Question

11.31 (a) fair value + nil initial direct costs = PV minimum lease payments + any unguaranteed residual Initial payment on 1 July 2019 payment $50 000 PV of remaining lease rental $50 000 paid at the beginning of each 128 855 year (meaning that the final payment is in three years and not four years as would be the case if the lease payments were made at the end of each lease year), number of year =3, interest rate=8% 40 000, number of years = 4 PV of guaranteed residual interest rate=8% 29 400 $208 255 Because the residual value is guaranteed it is included in the lease liability. We have not been provided with any information about what the lessor expects the asset to be worth at the end of the lease term, therefore we have included the whole amount within the lease payments.

Please explain how this answer is achieved. However, please explain using a scientific calculator only. - no appendix tables or excel can be used.

Answer 1

Generally, the fair value of an item of asset / liability is arrived by calculating the present value of expected future cash flows. Fair value of a leased asset on date of entering into a lease is calculated by calculating the present value all the future cash flows relating to the right to use of that asset, which include the periodic lease rentals to be paid in the future during the lease term, as well as the residual value obtained at the end of the lease.

Here, the future payments are discounted using 8% discount rate, which is the interest rate implicit in the lease. So, the discounting factors from Year 0 to Year 5 will be arrived by using the formula 1/(1+.08)ⁿ where n is the number of years.

Discounting factors will be:

Year	Discounting factor
0	1
1	0.925926
2	0.857339
3	0.793832
4	0.73503
5	0.680583

Using a calculator, this can be done by the following steps:

1. press 1
2. Divide by 1.08
3. Press = for year 1 discounting factor
4. Press = again for year 2 discounting factor
5. Press = again for year 3 discounting factor
6. Press = again for year 4 discounting factor

If you want annuity factor, it is the sum of discounting factors from year 1 to year n. use memory function of calculator (M+) for this. That is, after each = in the above step, press M+. After that you can obtain the annuity factor once you press memory recall(MRC) in calculator. Annuity factor may be used when you have to find the present value of the same amount repeating annually.

Calculation of Present value

Particulars	Year	Payment date	Discounting factor	Amount	Discounted value = Amount * discounting factor
Lease rental	0	01-07-2019	1	50000	50000
Lease rental	1	01-07-2020	0.925926	50000	46296
Lease rental	2	01-07-2021	0.857339	50000	42867
Lease rental	3	01-07-2022	0.793832	50000	39692
Residual value	4	01-07-2023	0.73503	40000	29401
					208256

As the lease payments are due at the beginning of year, the first payment is not to be discounted, as the amount is paid on the same date of valuation. So, it is taken as year 0. The next payment is happening after 1 year from the valuation date. So, it is taken as year 1 and so on.

Hope, it is clear.