[michaela.xu]

Hi all, I have a question about the following MCQ. The question is long but I have underlined the part of explanation that confuses me. My question is: why is the Present Value calculation underlined not including Present Value of interest payments?

In another similar MCQ, the explanation included PV of interest in its explanation.

Thanks for your help!

On January 1, Year 1, Fring Chicken Co. purchased a bond with a face value of $1000, maturing after 7 years, and classified as an available-for-sale debt security on its balance sheet. The coupon rate on the bond was stated to be 8%, payable semi-annually on June 30 and December 31. On January 1, Year 5, the fair value of the said bond was estimated to be $650. What is the impact of the loss on the financial statements of Fring? Assume a discount rate of 10%.

Given:

Present Value of $1 at 5% and n=14: 0.505
Ordinary Annuity of $1 at 5% and n=14: 9.8986
Present Value of $1 at 5% and n=6: 0.746
Ordinary Annuity of $1 at 5% and n=6: 5.0757
# Income Statement Other Comprehensive Income
A 0 350
B 350 0
C 96 203.14
D 203.14 96
The correct answer is (D).

Impairment for Available-for-Sale Securities is calculated as the difference between Amortized Cost (i.e. Carrying Value) and the Fair Value of the security. However, Credit Losses on the Income Statement are limited to Amortized Cost – Present Value (calculated the same way as a Held-to-Maturity investment) because if the unrealized loss at any given time is more than the expected credit loss till maturity, the Investor can minimize the loss by holding the security.

Excess losses are charged to OCI.

Carrying Value of the Bond on January 1, Year 1:

⇒ $1,000 x Present Value of $1 at 5% for 14 periods + $40 x Present Value of Ordinary Annuity $1 at 5% for 14 periods
⇒ $1,000 x 0.505 + $40 x 9.8986
⇒ $505 + $395.94
⇒ $900.94

Carrying Value of the Bond on January 1, Year 5 (after 8 Periods):

Period Interest Income (5%) Interest Received (4%) Interest Received (4%) Carrying Value
0 $900.94
1 $45.05 40 $5.05 $905.99
2 $45.30 40 $5.30 $911.29
3 $45.56 40 $5.56 $916.86
4 $45.84 40 $5.84 $922.70
5 $46.13 40 $6.13 $928.83
6 $46.44 40 $6.44 $935.27
7 $46.76 40 $6.76 $942.04
8 $47.10 40 $7.10 $949.14

In the given case, Present value of the bond on January 1, Year 5 (after 8 Periods):
⇒ $1,000 x Present Value of $1 at 5% for 6 years
⇒ 1,000 x 0.746
⇒ $746

Expected Credit Loss = Carrying Value – Fair Value = $949.14 – $650 = $299.14

Expected Credit loss = $949.14 – $746 = $203.14.

Loss Charged to Income Statement = $299.14 – $203.14 = $203.14

Loss Charged to OCI = $96

[michaela.xu]

Somehow the part I was talking about didn't come out underlined, so I am copy-pasting it below:

In the given case, Present value of the bond on January 1, Year 5 (after 8 Periods):
⇒ $1,000 x Present Value of $1 at 5% for 6 years
⇒ 1,000 x 0.746
⇒ $746

Why didn't the above calculation include present value of interest payments?

[Author]

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