Kingtim CO

The government yields are those given by the government. Investing in individual companies is more risky than investing in the government and therefore the interest they need to pay will always be higher than government rate depending on their credit rating. The credit spreads are the extra that has to be paid and are therefore always added. Here they are being added so as to determine that interest that Kingtim will end up having to pay.

The value of the new bonds is therefore the PV of the coupon interest rate discounted at the relevant rates for each of the years.

As far as the workings you quote in your second line is concerned, for 1 year the rate is 4% in this question and is 4.3% per year if it is 2 years. The 4.3% per year is the average per year, and so if we wanted a rate for the second year on its own (which is not needed for this question) then we would then need to use the workings that you have written. After 2 years at an average of 4.3% per year, we would be multiplying by 1.043^2. This is equivalent to multiplying by 1.04 for 1 year and then by 1.046 for the second year. (1.046 = 1.043^2 / 1.04).

You might find the following article on the ACCA website to be helpful:
https://www.accaglobal.com/gb/en/student/exam-support-resources/professional-exams-study-resources/p4/technical-articles/bond-valuation-yields.html

In Kingtim the question gives the spot yield rates as part of the question.

The time you would need to use that ‘formula’ approach as part of the workings is when you were not given the spot yield rates but were given the coupon rates and were asked to calculate the spot yield rates (as is the case in example 4 of the article).