Reinvestment Rate Assumption

CFA Level I Fixed Income
#1

Hey guys,

I was hoping someone could help me out with a question on the reinvestment of coupon payments as they are received.

I have read an know how to apply the statement that “NPV and other future types of discounting methods, implicity assume that coupon payments are reinvested at the discount rate being used” but I am having a hard time really grasping the concept.

There is a great example of this on page 21 in the corporate finance reading 36. I understand that if the cost of money is 10% and you are going to recieve $100 dollars 1 year from now, the present value would be 100/1.1 = $90.91. That makes perfect sense to me.

But I dont follow how that gets carried through to bond payments (for example.) Is it as simple as stating that once you have some of your money returned to you via coupon payments you are putting in an intrest bearing account as opposed to now having access to it at all?

Any clarifications would be hugely appreciated.

Thanks in advance for any help

Rob

#2

Hi Rob,

The reading you mentioned is describing the rates of NPV and IRR. IRR is the discount rate required for the NPV of the project to equal zero and I’m sure you already know this. The reinvestment rate assumption states that any proceeds received are reinvested at the prevailing rate (the discount rate for NPV and the IRR for IRR).

Specifically in regards to bonds, the reinvestment rate is the rate at which the proceeds received (coupon payments, principal repayments) by the investor must be reinvested. So yes - it is as simple as the bondholder reinvesting their coupon payments into the market and the assumption is that, if an investor was to reinvest their proceeds, they would earn the same rate of interest as they did from the bond yield for the remaining maturity of the bond.

This assumption does not hold in practice and gives rise to reinvestment risk - if a bond yield falls over time, subsequent coupon payments will not be able to be reinvested at the rate that the bond was bought at. As such, the investor cannot realise the bond yield at purchase.

This took me some time to wrap my head around as well as there are a few references to this in the material. There is a section on reinvestment risk in the fixed income topic if you want to look in greater detail.

Good luck