# Determine the interest rate implicit in the lease and Calculate the basic EPS for ABC Ltd for the year ending

Home, - Annual outstanding per share of stock

Question 1: ABC Ltd has entered into an agreement to lease an item of equipment that produces teddy bears. The terms of the lease are as follows:

Date of entering lease: 1 July 2023.
Duration of lease: 10 years.
Life of leased asset: 10 years.
There is no residual value.
Lease payments: \$5000 at lease inception, \$5500 on 30 June each year (that is, 10 payments).
Included within the lease payments are executory costs of \$500.
Fair value of the machine at lease inception: \$27 470.

Required:
Determine the interest rate implicit in the lease.

In any business process lease can be identified as a key factor to consider. In this process, from the considered scenario the present value or PV of the up-front or inception payment of \$5,000 is not discounted. Hence, through implying a rate of 18% for the purposes of discounting the PV of the lease payments and the unguaranteed residual can be determined as-

 Date of entering lease 1 July 2023 Duration of lease ( years ) 10 Life of leased asset ( years ) 10 Residual value Nil Lease payments: Lease inception \$5,000 Instalment payment on 30 June each year \$5,500 Executory costs ( included within the lease payments ) \$500 Lease payments excluding executory cost \$5,000 Fair value of the machine at lease inception \$27,470 PV of the payment made on 1 July 2023 \$5,000 PV of the 10 yearly payments \$22,470 \$27,470

Table 4: Discounted value

Thus, from the above table (Table 4) the discounted value can be estimated to be \$27,470 and it is exactly the same as the fair value of the asset at the lease inception date of 1 July 2023. Hence, the implicit rate of interest in the lease can be estimated to be 18%.

 Years Fixed annual lease payment Amount ( in \$ ) Discounting factor @ 18% PV of the lease payment Amount ( in \$ ) 1 \$5,000 0.85 \$4,237 2 \$5,000 0.72 \$3,591 3 \$5,000 0.61 \$3,043 4 \$5,000 0.52 \$2,579 5 \$5,000 0.44 \$2,186 6 \$5,000 0.37 \$1,852 7 \$5,000 0.31 \$1,570 8 \$5,000 0.27 \$1,330 9 \$5,000 0.23 \$1,127 10 \$5,000 0.19 \$955 \$22,470

Question 2:
ABC Ltd is an Australian listed company. Its results for the financial year ending 30 June 2023 have exceeded expectations-profit before tax is \$5.597 million and income tax expense is \$1.847 million. As at 30 June 2022, there were 9.75 million ordinary shares on issue. On 11 May 2023, 3.25 million further ordinary shares were issued at a price of \$2.30-paid to \$2.00. The partly paid shares carry rights to dividends in proportion to the amount paid relative to the total issue price.

Required:
Calculate the basic EPS for ABC Ltd for the year ending 30 June 2023.

EPS (Earning Per Share) is defined to be the company's profit in the annual outstanding per share of stock. The annual income of the firm is taken into calculation with the company's preferred stock of shares with the average outstanding shares amount. It is the portion of the company's annual profit that is taken as an important profitability measure gauging the frequency of investment to be made by the firm in the stock market (Sagala, 2019). The higher the EPS, the higher the profitability amount of the firm.

 Calculation of EPS for ABC Ltd for the year ending 30 June 2023 Number of shares available as on 30 June 2022 ( in million ) 9.75 New shares issued on 11 May 2023 ( in million ) 3.25 Profit before tax ( PBT ) ( in million ) \$5.597 Income tax expense ( in million ) \$1.847 Therefore, Profit after tax ( in million ) \$3.75 Less: Preference share dividends 0 Earnings for basic EPS ( in million ) \$3.75 Hence, basic EPS = Available net earnings / Weighted average number of ordinary equity shares \$0.38

The PBT of ABC Ltd for the period was \$5.597 million and it has also reported the income tax expense for the considered period to be \$1.847 million. In this process, it is needed to highlight that the considered firm did not pay any amount as preference share dividend as of 30 June 2023. Thus, the available earnings for the distribution of basic EPS can be estimated to be \$3.75. From the above table (Table 6) the estimated value of the EPS for the period can be estimated to be \$0.38 (i.e., \$3.75 million / 9.97 million). In this process, based on the following table (Table 7) the overall weighted average number of ordinary shares for the organisation has been estimated to be 9.97.

Working note

 Period Proportion of year Number of shares outstanding Weighted average Fully paid ordinary shares 1/7/22-10/5/2023 314 / 365 9750000 8387671 Partly paid ordinary shares 11/5/2023-30/6/2023 ( 51 / 365 ) * ( \$2.00 / \$2.30 ) 13000000 1579512 365 days 9967183 Total weighted average number of ordinary shares 9.97

Table 7: Weighted average number of shares