Question

Sadik Industries must install $1 million of new machinery in its Texas plant. It can obtain a 6-year bank loan for 100% of the cost at a 14% interest rate with equal payments at the end of each year. Sadik’s tax rate is 34%. The equipment falls in the MACRS 3-year class.

Alternatively, a Texas investment banking firm that represents a group of investors can arrange a guideline lease calling for payments of $320,000 at the end of each year for 3 years. Under the proposed lease terms, the Sadik must pay for insurance, property taxes, and maintenance.

Sadik must use the equipment if it is to continue in business, so it will almost certainly want to acquire the property at the end of the lease. If it does, then under the lease terms, it can purchase the machinery at its fair market value at Year 3. The best estimate of this market value is $200,000, but it could be much higher or lower under certain circumstances. If purchased at Year 3, the used equipment would fall into the MACRS 3-year class. Sadik would actually be able to make the purchase on the last day of the year (i.e., slightly before Year 3), so Sadik would get to take the first depreciation expense at Year 3 (the remaining depreciation expenses would be from Year 4 through Year 6). On the time line, Sadik would show the cost of purchasing the used equipment at Year 3 and its depreciation expenses starting at Year 3.

To assist management in making the proper lease-versus-buy decision, you are asked to answer the following questions:

1. What is the net advantage of leasing? Should Sadik take the lease?

   Answer

   PV of leasing = −$637,702; PV of owning = −$713,300; NAL = $75,598.

2. Consider the $200,000 estimated residual value. How high could the residual value get before the net advantage of leasing falls to zero?

   Answer

   $343,489.

3. I do not know how to calculate this....this is the answer but i need a step by step since i am not understanding the process?

   )	If the NAL is to be zero, the residual value at t3 should be increased such that the PV of the increase in price-the PV of tax shields on the addl depreciation
   	should be 0.
   	If x is the increase in residual value:
   	PV of increase in residual value = x*0.76711
   	The PV of depreciation tax shield will be x*0.34*(0.3333*.76711+0.4445*0.70222+0.1481*0.64282+0.0741*0.58845) = x*0.24025
   	So 75598 = x*(0.76711-0.24025)
   	x = 75598/(0.76711-0.24025) =	143488
   	The increase in price should be $143488.
   	That is the residual value should be 200000+143488 =	343488
   	for NAL to be 0.

Answer 1

For the NAL to be zero, the present value (PV) of the increase in residual value has to equal the sum of the PVs of the depreciation tax shields of the increase in residual value.

Discount rate = after-tax cost of debt = interest rate*(1-Tax rate) = 14%*(1-34%) = 9.24%

Let the increase in value be X. Then, PV of increase in value

= X/(1+9.24%)^3 = 0.76711*X

The 3-year MACRs depreciation rates are 33.33%, 44,45%, 14.81% and 7.41%

Depreciation tax shield = increase in residual value*depreciation rate*Tax rate

PV of depreciation tax shield = X*33.33%*34%/(1+9.24%)^3 + X*44.45%*34%/(1+9.24%)^4 + X*14.81%*34%/(1+9.24%)^5 + X*7.41%*34%/(1+9.24%)^6

(Note: The equipment is bought just before the end of Year 3, so depreciation is charged for Years 3, 4, 5 and 6.)

= X(0.08693 + 0.10613 + 0.03237 + 0.01483) = 0.24025*X

So,

NAL = PV of increase in residula value - PV of depreciation tax shield

75,598 = 0.76711*X - 0.24025*X

X = 75,598/(0.76711 - 0.24025) = 143,489

Residual value for NAL to be zero is original residual value + increase in residual value

= 200,000 + 143,489 = 343,489