Question

Suppose Proctor​ & Gamble​ (P&G) is considering purchasing $12 million in new manufacturing equipment. If it purchases the​ equipment, it will depreciate it for tax purposes on a​ straight-line basis over five​ years, after which the equipment will be worthless. It will also be responsible for maintenance expenses of $1.00 million per​ year, paid in each of years 1 through 5. It can also lease the equipment under a true tax lease for ​$3.3 million per year for the five​ years, in which case the lessor will provide necessary maintenance. Assume​ P&G's tax rate is 30% and its borrowing cost is 6.0%.

a. What is the NPV associated with leasing the equipment versus financing it with the​ lease-equivalent loan?

b. What is the​ break-even lease rate - that ​is, what lease amount could​ P&G pay each year and be indifferent between leasing and financing a​ purchase?

Answer 1

Part a)

Step 1: Calculate Free Cash Flow Associated with Purchase and Lease of Equipment

The value of free cash flow for each year associated with purchase is calculated as below:

	Annual Free Cash Flow (Purchase)
	1	2	3	4	5
Depreciation Tax Shield (12,000,000/5*30%)	720,000	720,000	720,000	720,000	720,000
Less After-Tax Maintenance Expenses [1,000,000*(1-30%)]	700,000	700,000	700,000	700,000	700,000
Annual Free Cash Flow (Purchase)	$20,000	$20,000	$20,000	$20,000	$20,000

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Value of Free Cash Flow (Lease) = Annual Lease Payment*(1-Tax Rate) = -3,300,000*(1-30%) = -$2,310,000

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Step 2: Calculate Net Free Cash Flow Each Year (Lease Versus Buying)

The net free cash flow each year is calculated as below:

Year 0 = Value of Free Cash Flow with Lease - Purchase Cost = -2,310,000 - (-12,000,000) = $9,690,000

Year 1 to Year 4 = Value of Free Cash Flow with Lease - Value of Free Cash Flow with Purchase = -2,310,000 - 20,000 = -$2,330,000

Year 5 = Value of Free Cash Flow with Lease - Value of Free Cash Flow with Purchase = -$20,000

_____

Step 3: Calculate NPV with Use of After-Tax Borrowing Rate

The NPV is calculated as below:

NPV = Net Free Cash Flow Year 0 + Net Free Cash Flow Year 1/(1+After-Tax Borrowing Rate)^1

+ Net Free Cash Flow Year 2/(1+After-Tax Borrowing Rate)^2

+ Net Free Cash Flow Year 3/(1+After-Tax Borrowing Rate)^3

+ Net Free Cash Flow Year 4/(1+After-Tax Borrowing Rate)^4

+ Net Free Cash Flow Year 5/(1+After-Tax Borrowing Rate)^5

Using the values calculated in Step 2 in the above formula, we get,

NPV = 9,690,000 - 2,330,000/(1+4.20%)^1 - 2,330,000/(1+4.20%)^2 - 2,330,000/(1+4.20%)^3 - 2,330,000/(1+4.20%)^4 - 20,000/(1+4.20%)^5 = $1,255,776.20

Based on the above calculations, it can be concluded that lease is more attractive than buying.

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Part b)

The break even lease rate is calculated with the use of equation given below:

NPV = Increase in Lease Payment*(1-Tax Rate)*[1+1/(After-Tax Borrowing Rate)*(1-1/(1+After-Tax Borrowing Rate)^4)]

Substituting values in the above formula, we get,

1,255,776.20 = Increase in Lease Payment*(1-30%)*[1+1/4.20%*(1-1/(1+4.20%)^4)]

Rearranging Values, we get,

Increase in Lease Payment = 1,255,776.20/3.2290 = $388,906.13

Break Even Lease Rate = Current Annual Lease Payment + Increase in Lease Payment = 3,300,000 + 388,906.13 = $3,688,906.13 or $3.69 million

The lease amount that P&G should pay each year should be $3.69 million to be indifferent between leasing and financing a​ purchase.