Chapter 27, Problem 9QP

Summary Introduction

To determine: Whether to lease equipment will be advantageous for WD Company.

Introduction:

Lease: An asset can be leased or purchased. A lease in a contractual agreement made between two parties; lessor and lessee. The agreement explains the use of asset for a particular time by lessee. In return, lessor gets periodical payments for the use of asset.

Explanation of Solution

Step 1: Determine NAL.

Net advantage to leasing (NAL) is the amount that an individual or a firm saves through leasing an asset instead of purchasing it. The security deposit is a cash outflow. It is a payment made in the beginning of the lease and it is an inflow when the lease is being returned. Therefore, as per the above assumption, NAL is determined as follows:

$\begin{array}{c}\text{NAL = Cost}\text{?}-\text{?}\text{?}\text{PVIFA}\text{?}\text{of Total}\text{?}\text{cash}\text{?}\text{flow}\text{?}\text{from}\text{?}\text{leasing }\\ \text{= }\left(\begin{array}{c}\text{\$8,300,000}\\ -\text{?}\text{Security}\text{?}\text{deposit }-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$1,237,500\left(\text{PVIFA}{\text{?}}_{4.62\%,,4}\right)\\ -\$564,400\left(\text{PVIFA}{\text{?}}_{4.62\%,,5}\right)+\frac{\text{Security}\text{?}\text{deposit}}{{1.0462}^5}\end{array}\right)\end{array}$

$=\left(\begin{array}{c}\text{\$8,300,000}\\ -\text{?}\text{Security}\text{?}\text{deposit }-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$1,237,500\times \left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]\\ -\$564,400\times \left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]+\frac{\text{Security}\text{?}\text{deposit}}{{1.0462}^5}\end{array}\right)$

$=\left(\begin{array}{c}\text{\$8,300,000}\\ -\text{?}\text{Security}\text{?}\text{deposit }-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$1,237,500\times \left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]\\ -\$564,400\times \left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]+\frac{\text{Security}\text{?}\text{deposit}}{{1.0462}^5}\end{array}\right)$

$=\left(\begin{array}{c}\text{\$8,300,000}-\text{?}\$600,000-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$1,237,500\times \left[\left\{\text{1–1/}{\left(\text{1}+0.0462\right)}^{\text{4}}\right\}/0.0462\right]\\ -\$564,400\times \left[\left\{\text{1–1/}{\left(\text{1}+0.0462\right)}^{\text{5}}\right\}/0.0462\right]+\frac{\text{\$60,000}}{{1.0462}^5}\end{array}\right)$

$\begin{array}{c}=\left(\begin{array}{c}\text{\$8,300,000}-\text{?}\$600,000-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$1,237,500\times 3.57747\\ -\$564,400\times 4.37533+\frac{\text{\$600,000}}{{1.0462}^5}\end{array}\right)\\ =\left(\begin{array}{c}\text{\$8,300,000}-\text{?}\$600,000-\text{?}\text{?}\$1,237,500\\ -\text{?}\text{?}\$4,427,119.125\\ -\$2,469,436.252+\$478,715.7012\end{array}\right)\\ \text{NAL}=\$44,660.3242\end{array}$

Step 2: Determine the present value of the security deposit.

The NAL of the equipment is greater than zero. So, the firm has to lease the equipment with the security deposit. From solution 7, NAL without security deposit can be derived as $165, 927.992. Now, add present value of the security deposit.

$\begin{array}{c}\text{Present}\text{?}\text{value of security deposit = }-\text{Security deposit +}\frac{\text{Security deposit}}{{\left(\text{1+0}\text{.0462}\right)}^5}\\ =-\$600,000+\text{?}\text{}\frac{\$600,000}{{1.0462}^5}\\ =-\$600,000+\text{?}\text{}\$478,715.70116\\ =\$121,284.29\end{array}$

Step 3: Determine the NAL with the security deposit.

$\begin{array}{c}\text{NAL = NAL}\text{}\text{without security deposit }-\text{?}\text{PV}\text{}\text{?}\text{of}\text{?}\text{security}\text{?}\text{deposit}\\ \text{=}\text{?}\text{\$165,927}\text{.992}-\$121,284.29\\ =\$44,643.702\end{array}$

The NAL with the security deposit is $44,643.702. Hence, the leasing would be advantageous for WD Company.