Chapter 21, Problem 1MC

THE DECISION TO LEASE OR BUY AT WARF COMPUTERS

Warf Computers has decided to proceed with the manufacture and distribution of the virtual keyboard (VK) the company has developed. To undertake this venture, the company needs to obtain

equipment for the production of the microphone for the keyboard. Because of the required sensitivity of the microphone and its small size, the company needs specialized equipment for production.

Nick Warf, the company president, has found a vendor for the equipment. Clapton Acoustical Equipment has offered to sell Warf Computers the necessary equipment at a price of $3.6 million. Because of the rapid development of new technology, the equipment falls in the three-year MACRS depreciation class. At the end of four years, the market value of the equipment is expected to be $440,000.

Alternatively, the company can lease the equipment from Hendrix Leasing. The leas-e contract calls for four annual payments of $935,000 due at the beginning of the year. Additionally,

Warf Computers must make a security deposit of $210,000 that will be returned when the lease expires. Warf Computers can issue bonds with a yield of 11 percent, and the company has a marginal tax rate of 35 percent.

I. Should Warf buy or lease the equipment?

Summary Introduction

To identify: Whether to lease or buy the system.

Leasing:

A contractual agreement between two persons to use the right of the property from one person to another is termed as leasing.

Explanation of Solution

Decision of lease or buy the system can be taken by evaluating the net advantage of leasing.

Given,

Cost of system is $3,600,000.

Calculated values,

After cost of debt rate is 0.0715.

Cash flows from leasing in year 1 are $1,027,708.

Cash flows from leasing in year 2 are $1,167,820.

Cash flows from leasing in year 3 are $794,356.

Cash flows from leasing in year 4 are $379,366.

Cost flow from buying is $$2,782,250.

Formula to calculate net advantage of leasing,

$\text{Net}\text{advantage}\text{of}\text{leasing}=\left(\begin{array}{l}\text{Cash flow from buying}-\frac{\text{Cash flows from leasing}\text{in}\text{year}\text{1}}{{\left(1+\text{Rate}\right)}^1}\\ -\frac{\text{Cash flows from leasing}\text{in}\text{year}\text{2}}{{\left(1+\text{Rate}\right)}^2}\\ -\frac{\text{Cash flows from leasing}\text{in}\text{year}\text{3}}{{\left(1+\text{Rate}\right)}^3}\\ -\frac{\text{Cash flows from leasing}\text{in}\text{year}\text{4}}{{\left(1+\text{Rate}\right)}^4}\end{array}\right)$

Substitute $2,782,250 for cost flow from buying, $1,027,708 for cash flow from leasing in year 1, $1,167,820 for cash flow from leasing in year 2, $794,356 for cash flow from leasing in year 3, $379,366 for cash flow from leasing in year 4 and 0.0715 for rate.

$\begin{array}{c}\text{Net}\text{advantage}\text{of}\text{leasing}=\left(\begin{array}{l}\$2,782,250-\frac{\$1,027,708}{{\left(1+0.0715\right)}^1}-\frac{\$1,167,820}{{\left(1+0.0715\right)}^2}\\ -\frac{\$794,356}{{\left(1+0.0715\right)}^3}-\frac{\$379,366}{{\left(1+0.0715\right)}^4}\end{array}\right)\\ =\left(\begin{array}{l}\$2,782,250-\frac{\$1,027,708}{1.0715}-\frac{\$1,167,820}{1.1481}\\ -\frac{\$794,356}{1.2302}-\frac{\$379,366}{1.3181}\end{array}\right)\\ =\left(\begin{array}{l}\$2,782,250-\$959,130.191-\$1,017,176.204\\ -\$645,712.892-\$287,812.76\end{array}\right)\\ =-\$127,582.047\end{array}$

Net advantage of leasing under MACRS depreciation is $-\$127,582.047$. As net advantage of leasing is negative therefore, one must buy the system.

Working note:

Given,

Cost of system is $3,600,000.

MACRS depreciation rate for first year is 33.33% or 0.3333.

MACRS depreciation rate for second year is 44.45% or 0.4445.

MACRS depreciation rate for third year is 14.81% or 0.1481.

MACRS depreciation rate for forth year is 7.41% or 0.0741.

Lease payment is $935,000 per year.

Tax rate is 35%.

Interest on borrowed amount is 11%.

Calculation of cash flow from buying,

$\begin{array}{c}\text{Cash flow from buying}=\left(\begin{array}{l}\text{Cost}\text{of}\text{asset}-\text{Security}\text{deposit}\\ -\text{After}\text{tax}\text{lease}\text{payment}\end{array}\right)\\ =\$36,000,000-\$2,100,000-\$607,750\\ =\$2,782,250\end{array}$

First year,

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$3,600,000\times 0.3333\times 0.35\\ =\$1,199,880\times 0.35\\ =\$419,958\end{array}$

Note: MACRS depreciation rate for equipment is 33.33%

Calculation of after tax lease payment,

$\begin{array}{c}\text{After}\text{tax}\text{lease}\text{payment}=\text{Annual}\text{Lease}\text{payment}\times \left(1-\text{Tax}\text{rate}\right)\\ =\$935,000\times \left(1-0.35\right)\\ =\$935,000\times 0.65\\ =\$607,750\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$419,958+\$607,750\\ =\$1,027,708\end{array}$

Calculation of after tax cost of debt,

$\begin{array}{c}\text{After}\text{tax}\text{cost}\text{of}\text{debt}=\text{Cost}\text{of}\text{debt}\times \left(1-\text{Tax}\text{rate}\right)\\ =0.11\times \left(1-0.35\right)\\ =0.11\times 0.65\\ =0.0715\text{or}7.15\%\end{array}$

Second year,

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$3,600,000\times 0.4445\times 0.35\\ =\$1,600,200\times 0.35\\ =\$560,070\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$560,070+\$607,750\\ =\$1,167,820\end{array}$

Third year,

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$3,600,000\times 0.1481\times 0.35\\ =\$533,160\times 0.35\\ =\$186,606\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$186,606+\$607,750\\ =\$794,356\end{array}$

Forth year,

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$3,600,000\times 0.0741\times 0.35\\ =\$266,760\times 0.35\\ =\$93,366\end{array}$

Calculation of after tax salvage value,

$\begin{array}{c}\text{After}\text{tax}\text{salvage}\text{value}=\text{Salvage}\text{value}\times \left(1-\text{Tax}\text{rate}\right)\\ =\$440,000\times 0.65\\ =\$286,000\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{salvage}\text{value}\\ =\$93,366+\$286,000\\ =\$379,366\end{array}$

Hence, net advantage of leasing is negative. Thus, buy decision is best.