Calculation of Expected Credit loss (ECLs)

Hello Tutor,

I have questions about question 1d March-June 2020 related to impairment of financial instrument.

1) the formula of ‘lifetime ELCs’ = Weighted default chance * PV of expected cash flow
Therefore in this question 1d), I calculated:
+) PV of expected cash flow = 500,000/1.08 + 462,963 + 6,858,710
+) Weighted default chance =(500,000/1.08*0%+462,963*3%+6,858,710*5%)/(500,000/1.08+462,963+6,858,710)

I make this messy calculation because I want to match the definition.

2) Apart this formula of lifetime ELCs above,
lifetime ELCs = Contractual cashflow @PV – Expected cashflow @PV

3) If 12-months ELCs appear in initial (same as question 1d) so initial cash that The buyer paid the seller = Cost – 12months ELCs = 10m$ -10,000=99.9m$

If I’m wrong, please fix and explain. Thank you

Question 1d (march-june 2020):
Impairment of bonds
On 31 December 20X3, Hummings Co purchased $10 million 5% bonds in Stave Co at par value. The bonds are repayable on 31 December 20X6 and the effective rate of interest is 8%. Hummings Co’s business model is to collect the contractual cash flows over the life of the asset. At 31 December 20X3, the bonds were considered to be low risk and as a result the 12-month expected credit losses are expected to be $10,000.
On 31 December 20X4, Stave Co paid the coupon interest, however, at that date the risks associated with the bonds were deemed to have increased significantly. The present value of the repayments for the year ended 31 December 20X5 were estimated to be $462,963 and the probability of default is 3%. At 31 December 20X4, it is also anticipated that no further coupon payments would be received during the year ended 31 December 20X6 and only a portion of the nominal value of the bonds would be repaid. The present value of these cash shortfalls was assessed to be $6,858,710 with a 5% likelihood of default in the year ended 31 December 20X6.