Question

Assume you are evaluating a lease with annual payments of $530,000 per year under a 5 year lease. The after-tax cost of debt is 6% and the tax rate is 40%. Rather than occurring at the end of each year, you have realized that tax payments actually occur evenly throughout the year. Using the mid-year approximation, by how much (in present value terms) are you underestimating the tax benefits from the lease by assuming end of year rather than mid-year tax payments? Please show all work in excel.

Answer 1

PV Discount factor assuming end of year
payments =1/(1+r)^n
Ans PV discount factor assuming mid year
payment convention =1/(1+r)^(n-0.5)
where r=interest rate , n=period
here r=6%
Let use find the Lease Tax benefits difference between two payment
timing assumptions

	a.	b	c	d	e	f
Year	Annual Lease Payment	Tax Benefit =a*40%	PV factor with end of year Payment assumption =1/(1+r)^n	PV of Tax benefits assuming end of year payment =b*c	PV factor with end of year Payment assumption =1/(1+r)^(n-0.5)	PV of Tax benefits assuming mid year payment =b*e
1	530,000.00	212,000.00	0.9434	200,000.80	0.9713	205,915.60
2	530,000.00	212,000.00	0.8900	188,680.00	0.9163	194,255.60
3	530,000.00	212,000.00	0.8396	177,995.20	0.8644	183,252.80
4	530,000.00	212,000.00	0.7921	167,925.20	0.8155	172,886.00
5	530,000.00	212,000.00	0.7473	158,427.60	0.7693	163,091.60
			Total	893,028.80		919,401.60

So underestimation of lease tax benefits by using end of year than mid of year tax payment is $919,401.60-$893,028.80=

$        26,372.80