Chapter 27, Problem 7QP

Lease or Buy [LO3] What is the NAL for Wildcat? What is the maximum lease payment that would be acceptable to the company?

Summary Introduction

To determine: The NAL for WD Company and the minimum lease payment that would be acceptable to the firm.

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.

Answer to Problem 7QP

The NAL value of WD Company is $1,273,752.48. The minimum lease payment is $1,929,927.995.

Explanation of Solution

Step 1: Determine the cash flows from the depreciation tax shield.

The pretax cost savings is not appropriate as the lease versus the purchase decision. The firm will definitely use the equipment and the savings will be realized. Therefore, depreciation tax shield is determined as follows:

$\begin{array}{c}\text{Depreciation tax}\text{?}\text{shield = }\frac{\text{Cost}}{\text{Number of years}}\times \text{Tax rate}\\ \text{= }\left(\frac{\text{\$8,300,000}}{\text{5}}\right)\times \left(\text{.34}\right)\\ \text{Depreciation tax}\text{?}\text{shield}\text{?}\text{= \$564,400}\end{array}$

Step 2: Determine the aftertax cost of the lease payments.

$\begin{array}{c}\text{After tax lease payment = Lease payment }\times \left(\text{1}-\text{?}\text{Tax}\text{?}\text{rate}\right)\\ =\text{?}\$1,875,000\times \left(\text{1}-\text{?}.34\right)\\ =\text{?}\$1,875,000\times 0.66\\ \text{After tax lease payment}=\$1,237,500\end{array}$

Step 3: Determine the after tax cost of debt.

$\begin{array}{c}\text{After tax debt cost = Interest rate }\times \left(\text{1}-\text{tax}\text{?}\text{rate}\right)\\ \text{= }\text{.07}\times \text{?}\left(1-0.34\right)\\ =\text{?}.07\times 0.66\\ =.0462\end{array}$

Step 4: Determine net advantage to leasing (NAL).

NAL is the amount that an individual or a firm saves through leasing an asset instead of purchasing it. NAL of leasing a diagnostic scanner is calculated as follows:

$\begin{array}{c}\text{NAL = Cost}\text{?}-\text{?}\text{?}\text{PVIFA}\text{?}\text{of Total}\text{?}\text{cash}\text{?}\text{flow}\text{?}\text{from}\text{?}\text{leasing}\\ =\left(\begin{array}{l}\text{\$8,300,000}-\text{?}\$1,237,500\\ -\$1,237,500\left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]\\ -\$564,400\left(\text{step 1}\right)\left[\left\{\text{1–1/}{\left(\text{1}+\text{r}\right)}^{\text{t}}\right\}/\text{r}\right]\end{array}\right)\\ =\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\left[\left\{\text{1–1/}{\left(\text{1}+.0462\right)}^{\text{4}}\right\}/.0462\right]\\ -\$564,400\left[\left\{\text{1–1/}{\left(\text{1}+.0462\right)}^{\text{5}}\right\}/.0462\right]\end{array}\right)\end{array}$

$\begin{array}{c}\text{NAL}=\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\left[\left\{\text{1–1/}{\left(\text{1}+.0462\right)}^{\text{4}}\right\}/.0462\right]\\ -\$564,400\left[\left\{\text{1–1/}{\left(\text{1}+.0462\right)}^{\text{5}}\right\}/.0462\right]\end{array}\right)\\ =\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\left[\left\{\text{1–1/1}\text{.19800}\right\}/.0462\right]\\ -\$564,400\left[\left\{\text{1–1/1}\text{.25335}\right\}/.0462\right]\end{array}\right)\end{array}$

$\begin{array}{c}\text{NAL}=\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\left[\left\{\text{1–}\text{?}\text{0}\text{.83472}\right\}/.0462\right]\\ -\$564,400\left[\left\{\text{1– 0}\text{.79786}\right\}/.0462\right]\end{array}\right)\\ =\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\left[0.16528/.0462\right]\\ -\$564,400\left[0.20214/.0462\right]\end{array}\right)\end{array}$

$\begin{array}{c}=\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\$1,237,500\\ -\$1,237,500\times 3.577488\\ -\$564,400\times 4.37532\end{array}\right)\\ \text{NAL}=\left(\begin{array}{l}\text{\$8,300,000 }-\text{?}\text{?}\$1,237,500\\ -\$4,427,141.4-\$2,469,430.608\end{array}\right)\\ \text{NAL}=\text{?}\$165,927.992\end{array}$

Note: PVIFA is the present value interest factor for an annuity.

The determined NAL is positive. Hence, equipment should be leased.

Step 5: Determine the maximum payment.

In order to find the maximum payment, NAL must be equal to zero and where X represents maximum payment.

$\begin{array}{c}\text{NAL = Cost}\text{?}-\text{?}\text{?}\text{PVIFA}\text{?}\text{of Total}\text{?}\text{cash}\text{?}\text{flow}\text{?}\text{from}\text{?}\text{leasing}\\ \text{0}\text{?}\text{= \$8,300,000}-\text{?}\text{X}\times 1.0462\times \left(\text{PVIFA}{\text{?}}_{4.62\%,,5}\right)-\$564,400\left(\text{PVIFA}{\text{?}}_{4.62\%,,5}\right)\\ =\left[\begin{array}{l}\text{\$8,300,000}\\ -\text{?}\text{X}\times 1.0462\times \left[\text{1–}\left\{\frac{\text{1}}{{\left(\text{1}+0.0462\right)}^{\text{5}}}\right\}/0.0462\right]\\ -\$564,400\left[\text{1–}\left\{\frac{\text{1}}{{\left(\text{1}+0.0462\right)}^{\text{5}}}\right\}/0.0462\right]\end{array}\right]\\ =\text{\$8,300,000 }-\text{X}\times 1.0462\times 4.37533\text{?}-\$564,400\times \text{?}4.37533\\ \text{0}=\$8,300,000-4.57747\text{X}-\$2,469,436.252\end{array}$

$\begin{array}{c}\text{X}=\frac{\$5,830,563.748}{\text{4}\text{.57747}}\\ \text{X}=\text{?}\$1,273,752.48\end{array}$

Step 6: Determine the pretax lease payment.

$\begin{array}{c}\text{Pretax}\text{?}\text{lease}\text{?}\text{payment}\text{?}\text{= }\frac{\text{Maximum payment}}{1-\text{tax}\text{?}\text{rate}}\\ =\text{?}\frac{\$1,273,752.48}{1-0.34}\\ =\text{?}\frac{\$1,273,752.48}{0.66}\\ \text{Pretax}\text{?}\text{lease}\text{?}\text{payment}=\$1,929,927.995\end{array}$

Hence, the pretax lease payment is $1,929,927.995.