Question

You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. ?? = (1 + ??)−?, where ?? is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate.

a) What is the price of a zero-coupon bond maturing in exactly 3 years?

b) Your friend makes the following observation about the above bond: “Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate)”. Explain why your friend is not entirely correct and how you would modify the statement to make it correct.

Answer 1

Given data follows below:

Default Risk free cash flows is r = 0.68 (assume as r)

T-year discount factor is the PV of = $1

All bonds have a face value of = $100

a) Calculating price of a zero-coupon bond maturing in exactly 3 years

Given formula ?? = (1 + ??)−?

Assume r =0.68

Time period t = 3 year

1/(1+r3)^3 = 0.68

r3 = (1/0.68)^(1/3)-1

= 1.47058823529^0.666666667

= 0.13718300876 or 13.72

100/(1+r3)^3

= 100*0.68

= $68

$68 price of a zero-coupon bond maturing in exactly 3 years

b)

The 3 years zero-coupon bond is a riskfree purchase just if the bond is held till capability, more the value of the bond will further adjust based on the present interest charges in the business.
There are zero guarantees that it will earn a 13.72% return p.a.

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