Question

In: Finance

Suppose an H1200 supercomputer has a cost of $ 450,000 and will have a residual market...

Suppose an H1200 supercomputer has a cost of $ 450,000 and will have a residual market value of $ 135,000 in 6years. The risk-free interest rate is 6.3 % APR with monthly compounding.

a. What is the risk-free monthly lease rate for a 6-year lease in a perfect market?

b. What would be the monthly payment for a 4-year $ 450,000 risk-free loan to purchase the H1200?

Note: Round the monthly interest rate to at least six decimal places.

Expert Solution

Answer : Calculation of Lease Payments :

We first need to calculate Present value of Lease Payments :

Present Value = Cost - Present Value of Residual Market Value

= 450000 - {Residual Value * [1 / (1 + Monthly rate of Interest)^number of months}

= 450000 - {135000 * [1 / (1 + 0.063/12)^72}

= 450000 - {135000 * [1 / 1.457921]}

= 450000 - 92597.63

= 357402.37

As the first lease payments are made immediately the rest will be paid as Annuity therefore payments remaining is 71

357402.37 = Monthly Lease Payments * [1 + {[1 / (0.063 / 12)] * [1 - [1 / (1 + 0.063/12)^71]}

357402.37 = Monthly Lease Payments * [1 + {[190.476190] * [1 - [1 / 1.450307]}

357402.37 = Monthly Lease Payments * [1 + {[190.476190] * [0.310491]}

==> Monthly Lease Payments = 357402.37 / [1 + 59.14107]

= 5942.73

(b.) Calculation of Monthly Payments for a 4-year $ 450,000 risk-free loan to purchase the H1200:

450000 = Monthly Lease Payments * {[1 / (0.063 / 12)] * [1 - [1 / (1 + 0.063/12)^48]}

450000 = Monthly Lease Payments * {[190.476190 * [1 - [1 / 1.285748]}

450000 = Monthly Lease Payments * {[190.476190 * [1 - 0.777757]}

450000 = Monthly Lease Payments * {[190.476190 * 0.222243}

==> Monthly Lease Payments = 450000 / 42.33195

= 10630.27

jeff jeffy answered 1 year ago

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