2 CPAs sitting here unable to figure out this problem. This is taken straight out of a public educational document https://www.grantthornton.com/-/media/content-page-files/audit/pdfs/2018/leases-navigating-guidance-ASC-842.ashx, page 155
For the life of me, I cannot figure out why the lease liability is 196,156. This is my calculation:
A) 5 sequential lease payments of 50K end of year. This alone would have a PV of 216,474
B) Lessee (company who is paying for the lease) spends 20K on day 1. They get reimbursed 90 days later. That’s essentially giving up 20,000 to get 19,752 back, or a 248 dollar loss.
So 216,474 - 20,000 + 248 = 196,722 whic hs is off by quite a bit. Help!
They’re assuming that the 5% finance rate is an annual (nominal) rate, compounded quarterly.
That’s not clear at all from the information given.
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I tried interest compounded monthly and quarterly and I still didn’t get it to tie out. My PV and right of use asset is still a pinch off. Can you please show me your math?
The cash flows I have are:
- $20,000 at time t = ¼
- −$50,000 at time t = 1
- −$50,000 at time t = 2
- −$50,000 at time t = 3
- −$50,000 at time t = 4
- −$50,000 at time t = 5
The present value is:
\frac{\$20,000}{\left(1+\frac{5\%}{4}\right)^{\frac14×4}}+\frac{-\$50,000}{\left(1+\frac{5\%}{4}\right)^{1×4}}+\frac{-\$50,000}{\left(1+\frac{5\%}{4}\right)^{2×4}}+\dots+\frac{-\$50,000}{\left(1+\frac{5\%}{4}\right)^{5×4}}
= \$19,753-\$47,576-\$45,270-\$43,075-\$40,987-\$39,000
=-\$196,156
Wow, they didn’t specify the compounding frequency??? 
The $248 isn’t a loss, per se: it just means that getting $20,000 in 3 months time is not worth $20,000 today. What you’re doing is recognizing the time value of money.
