Interest rate risk and return

CFA Level I Fixed Income
#1

Baywhite buys the 6.2%, 10 year eurobond at par, interest rates immediately rise to 7.2%, and it sells the bonds four years later.

Given the change in interest rates, I calculated the sale price 4 years later as $95.2627. Then, I just solved the following equation to determine IRR:

-100 + 6.2/(1+r) + 6.2/(1+r)^2 + 6.2/(1+r)^3 + 6.2/(1+r)^4 + 95.2627/(1+r)^4 = 0

Why wouldn’t this work? I know what the right answer is and how the text computed the right answer, but I don’t know what I am doing wrong here.

#2

Looks OK to me. Lemme try the CF worksheet for this one.

I get an IRR of 5.102%.

#3

Ye, but the actual answer was 5.28%. I think it might be because cash flows are being reinvested at a rate that is actually higher than the IRR but I need some confirmation on whether this reasoning makes sense.

#4

CF0 -100 C01 6.2 F01 3 C02 101.4627 F02 1 2nd Quit IRR CPT 5.1025647

:man_shrugging:

If I plug r=5.1% into your expression, I get darned near 0. :face_with_raised_eyebrow:

#5

That’s exactly what they’ve done.
You reinvest the coupons at 7.2% so at four years you have
6.2\times\left(1+1.072+1.072^2+1.072^3\right)+95.2627=122.8933721;
The internal rate of return r will be given by
1+r=\left(\frac{122.8933721}{100}\right)^{1/4}=1.228933721^{1/4}=1.052887853

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#6

Yep, that makes sense but why is this an IRR? Coupon cash flows are invested at 7.2% which is higher than the IRR, right? I thought one of the assumptions underlying the IRR was that all cash flows are reinvested at the IRR.

#7

For IRR for a bond, you look at the cashflows.
If there is no reinvestment, the IRR would be as you did it, with cashflows
6.2 end of year 1
6.2 end of year 2
6.2 end of year 3
106.2 end of year 4

Somewhere in that question, either explicitly or implicitly, you are told that the coupons will be reinvested at 7.2%, so that there is a single cashflow at the end of year 4.

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