Question

Wolf Corporation has decided to purchase a new machine that costs $4.5 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 30%. The Sur Bank has offered Wolf a four-year loan for $4.5 million. The repayment schedule is four-yearly principal repayments of $1,125,000 and an interest charge of 7% on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolf. Lease payments of $1,275,000 per year are due at the beginning of each of the four years of the lease.

1. What is the NAL of leasing for Wolf?

2. What is the maximum annual lease Wolf would be willing to pay?

Answer 1

SOLUTION TO QUESTION 1:

Step 1: Calculation of Net present value of buying

Corporate tax rate = 30%

Discount rate = After tax cost of debt = 7% (1 - 0.30) = 4.9%

								figures in $
End of year	Principal outflow (A)	Interest outflow (B) (See note 1 below)	Interest tax shield (C)	Depreciation (See note 2 below)	Depreciation tax shield (D)	Net Cash flow (A+B+C+D)	Discounting factor @ 4.90%	Present Value
1	(1,125,000.00)	(315,000.00)	94,500.00	1,125,000.00	337,500.00	(1,008,000.00)	0.9533	(960,926.40)
2	(1,125,000.00)	(236,250.00)	70,875.00	1,125,000.00	337,500.00	(952,875.00)	0.9088	(865,972.80)
3	(1,125,000.00)	(157,500.00)	47,250.00	1,125,000.00	337,500.00	(897,750.00)	0.8663	(777,720.83)
4	(1,125,000.00)	(78,750.00)	23,625.00	1,125,000.00	337,500.00	(842,625.00)	0.8258	(695,839.73)
							NPV	(3,300,459.75)

Notes:

1. Calculation of interest outflow:

		figures in $
Beginning of the year	Principal outstanding	Interest @ 7% for the year (Outflow at the end of year)
1	4,500,000.00	315,000.00
2	3,375,000.00	236,250.00
3	2,250,000.00	157,500.00
4	1,125,000.00	78,750.00

2. Depreciation per year:

Cost of the asset less Salvage value/Useful life = 4500000/4 = $1,125,000

Step 2: Calculation of Net present value of leasing

Corporate tax rate = 30%

Discount rate = After tax cost of debt = 7% (1 - 0.30) = 4.9%

					figures in $
End of year	Lease out flow (See Note 1 below)	Tax shield on lease	Net cash flow	Discounting factor @ 4.90%	Present Value
0	(1,275,000.00)	382,500.00	(892,500.00)	1	(892,500.00)
1	(1,275,000.00)	382,500.00	(892,500.00)	0.9533	(850,820.25)
2	(1,275,000.00)	382,500.00	(892,500.00)	0.9088	(811,104.00)
3	(1,275,000.00)	382,500.00	(892,500.00)	0.8663	(773,172.75)
4	-	-	-	0.8258	-
				NPV	(3,327,597.00)

Note:

1. Lease payments are made at the beginning of each year

Step 3: Calculation of NAL of leasing

Net advantage of leasing = NPV of leasing - NPV of buying

=> NAL = -$3,327,597.00 - (-$3,300,459.75) = -$27,137.25

Since NAL is <0, Wolf Corporation should go for purchase of the new machine.

SOLUTION TO QUESTION 2:

The maximum annual lease that Wolf Corporation would be willing to pay is the amount where NAL = 0

i.e., where NPV of the leasing option = -$3,300,459.75

Now, let the after tax cash outflow of lease be x.

As per the NPV calculation table given above in Solution 1:

(x*1) + (x*0.9533) + (x*0.9088) + (x*0.8663) = 3300459.75

or, 3.7284x = 3300459.75

x = $885,221.48

Therefore before tax annual lease = 885221.48 / (1-0.30) = 885221.48/0.70 = $1,264,602.11

Hence, the maximum annual lease that Wolf Corporation would be willing to pay is $1,264,602.11