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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