Concept explainers
Suppose an H1200 supercomputer has a cost of $200,000 and will have a residual market value of $60,000 in five years. The risk-free interest rate is 5% APR with monthly compounding.
- a. What is the risk-free monthly lease rate for a five-year lease in a perfect market?
- b. What would be the monthly payment for a five-year $200,000 risk-free loan to purchase the H1200?
a.
To determine: The risk-free monthly lease rate payment in a perfect market.
Introduction: Lease is a contract between the lessee and lessor for the use of an asset. Lessee agrees to pay a specific amount as per contract to the lessor for the use of the lessor asset.
Answer to Problem 1P
Explanation of Solution
Given information:
Supercomputer cost: $200,000.
Lease term: 5 years.
Lease payment period:
Residual market value: $60,000.
Risk free interest rate: 5.00%
Formula for the calculation of present value of the payment:
Formula for the calculation of the monthly lease payment in perfect market:
Calculate the present value (PV) of the lease payment:
Therefore, the PV of the lease payment is $153,248.60.
Calculate the monthly lease payment in a perfect market:
Lease payment remains for 59 payments that are paid as an annuity because the first lease payment is paid in upfront.
Therefore, the monthly lease payment in a perfect market is $2,880.02.
b.
To determine: The monthly payment for a five-year risk free loan.
Answer to Problem 1P
Explanation of Solution
Given information:
Lease term: 5 years.
Lease payment period:
Interest rate: 5.00%.
Formula for the calculation of the monthly lease payment:
Calculation of the monthly payment for a five-year risk free loan:
Therefore, the monthly payment for a five-year risk free loan is $3,774.24.
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Chapter 25 Solutions
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