so in cfa volume 4, reading 23 page 63 there is a blue box example on cash flow matching. I struggle with the given solution on the example.
It suggests to buy a 4 year bond with 5,50% coupon rate to cover a fixed liability at at the end of the holding period. So far so good.
I don’t understand the way the book calculates the par value since it discounts the bond only by one year but holds it for 4 years. I can tell that the holding period is 4 years since the coupon payments are received throughout the holding period.
My problem is not listed on that errata list. So is somebody at this chapter (Volume 4, Reading 23, Example 3 page 63) right now and could possibly help me out here.
I dont understand why an investor will calculate the par value of a 5 year bond with 5,50% coupon by discounting it simply by 1,055. According to my understanding it should’ve been 1,0555 since the investor holds it for the entire 5 years and also receives the coupons throughout the holding period (so in period 1, 2, 3 and 4).
They’re not discounting the value of the bond (in the sense of finding a present value given a future value).
The final payment on a coupon-paying bond is the par value of the bond plus the last coupon. So, if you have an annual-pay bond with a par value of SEK 1,000 and a 5.5% coupon rate, the final payment will be SEK 1,055. If you need to pay a liability of, say, SEK 100,000, you don’t need 100 bonds, you need only 100 / 1.055 = 94.78673 bonds. That’s why they’re dividing by 1.055.
The final payment on those bonds will be SEK 94,786.73 in par value and SEK 94,786.73 × 5.5% = SEK 5,213.27 in coupon for a total of: