Chapter 25, Problem 15PS

Valuing financial leases In Section 25-5, we listed four circumstances in which there are potential gains from leasing. Check them out by conducting a sensitivity analysis on the Greymare Bus Lines lease, assuming that Greymare does not pay tax. Try, in turn, (a) a lessor tax rate of 50% (rather than 21%), (b) straight-line depreciation in years 1 to 6 (rather than immediate expensing), (c) a four-year lease with four annual rentals (rather than an eight-year lease), and (d) an interest rate of 20% (rather than 10%). In each case, find the minimum rental that would satisfy the lessor and calculate the NPV to the lessee.

Summary Introduction

To determine: The minimum rental that would please the lessor and compute NPV to the lessee if a lessor tax rate is 50%.

Explanation of Solution

The NPV of the lessor’s cash flow contains of the cost of the bus, the PV of the depreciation tax shield, and the present value of the post-tax lease payments. To ascertain the minimum rental P, we set the NPV o zero and solve for P. we can then utilize this value for to calculate the value of the lease to the lessee.

Computation of minimum rental that would satisfy the lessor and NPV to the lessee is as follows:

At a lessor tax rate of 50%, the cash flows for the lessor are:

$\begin{array}{c}\text{0}=-100+\left(0.50\times 100\right)+\text{P}\left(1-0.50\right)\left(1+\frac{1}{1.05}+\frac{1}{{1.05}^2}+\mathrm{.....}+\frac{1}{{1.05}^7}\right)\\ \text{P}=\text{14}\text{.74 or \$14,735}\end{array}$

For company G, the NPV of the cash flows is the cost of the bus saved (100) lesser the present value of the lease payments.

$\begin{array}{c}{\text{PV}}_{\text{Lessee}}=100-14.74\times \left(1+\frac{1}{1.10}+\frac{1}{{1.10}^2}+\mathrm{....}+\frac{1}{{1.10}^7}\right)\\ =13.53\end{array}$

Summary Introduction

To determine: The minimum rental that would satisfy the lessor and calculate NPV to the lessee if straight line depreciation in year1 to 6.

Explanation of Solution

Computation of minimum rental that would satisfy the lessor and NPV to the lessee is as follows:

Lessor depreciation straight-line method over 6 years (tax rate back at 21%). Cash flow for the lessor are:

$\begin{array}{c}\text{0}=\left[\begin{array}{l}-100+\left(0.21\times 100\times \frac{1}{6}\right)\times \left(\frac{1}{1.079}+\frac{1}{{1.079}^2}+\mathrm{...}+\frac{1}{{1.079}^6}\right)\\ +\left(1-0.21\right)\text{P}\times \left(1+\frac{1}{1.079}+\frac{1}{{1.079}^2}+\mathrm{...}+\frac{1}{{1.079}^7}\right)\end{array}\right]\\ \text{P}=\text{17}\text{.04}\text{or \$17,036}\end{array}$

For company G, the NPV of the cash flow is:

$\begin{array}{c}{\text{PV}}_{\text{Lessee}}=100-17.04\times \left(1+\frac{1}{1.10}+\frac{1}{{1.10}^2}+\mathrm{....}+\frac{1}{{1.10}^7}\right)\\ =0.02\end{array}$

Summary Introduction

To determine: The minimum rental that would satisfy the lessor and calculate NPV to the lessee if a four-year lease with four annual rentals.

Explanation of Solution

Computation of minimum rental that would satisfy the lessor and NPV to the lessee is as follows:

Four-year lease with four annual rental payments. Cash flows for the lessor are:

$\begin{array}{c}\text{0}=\left[-100+\left(0.21\times 100\right)+\left(1-0.21\right)\text{P}\times \left(1+\frac{1}{1.079}+\frac{1}{{1.079}^2}+\frac{1}{{1.079}^3}\right)\right]\\ \text{P}=2\text{7}\text{.92}\text{or \$27,919}\end{array}$

For company G, the NPV of cash flow is:

$\begin{array}{c}{\text{PV}}_{\text{Lessee}}=100-27.92\times \left(1+\frac{1}{1.10}+\frac{1}{{1.10}^2}+\frac{1}{{1.10}^3}\right)\\ =2.65\end{array}$

Summary Introduction

To determine: The minimum rental that would satisfy the lessor and calculate NPV to the lessee if an interest rate of 20%.

Explanation of Solution

Computation of minimum rental that would satisfy the lessor and NPV to the lessee is as follows:

At an interest rate of 20% the cash flows for the lessor are:

$\begin{array}{c}\text{0}=\left[-100+\left(0.21\times 100\right)+\left(1-0.21\right)\text{P}\times \left(1+\frac{1}{1.158}+\frac{1}{{1.158}^2}+\mathrm{...}+\frac{1}{{1.158}^7}\right)\right]\\ \text{P}=1\text{9}\text{.75}\text{or \$19,753}\end{array}$

For company G, the NPV of cash flow is:

$\begin{array}{c}{\text{PV}}_{\text{Lessee}}=100-19.75\times \left(1+\frac{1}{1.20}+\frac{1}{{1.20}^2}+\mathrm{....}+\frac{1}{{1.20}^7}\right)\\ =9.04\end{array}$