Corporate Finance
Corporate Finance
3rd Edition
ISBN: 9780132992473
Author: Jonathan Berk, Peter DeMarzo
Publisher: Prentice Hall
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Chapter 25, Problem 1P

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.

  1. a. What is the risk-free monthly lease rate for a five-year lease in a perfect market?
  2. b. What would be the monthly payment for a five-year $200,000 risk-free loan to purchase the H1200?

a.

Expert Solution
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Summary Introduction

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

The risk-free monthly lease rate payment in a perfect market is $2,880.02.

Explanation of Solution

Given information:

Supercomputer cost: $200,000.

Lease term: 5 years.

Lease payment period: Totalyearforlease×monthina year = 5×12=60 .

Residual market value: $60,000.

Risk free interest rate: 5.00%

Formula for the calculation of present value of the payment:

PV(Lease Payments)=Purchase PricePV(Residual Value)

Formula for the calculation of the monthly lease payment in perfect market:

PV(Lease Payments)=Monthlylease(1+1Rate/Month(11(1+Rate/Month)Period-1))

Calculate the present value (PV) of the lease payment:

PV(Lease Payments)=Purchase PricePV(Residual Value)=Purchase PriceResidual Value(1+Rate)period=$200,000$60,000(1+5.00%12)5×12=$200,000$46,751.39=$153,248.60.

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.

PV(Lease Payments)=Monthlylease(1+1Rate/Month(11(1+Rate/Month)Period))$153,247.68=Monthlylease×[(1+15.00%/12)×(11(1+5.00%/12)59)]$153,247.68=Monthlylease×[53.211]Monthlylease=$153,247.6853.211=$2,880.02.

Therefore, the monthly lease payment in a perfect market is $2,880.02.

b.

Expert Solution
Check Mark
Summary Introduction

To determine: The monthly payment for a five-year risk free loan.

Answer to Problem 1P

The monthly payment for a five-year risk free loan is $3,774.

Explanation of Solution

Given information:

Lease term: 5 years.

Lease payment period: Totalyearforlease×Monthina year= 5×12=60 .

Interest rate: 5.00%.

Formula for the calculation of the monthly lease payment:

PV(Lease Payments)=Monthlylease(1+1Rate/Month(11(1+Rate/Month)Period))

Calculation of the monthly payment for a five-year risk free loan:

PV(Lease Payments)=Monthlylease×1Monthlyrate(11(1+Monthlyrate)Period)$153,247.68=Monthlylease×[1(5.00%/12)(11(1+(5.00%/12))60)]$153,247.68=Monthlylease×[52.99]Monthlylease=$3,774.24752.99=$3,774.24

Therefore, the monthly payment for a five-year risk free loan is $3,774.24.

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