Question

You work for Instacart. The company is considering leasing mobile distribution centers to speed up its delivery services and make them more efficient. The mobile distribution centers cost a total of $4,500,000, and they would be depreciated straight-line to zero over 4 years. Because of their expected extensive use, they will be completely valueless in 4 years. Instacart can lease the mobile distribution centers for $1,350,000 per year for 4 years from another company. Assume that Instacart is in 35% tax rate bracket, and can borrow at 8% before taxes.

1. Should Instacart lease or buy the mobile distribution centers? Show and explain all calculations.

1. Suppose the entire purchase price of the mobile distribution centers is borrowed. The rate on the loan is 8%, and the loan will be repaid in equal installments. Create a lease-vs-buy analysis that explicitly incorporates the loan payments. Show that the NPV of leasing instead of buying is not changed from what it was in (a). Why is this so?? Show and explain all calculations.

Answer 1

A)
Annual Cash Outflow of Leasing = After tax outflow of cash
	= lease rentals * (1- tax rate)
	=1350000 *(1-0.35)
	$ 877,500.00 per year
After-tax cost of debt = 8% * (1-35%) =	5.20%
NPV of Leasing @ 5.2%	$3,365,501.90
NPV of buying		$4,500,000.00

NPV of leasing = periodic payment * (1-(1+r)^n) / r

So, Instacart should opt for Leasing.

B)
Period		1	2	3	4
Loan repayment	A	1,358,644	1,358,644	1,358,644	1,358,644	From amortization schedule below
Depreciation	D	1,125,000	1,125,000	1,125,000	1,125,000	From amortization schedule below
Interest expense	I	360,000	280,109	193,826	100,640	Total cost divided by number of years
Total tax deductions	T = D+I	1,485,000	1,405,109	1,318,826	1,225,640
Tax shield @ 35%	t = 0.35×T	519,750	491,788	461,589	428,974
Net cash flows	N = A–t	838,894	866,856	897,055	929,670
PV of future cashflow		797,427	824,007	852,714	883,716
NPV of Buying - select	3,357,864
NPV of leasing	3,365,501
Annual loan repayment is based on present value calculation; it is the amount paid at the end of each year for 4 years that would write off the loan completely.
So, loan repayment =	$                  4,500,000.00	@8%	4 years	($1,358,643.62)
		Bank amortization schedule
Period	Opening Principal	Loan repayment	Interest	Principal Repayment	Closing principal
0	$                    4,500,000	$                     -	$                  -	$                           -	$         4,500,000
1	$                    4,500,000	$       1,358,644	$      360,000	$               998,644	$         3,501,356
2	$                    3,501,356	$       1,358,644	$      280,109	$            1,078,535	$         2,422,821
3	$                    2,422,821	$       1,358,644	$      193,826	$            1,164,818	$         1,258,003
4	$                    1,258,003	$       1,358,644	$      100,640	$            1,258,003	$                       (0)

As we can see the PV of both the outcomes is almost same .