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%?

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:

$\begin{array}{c}\text{After tax cash outflow from the lease}=\text{Per year lease amount}\times \left(1-\text{Tax bracket}\right)\\ =25,000\times \left(1-0.34\right)\\ =25,000\times 0.66\\ =16,500\end{array}$

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:

$\text{Present Value of lease payments}=\text{PMT}\times \left[\frac{1-\frac{1}{{\left(1+\text{i}\right)}^{\text{N}}}}{\text{i}}\right]+\frac{\text{FV}}{{\left(1+\text{i}\right)}^{\text{N}}}$

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:

$\begin{array}{c}\text{Present Value of lease payments}=\text{16,500}\times \left[\frac{1-\frac{1}{{\left(1+\text{7}\right)}^{\text{5}}}}{\text{7}}\right]+\frac{3,500}{{\left(1+\text{7}\right)}^{\text{5}}}\\ =67,653.26\end{array}$

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:

$\begin{array}{c}\text{Present Value}=\text{Future Value}\times \left[\frac{1}{{\left(1+\text{i}\right)}^{\text{N}}}\right]\\ =3,500\times \left[\frac{1}{{\left(1+0.07\right)}^5}\right]\\ =2,495.45\end{array}$

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:

$\begin{array}{c}\text{Present Value of all cash outflows}=\left(\begin{array}{l}\text{Present value of lease payments}+\\ \text{Present Value of end-of-lease purchase}\end{array}\right)\\ =67,653.26+2,495.45\\ =70,148.71\end{array}$

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