Question

Suppose an H1200 supercomputer has a cost of 450,000 and will have a residual market value of 67.000 in 5 years. The risk-free interest rate is 6.5% APR with monthly compounding.

a. What is the risk-free monthly lease rate for 5-year lease in a perfect market?

b. The risk-free monthly lease rate for a five-year lease in a perfect market?

Answer 1

For Five year (60 month) lease

PV (Lease payments) = 450000 – 67000/ (1+ 0.065/12)⁶⁰

= 450000 - (67000 / 1.382817)

= 401548.2

Because the first lease payment is paid upfront, and the remaining 59 Payments are paid as an annuity

401548 = L {1+ 1 /0.065/12 * [1 – 1/(1+0.065/12)⁵⁹)]}

L = 401548 / 51.38552

Therefore, L = 7814

b)

450000 = M* 1/ (0.065/12) * [ 1 – 1/(1+0.065/12)⁶⁰ ]

M = 450000 / 51.10868

M = 8805