Question

Suppose the risk-free interest rate is 6.3% APR with monthly compounding. If a $1.9 million MRI machine can be leased for seven years for $24,000 per month, what residual value must the lessor recover to break even in a perfect market with no risk?

The residual value must be____________ $. (Round to the nearest dollar)

Answer 1

The value the lessor recovers to break even in a perfect market with no risk only when cost of the machine is equal to the present value of the lease rentals discounted at the risk free rate and salvage value discounted at risk free rate.

Machine cost = PV of the lease payments + pv of salvage value

PV of the lease payments = lease payments ( PVAF , R,N)

Here R = 6.3 / 12 = 0.525 %

N = 7*12 = 84

Pv of lease payments = 24000 * ( PVAF,0.525%,84)

= 24000 * 67.78

= 1,626,720

PV of salvage value = 1,900,000 - 1,626,720

= 273,280

We need to calculate the future value of the salvage value to find out the required amount

FV of salvage value = salvage value * ( 1 + r) ^n

= 273280 * ( 1+ 0.00525 )^84

= 273280*1.5525

= $424,267

Residual value = $ 424,267