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Chapter 17, Problem 17.1WUE

N and M Corp, is considering leasing a new machine for $25,000 per year. The lease arrangement calls for a 5-year lease with an option to purchase the machine at the end of the lease for $3,500. The firm is in the 34% tax bracket. What is the present value of the lease outflows, including the purchase option, if lease payments are made at the end of each year and if the after-tax cost of debt is 7%?

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Summary Introduction

To determine:

Present value of lease cash flows.

Introduction:

The Present Value is the present sum of future money at a discounted rate of interest.

Explanation of Solution

The N and M corp. is considering leasing a new machine and the value of lease is $25,000 per year for the period of 5 years. At the end of 5 years, the corp. can purchase the machine at a price of $3,600. It is also given that the firm comes under the tax bracket of 34 percent.

The after tax cost of debt is 7 percent and thus the after tax cash outflow from the lease can be calculated by the following formula:

After tax cash outflow from the lease=Per year lease amount×(1Tax bracket)=25,000×(10.34)=25,000×0.66=16,500

Thus, the after tax cash outflow from the lease is $16,500.

Present Value of the lease payments can be calculated by the use of the discounting method as follows:

Present Value of lease payments=PMT×[11(1+i)Ni]+FV(1+i)N

Here, the number of years N is 5 years, Interest rate is 7 percent and the PMT is -$16,500. Thus, the PV can be calculated as follows:

Present Value of lease payments=16,500×[11(1+7)57]+3,500(1+7)5=67,653.26

The present value of the lease payments at the end of the year is $67,653.26.

The present value of the end-of-lease purchase can be calculated as follows:

Present Value=Future Value×[1(1+i)N]=3,500×[1(1+0.07)5]=2,495.45

The present value of the end-of-lease purchase is $2,495.45.

Thus, the present value of all cash outflows can be calculated by summating the two as follows:

Present Value of all cash outflows=(Present value of lease payments+Present Value of end-of-lease purchase)=67,653.26+2,495.45=70,148.71

Thus, the present value of all cash outflows is $70,148.71.

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Chapter 17 Solutions

Principles of Managerial Finance, Student Value Edition Plus MyLab Finance with Pearson eText - Access Card Package (15th Edition) (Pearson Series in Finance)

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