# Zero-Bond question

If an investor’s required return is 12 percent, the value of a 10-year maturity zero-coupon bond with a maturity value of \$1,000 is closest to: A. \$312. B. \$688. C. \$1,000. D. \$1,312. How do you calculate this? Financial mngmnt class was so long ago =(. Guessed the right ans. though. I tried doing X*1.12^10=1000. bear w/ me here, ive forgotten how to correctly use FV, PV, etc… so im usin my own variables. I dunno if this is even the correct approach. Thx

A. \$312 FV = -1,000 n = 20 (semiannual payments) i = 6% PV = 311.80

thx. i see now.

CFABLACKBELT Wrote: ------------------------------------------------------- > If an investor’s required return is 12 percent, > the value of a 10-year maturity zero-coupon > bond with a maturity value of \$1,000 is closest > to: > A. \$312. > B. \$688. > C. \$1,000. > D. \$1,312. > > How do you calculate this? Financial mngmnt class > was so long ago =(. > > Guessed the right ans. though. > > I tried doing X*1.12^10=1000. bear w/ me here, > ive forgotten how to correctly use FV, PV, etc… > so im usin my own variables. I dunno if this is > even the correct approach. Thx it should’ve been x*(1+12%/2)^2*10 = 1000 -> x=311.80

I didnt realize it was compounded semi-annually

unless noted otherwise in a CFA exam question, always assume semiannual coupon payments.

If you want to use the calculator (BAII PLUS) N=20 I/Y=6 PMT=0 FV=1000 CPT PV= -311.80

Char-Lee Wrote: ------------------------------------------------------- > unless noted otherwise in a CFA exam question, > always assume semiannual coupon payments. Thx for the tip!

Charlee - Can you please explain why semiannual payments? Do you mean for all types of bonds…the coupon payments go semiannually?

amitahuja Wrote: ------------------------------------------------------- > Charlee - Can you please explain why semiannual > payments? > Do you mean for all types of bonds…the coupon > payments go semiannually? This is just the convention used for the exam,i suspect because it is the most common payment structure. Bonds can have a variety of payment structures (i.e. monthly, quarterly, semi annually, and annually) although semi-annual is the most common in the US corporate and muni markets. Also in order to compare apples to apples a semi-annual (“bond equivalent”) payment is assumed (eg when comparing yields on zero coupon, annual payment and semi-annual payment bonds)

Unless they specify in the question that it is an Annual Coupon, you have to use the Semi-annual convention. And they do mention it very clearly. CP

The Schweser book said that it would be stated on the CFA exam. But a note for this question should be that both discount period yield the same answer. I doubt the CFA exam will have 2 answers so close to each other without stating which discount rate they want you to use(the difference between semi and annual discount rate on a zero coupon bond is small) but to be on the safe side, if no discount rate is shown, use the semi annual one.

why did you guys use semiannual payments (the question doesnt mention that at all)??? so if just use annual payments and the given rate : N=10 I/Y = 12 FV = 1000 —> PV = 321.97 —> ???

nhung… pls read the post in its entirety first… this has been discussed above.

cpk123 Wrote: ------------------------------------------------------- > Unless they specify in the question that it is an > Annual Coupon, you have to use the Semi-annual > convention. > > And they do mention it very clearly. > > CP Umm, they can talk about whatever they want but a zero-coupon bond pays no coupons and thus it is continually compounded.

Go with choice E: 301.19 P*e^-rt 1000*e^(-.12*10) = 301.19

ok sorry for my quick reading… i’m kind of new candidate and new in the forum as well so not yet get familiar with the way it works… but i have another question… As far as I understand, for Zero coupon bond, even if there is no coupon payment during the life of the bond, companies still have to record interest expense on each period in FSs. Is my understand correct??? this thing makes me crazy because the CFA curriculumn is not clear at all in this subject… thanks in advance for your help

Upon issue of a discount bond (5 yr 10% Semi-Annual compounding): CASH -------------------------------------- 613.91 Discount on Bonds Payable----------- 386.09 ----------Bonds Payable------------------------------ 1000.00 6 months later: Interest Expense (.05 x 613.91)-------30.70 ----------Discount on Bonds Payable -----------------30.70 6 months later: Interest Expense (.05 x 644.61) ---------32.23 ----------Discount on Bonds Payable ----------------- 32.23 6 months later: Interest Expense (.05 x 676.84)---------- 33.84 ----------Discount on Bonds Payable------------------ 33.84 etc, until the discount is fully amortized and the bond is paid off. Final entry: Bonds Payable------------------------------1000.00 ----------CASH--------------------------------------------1000.00 The same applies for a discount bond paying a coupon only the Interest Expense is split between “discount on bonds payable” and CASH.

In response to JDV’s point: Yes a zero coupon bond pays no interest/coupon periodically. But 1000 / 1.12^10 = 322 1000/1.06^20 = 311.8 and there is a difference of about 10\$ due to the compounding convention – which increases the number of periods the formula uses.

And another \$10 difference if you use continuous compounding. So valuing the bond with annual compounding would give you a value that is about 6% higher (322 vs 301.19).