Chapter 21, Problem 6QP

Use the following information to work Problems 1-6. You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $5,800,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it will actually be completely valueless in four years. You can lease it for $690,000 per year for four years.

6. MACRS Depreciation and Leasing Rework Problem 1 assuming that the scanner will be depreciated as three-year property under MACRS (see Chapter 6 for the depreciation allowances).

Summary Introduction

To identify: Whether to lease or buy the scanner when scanner are depreciated under MACRS.

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 scanner can be taken by evaluating the net advantage of leasing.

Given,

Cost of scanner is $5,800,000.

Calculated values,

After cost of debt rate is 0.052.

Cash flows from leasing in year 1 is $2,872,990.

Cash flows from leasing in year 2 is $1,999,820.

Cash flows from leasing in year 3 is $1,398,940.

Cash flows from leasing in year 4 is $1,248,923.

Formula to calculate net advantage of leasing,

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

Substitute $5,800,000 for cost of asset, $1,775,099 for cash flow from leasing in year 1, $2,000,835 for cash flow from leasing in year 2, $1,399,143 for cash flow from leasing in year 3, $1,248,923 for cash flow from leasing in year 4 and 0.052 for rate.

$\begin{array}{c}\text{Net}\text{advantage}\text{of}\text{leasing}=\left(\begin{array}{l}\$5,800,000-\frac{\$1,775,099}{{\left(1+0.052\right)}^1}-\frac{\$2,000,835}{{\left(1+0.052\right)}^2}\\ -\frac{\$1,399,143}{{\left(1+0.052\right)}^3}-\frac{\$1,248,923}{{\left(1+0.052\right)}^4}\end{array}\right)\\ =\left(\begin{array}{l}\$5,800,000-\frac{\$1,775,099}{1.052}-\frac{\$2,000,835}{1.1067}\\ -\frac{\$1,399,143}{1.1642}-\frac{\$1,248,923}{1.2248}\end{array}\right)\\ =-\$83,268.34\end{array}$

Net advantage of leasing under MACRS depreciation is $-\$83,268.34$. As net advantage of leasing is negative therefore, one must buy the scanner.

Working note:

Given,

Cost of scanner is $5,800,000.

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 $1,690,000 per year.

Tax rate is 35%.

Interest on borrowed amount is 8%.

First year

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$5,800,000\times 0.3333\times 0.35\\ =\$1,933,140\times 0.35\\ =\$676,599\end{array}$

Calculation of after tax lease payment,

$\begin{array}{c}\text{After}\text{tax}\text{lease}\text{payment}=\text{Annual}\text{Lease}\text{payment}\times \left(1-\text{Tax}\text{rate}\right)\\ =\$1,690,000\times \left(1-0.35\right)\\ =\$1,690,000\times 0.65\\ =\$1,098,500\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$676,599+\$1,098,500\\ =\$1,775,099\end{array}$

Calculation of after tax cost of debt,

$\begin{array}{c}\text{After}\text{tax}\text{cost}\text{of}\text{debt}=\text{Cost}\text{of}\text{debt}\times \left(1-\text{Tax}\text{rate}\right)\\ =0.08\times \left(1-0.35\right)\\ =0.08\times 0.65\\ =0.052\text{or}5.20\%\end{array}$

Second year

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$5,800,000\times 0.4445\times 0.35\\ =\$2,578,100\times 0.35\\ =\$902,335\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$902,335+\$1,098,500\\ =\$2,000,835\end{array}$

Third year

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$5,800,000\times 0.1481\times 0.35\\ =\$858,980\times 0.35\\ =\$300,643\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$300,643+\$1,098,500\\ =\$1,399,143\end{array}$

Fourth year

Calculation of depreciation tax shield,

$\begin{array}{c}\text{Depreciation}\text{tax}\text{sheild}=\text{Cost}\text{of}\text{asset}\times \text{MACRS depreciation rate}\times \text{Tax}\text{rate}\\ =\$5,800,000\times 0.0741\times 0.35\\ =\$429,780\times 0.35\\ =\$150,423\end{array}$

Calculation of cash flows from leasing,

$\begin{array}{c}\text{Cash}\text{flow}\text{from}\text{leasing}=\text{Depreciation}\text{tax}\text{sheild}+\text{After}\text{tax}\text{lease}\text{payment}\\ =\$150,423+\$1,098,500\\ =\$1,248,923\end{array}$

Conclusion

Hence, net advantage of leasing is negative so lease decision is best.