6years
ANALYSIS OF CASH FLOW FOR A
N Six monthly period 0 1 2 3 4 5 6 7 8 9 10 11 12
CF Cash Flow $200,000 $200,000 $200,000 $200,000 $200,000 $200,000 SUM
PV=CF/(1.09^N) Present Value of Cash Flow $200,000 $0 $168,336 $0 $141,685 $0 $119,253 $0 $100,373 $0 $84,482 $0 $0 $814,130
Net Present Value of Alternative A $814,130
ANALYSIS OF CASH FLOW FOR B
N Six monthly period 0 1 2 3 4 5 6 7 8 9 10 11 12
CF Cash Flow $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 $150,000 SUM
PV=CF/(1.09^N) Present Value of Cash Flow $150,000 $137,615 $126,252 $115,828 $106,264 $97,490 $89,440 $82,055 $75,280 $69,064 $63,362 $58,130 $0 $1,170,779
Net Present Value of Alternative B $1,170,779
ANALYSIS OF CASH FLOW FOR C
N Six monthly period 0 1 2 3 4 5 6 7 8 9 10 11 12
CF Cash Flow $500,000 $200,000 $500,000 $200,000 SUM
PV=CF/(1.09^N) Present Value of Cash Flow $500,000 $0 $0 $0 $141,685 $0 $298,134 $0 $0 $0 $84,482 $0 $0 $1,024,301
Net Present Value of Alternative C $1,024,301
ALTERNATIVE Net Present Value
A $814,130
B $1,170,779
C $1,024,301

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