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Rob's 2700 Notes

🔎 PV and IRR vs Bond Price and YTM

There are five concepts that it is easy to mix up:

Earlier, we covered:

  • PDV - Present Discounted Value of an Investment
    • “The PDV of investing in that apartment projects is $21.64 million” means that the fair value of the apartments is $21.64. (fair value = the most you should pay for it)
  • NPV - Net Present Value of an Investment
    • “The present value of the cash generated by the apartment complex is $21.64 million, but we only have to pay $10 million for it, so our NPV is $11.64 million” means that we have a $11.64 profit on the investment.
    • NPV = PDV of cash Inflows - PDV of cash outflows.
  • IRR - Internal Rate of Return for an Investment
    • “Our investment in that apartment project had an IRR of 21%” means that we had a 21% return on our investment. IRR tells you the percent return on an investment.

When we cover bonds, we refer to:

  • PB - The price of a bond
    • To calculate the price of a bond, you calculate the PDV of the cash flows from the bond. This tells you the fair value of the bond - ie it tells you the most you should pay for the bond.
  • YTM - Yield to Maturity of a Bond
    • To calculate the percent return on the bond, you just calculate the IRR of purchasing the bond. Practically, this means that you write down the relevant bond pricing formula and solve for i.

Conclusion: Bond Pricing and YTM are just applications of PDV and IRR .

PZCB=F(1+i)TP_{ZCB} = \frac{F}{(1+i)^T} PConsol=FciP_{Consol} = \frac{Fc}{i} PCouponBond=Fc(1+i)1+Fc(1+i)2+Fc(1+i)3+⋯+Fc(1+i)T+F(1+i)TP_{CouponBond} = \frac{Fc}{(1+i)^1} + \frac{Fc}{(1+i)^2} + \frac{Fc}{(1+i)^3} + \cdots + \frac{Fc}{(1+i)^T} + \frac{F}{(1+i)^T}