# Cash flow matching - par value for a government bond

Hi everyone, I came across an example question when studying Liability driven strategies - cash flow matching topic in Level 3 textbook.

The example question has left me with some confusion regarding how to calculate the par value for a government bond. The question is as follows: ‘How much in par value for each gov’t bond will Mr.S need to buy to defease the debt liabilities?’ In the answer key, the liability amount is discounted using one plus the coupon rate, resulting in a par value of SEK 4,976,303 for 5.5% bonds due in May 2021 ( SEK 4,976,303 (=SEK 5,250,000/1.0550)

I’m wondering why the discount rate is not raised to the power of the period number, for example, 1.0550^4 . Additionally, I’m also unclear why the coupon rate is used to discount the cash flow.

Thanks!

On the maturity date of the bond, we will receive the original face plus the last coupon.

Face + coupon = defeasance
Face + coupon rate * face = defeasance
Face * [1 + coupon rate] = defeasance
Face = defeasance /(1 + coupon rate)

QED

Because it’s not a discount rate.

Because it’s not a discount rate.